Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, D

Time bar (total: 18.1s)

analyze492.0ms (2.7%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.8%0.2%0%0%0%0
0%0%99.8%0.2%0%0%0%1
0%0%99.8%0.2%0%0%0%2
0%0%99.8%0.2%0%0%0%3
0%0%99.8%0.2%0%0%0%4
0%0%99.8%0.2%0%0%0%5
0%0%99.8%0.2%0%0%0%6
0%0%99.8%0.2%0%0%0%7
0%0%99.8%0.2%0%0%0%8
4.2%3.1%71.7%0.2%0%25%0%9
4.2%3.1%71.3%0.2%0%25.3%0%10
6.3%4.7%69.2%0.2%0%25.9%0%11
9.2%6.6%65.8%0.2%0%27.4%0%12
Compiler

Compiled 24 to 19 computations (20.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 214.0ms
ival-mult: 92.0ms (42.9% of total)
ival-div: 71.0ms (33.1% of total)
ival-sqrt: 22.0ms (10.3% of total)
ival-acos: 21.0ms (9.8% of total)
const: 7.0ms (3.3% of total)
backward-pass: 1.0ms (0.5% of total)

sample4.4s (24.6%)

Results
2.1s15545×0invalid
1.2s8256×0valid
Precisions
Click to see histograms. Total time spent on operations: 2.2s
ival-mult: 1.1s (47.9% of total)
ival-div: 640.0ms (29.1% of total)
ival-sqrt: 233.0ms (10.6% of total)
ival-acos: 198.0ms (9% of total)
const: 65.0ms (3% of total)
backward-pass: 10.0ms (0.5% of total)
Bogosity

preprocess186.0ms (1%)

Algorithm
2×egg-herbie
Rules
2044×*-lowering-*.f32
2044×*-lowering-*.f64
1430×associate-*r/
1388×fma-define
1316×sum3-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
092263
1281227
2988197
33692197
44386197
55771197
67648197
01917
13915
211713
339213
4138613
5314813
6324013
7329013
8329013
9329013
10391313
11395213
12395213
0395213
Stop Event
1×iter limit
1×saturated
1×node limit
Calls
Call 1
Inputs
(* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))))
Outputs
(* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y))))
Call 2
Inputs
(* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))))
(* (/ 1 3) (acos (* (/ (* 3 (/ (neg x) (* y 27))) (* z 2)) (sqrt t))))
(* (/ 1 3) (acos (* (/ (* 3 (/ x (* (neg y) 27))) (* z 2)) (sqrt t))))
(* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* (neg z) 2)) (sqrt t))))
(* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt (neg t)))))
(neg (* (/ 1 3) (acos (* (/ (* 3 (/ (neg x) (* y 27))) (* z 2)) (sqrt t)))))
(neg (* (/ 1 3) (acos (* (/ (* 3 (/ x (* (neg y) 27))) (* z 2)) (sqrt t)))))
(neg (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* (neg z) 2)) (sqrt t)))))
(neg (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt (neg t))))))
(* (/ 1 3) (acos (* (/ (* 3 (/ y (* x 27))) (* z 2)) (sqrt t))))
(* (/ 1 3) (acos (* (/ (* 3 (/ z (* y 27))) (* x 2)) (sqrt t))))
(* (/ 1 3) (acos (* (/ (* 3 (/ t (* y 27))) (* z 2)) (sqrt x))))
(* (/ 1 3) (acos (* (/ (* 3 (/ x (* z 27))) (* y 2)) (sqrt t))))
(* (/ 1 3) (acos (* (/ (* 3 (/ x (* t 27))) (* z 2)) (sqrt y))))
(* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* t 2)) (sqrt z))))
Outputs
(* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))))
(* 1/3 (acos (* (* 1/18 (/ (/ x y) z)) (sqrt t))))
(* (/ 1 3) (acos (* (/ (* 3 (/ (neg x) (* y 27))) (* z 2)) (sqrt t))))
(* 1/3 (acos (* (sqrt t) (* -1/18 (/ (/ x y) z)))))
(* (/ 1 3) (acos (* (/ (* 3 (/ x (* (neg y) 27))) (* z 2)) (sqrt t))))
(* 1/3 (acos (* (sqrt t) (* -1/18 (/ (/ x y) z)))))
(* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* (neg z) 2)) (sqrt t))))
(* 1/3 (acos (* (sqrt t) (* -1/18 (/ (/ x y) z)))))
(* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt (neg t)))))
(* 1/3 (acos (* (* 1/18 (/ (/ x y) z)) (sqrt (neg t)))))
(neg (* (/ 1 3) (acos (* (/ (* 3 (/ (neg x) (* y 27))) (* z 2)) (sqrt t)))))
(* (acos (* (sqrt t) (* -1/18 (/ (/ x y) z)))) -1/3)
(neg (* (/ 1 3) (acos (* (/ (* 3 (/ x (* (neg y) 27))) (* z 2)) (sqrt t)))))
(* (acos (* (sqrt t) (* -1/18 (/ (/ x y) z)))) -1/3)
(neg (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* (neg z) 2)) (sqrt t)))))
(* (acos (* (sqrt t) (* -1/18 (/ (/ x y) z)))) -1/3)
(neg (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt (neg t))))))
(* (acos (* (* 1/18 (/ (/ x y) z)) (sqrt (neg t)))) -1/3)
(* (/ 1 3) (acos (* (/ (* 3 (/ y (* x 27))) (* z 2)) (sqrt t))))
(* 1/3 (acos (* (sqrt t) (* 1/18 (/ (/ y x) z)))))
(* (/ 1 3) (acos (* (/ (* 3 (/ z (* y 27))) (* x 2)) (sqrt t))))
(* 1/3 (acos (* (sqrt t) (* 1/18 (/ (/ z y) x)))))
(* (/ 1 3) (acos (* (/ (* 3 (/ t (* y 27))) (* z 2)) (sqrt x))))
(* 1/3 (acos (* (* 1/18 (/ (/ t y) z)) (sqrt x))))
(* (/ 1 3) (acos (* (/ (* 3 (/ x (* z 27))) (* y 2)) (sqrt t))))
(* 1/3 (acos (* (* 1/18 (/ (/ x y) z)) (sqrt t))))
(* (/ 1 3) (acos (* (/ (* 3 (/ x (* t 27))) (* z 2)) (sqrt y))))
(* 1/3 (acos (* (* 1/18 (/ (/ x t) z)) (sqrt y))))
(* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* t 2)) (sqrt z))))
(* 1/3 (acos (* (* 1/18 (/ (/ x y) t)) (sqrt z))))
Symmetry

(sort y z)

explain207.0ms (1.1%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
261(-1.7088504581463616e-168 -4.7558609182106145e+234 -5.44732889921765e-82 9.291925296287727e-77)4(1.1442780460787748e-135 -9.175311889087647e+183 5.283538579979487e-197 2.82710780193072e+247)(/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64)))
160-4(-4.311570676438305e-187 -9.018267244087728e+119 -493894.0951031641 1.1010035362892656e+180)(*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))
00-0-x
00-0-(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) (acos.f64 (*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))))
00-0-(sqrt.f64 t)
00-0-(*.f64 z #s(literal 2 binary64))
00-0-#s(literal 2 binary64)
00-0-(acos.f64 (*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t)))
00-0-z
00-0-(/.f64 #s(literal 1 binary64) #s(literal 3 binary64))
00-0-#s(literal 27 binary64)
00-0-(/.f64 x (*.f64 y #s(literal 27 binary64)))
00-0-y
00-0-(*.f64 y #s(literal 27 binary64))
00-0-(*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64))))
00-0-#s(literal 1 binary64)
00-0-#s(literal 3 binary64)
00-0-t
Results
141.0ms512×0valid
Compiler

Compiled 213 to 56 computations (73.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 43.0ms
ival-mult: 19.0ms (44% of total)
ival-div: 13.0ms (30.1% of total)
ival-acos: 5.0ms (11.6% of total)
ival-sqrt: 4.0ms (9.3% of total)
const: 1.0ms (2.3% of total)
backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 17 to 13 computations (23.5% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶98.0%
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) (acos.f64 (*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))))
▶98.1%
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y))))
Compiler

Compiled 40 to 31 computations (22.5% saved)

simplify94.0ms (0.5%)

Algorithm
1×egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓cost-diff256
(/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64)))
✓cost-diff256
(*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))
✓cost-diff256
(acos.f64 (*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t)))
✓cost-diff384
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) (acos.f64 (*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))))
✓cost-diff0
(/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y)
✓cost-diff0
(*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y))
✓cost-diff0
(acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y)))
✓cost-diff0
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y))))
Rules
2044×*-lowering-*.f32
2044×*-lowering-*.f64
1186×associate-*l/
1120×associate-*r*
1096×associate-*l*
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
026134
155130
2156128
3482128
41540128
53040128
63079128
73098128
83098128
93098128
103658128
113674128
123674128
03674128
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(* 1/3 (acos (* 1/18 (/ (/ (* x (sqrt t)) z) y))))
1/3
(acos (* 1/18 (/ (/ (* x (sqrt t)) z) y)))
(* 1/18 (/ (/ (* x (sqrt t)) z) y))
1/18
(/ (/ (* x (sqrt t)) z) y)
(/ (* x (sqrt t)) z)
(* x (sqrt t))
x
(sqrt t)
t
z
y
(* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))))
(/ 1 3)
1
3
(acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))
(* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))
(/ (* 3 (/ x (* y 27))) (* z 2))
(* 3 (/ x (* y 27)))
(/ x (* y 27))
x
(* y 27)
y
27
(* z 2)
z
2
(sqrt t)
t
Outputs
(* 1/3 (acos (* 1/18 (/ (/ (* x (sqrt t)) z) y))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y))))
1/3
#s(literal 1/3 binary64)
(acos (* 1/18 (/ (/ (* x (sqrt t)) z) y)))
(acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y)))
(* 1/18 (/ (/ (* x (sqrt t)) z) y))
(*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y))
1/18
#s(literal 1/18 binary64)
(/ (/ (* x (sqrt t)) z) y)
(/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y)
(/ (* x (sqrt t)) z)
(/.f64 (*.f64 x (sqrt.f64 t)) z)
(* x (sqrt t))
(*.f64 x (sqrt.f64 t))
x
(sqrt t)
(sqrt.f64 t)
t
z
y
(* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y))))
(/ 1 3)
#s(literal 1/3 binary64)
1
#s(literal 1 binary64)
3
#s(literal 3 binary64)
(acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))
(acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y)))
(* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))
(*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y))
(/ (* 3 (/ x (* y 27))) (* z 2))
(/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 x y)) z)
(* 3 (/ x (* y 27)))
(*.f64 x (/.f64 #s(literal 1/9 binary64) y))
(/ x (* y 27))
(/.f64 x (*.f64 y #s(literal 27 binary64)))
x
(* y 27)
(*.f64 y #s(literal 27 binary64))
y
27
#s(literal 27 binary64)
(* z 2)
(*.f64 z #s(literal 2 binary64))
z
2
#s(literal 2 binary64)
(sqrt t)
(sqrt.f64 t)
t

localize236.0ms (1.3%)

Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓accuracy99.7%
(*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64))))
✓accuracy98.5%
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) (acos.f64 (*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))))
✓accuracy95.0%
(*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))
✓accuracy90.8%
(/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64)))
✓accuracy99.6%
(*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y))
✓accuracy98.5%
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y))))
✓accuracy96.4%
(/.f64 (*.f64 x (sqrt.f64 t)) z)
✓accuracy92.2%
(/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y)
Results
203.0ms256×0valid
Compiler

Compiled 155 to 27 computations (82.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 110.0ms
ival-div: 81.0ms (73.4% of total)
ival-mult: 15.0ms (13.6% of total)
...c/correct-round.rkt:119:19: 7.0ms (6.3% of total)
ival-acos: 5.0ms (4.5% of total)
ival-sqrt: 2.0ms (1.8% of total)
const: 1.0ms (0.9% of total)
backward-pass: 0.0ms (0% of total)

series40.0ms (0.2%)

Counts
10 → 432
Calls
Call 1
Inputs
#<alt (* 1/3 (acos (* 1/18 (/ (/ (* x (sqrt t)) z) y))))>
#<alt (acos (* 1/18 (/ (/ (* x (sqrt t)) z) y)))>
#<alt (* 1/18 (/ (/ (* x (sqrt t)) z) y))>
#<alt (/ (/ (* x (sqrt t)) z) y)>
#<alt (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))))>
#<alt (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))>
#<alt (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))>
#<alt (/ (* 3 (/ x (* y 27))) (* z 2))>
#<alt (/ (* x (sqrt t)) z)>
#<alt (* 3 (/ x (* y 27)))>
Outputs
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z)))))>
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#<alt (* 1/9 (/ x y))>
#<alt (* 1/9 (/ x y))>
#<alt (* 1/9 (/ x y))>
#<alt (* 1/9 (/ x y))>
#<alt (* 1/9 (/ x y))>
#<alt (* 1/9 (/ x y))>
Calls

108 calls:

TimeVariablePointExpression
3.0ms
z
@0
(/ (* x (sqrt t)) z)
3.0ms
t
@-inf
(* 1/18 (/ (/ (* x (sqrt t)) z) y))
2.0ms
x
@0
(/ (* 3 (/ x (* y 27))) (* z 2))
2.0ms
x
@0
(* 1/18 (/ (/ (* x (sqrt t)) z) y))
2.0ms
y
@-inf
(* 1/3 (acos (* 1/18 (/ (/ (* x (sqrt t)) z) y))))

rewrite359.0ms (2%)

Algorithm
1×batch-egg-rewrite
Rules
5482×*-lowering-*.f32
5482×*-lowering-*.f64
3118×/-lowering-/.f32
3118×/-lowering-/.f64
1776×pow-lowering-pow.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
026112
191102
259094
3534794
0896194
Stop Event
1×iter limit
1×node limit
Counts
10 → 812
Calls
Call 1
Inputs
(* 1/3 (acos (* 1/18 (/ (/ (* x (sqrt t)) z) y))))
(acos (* 1/18 (/ (/ (* x (sqrt t)) z) y)))
(* 1/18 (/ (/ (* x (sqrt t)) z) y))
(/ (/ (* x (sqrt t)) z) y)
(* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))))
(acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))
(* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t))
(/ (* 3 (/ x (* y 27))) (* z 2))
(/ (* x (sqrt t)) z)
(* 3 (/ x (* y 27)))
Outputs
(+.f64 (*.f64 #s(literal 1/3 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/3 binary64) (-.f64 #s(literal 0 binary64) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)))))
(+.f64 (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))) #s(literal 1/3 binary64)))
(fma.f64 #s(literal 1/3 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (-.f64 #s(literal 0 binary64) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)))))
(fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/3 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))) #s(literal 1/3 binary64)))
(/.f64 (*.f64 #s(literal 1/3 binary64) (-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 3 binary64)))) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))))))
(/.f64 (*.f64 #s(literal 1/3 binary64) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 2 binary64)))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))))
(/.f64 (*.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 3 binary64))) #s(literal 1/3 binary64)) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))))))
(/.f64 (*.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)))
(*.f64 (acos.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 1/3 binary64))
(acos.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))))
(+.f64 (-.f64 #s(literal 0 binary64) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))) (/.f64 (PI.f64) #s(literal 2 binary64)))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))) (acos.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)))
(-.f64 (PI.f64) (acos.f64 (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 x (/.f64 z (sqrt.f64 t)))) (/.f64 #s(literal 1/18 binary64) y))))
(-.f64 (PI.f64) (acos.f64 (*.f64 (neg.f64 (/.f64 x (*.f64 y (/.f64 z (sqrt.f64 t))))) #s(literal 1/18 binary64))))
(-.f64 (PI.f64) (acos.f64 (*.f64 #s(literal 1/18 binary64) (neg.f64 (/.f64 x (*.f64 y (/.f64 z (sqrt.f64 t))))))))
(-.f64 (PI.f64) (acos.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) (-.f64 #s(literal 0 binary64) y))))
(-.f64 (PI.f64) (acos.f64 (/.f64 (/.f64 #s(literal -1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)))
(-.f64 (/.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)))))) (/.f64 (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 3 binary64)) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)))))))
(-.f64 (/.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)))) (/.f64 (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 2 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)))))
(fma.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (-.f64 #s(literal 0 binary64) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))))
(fma.f64 #s(literal -1 binary64) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) (/.f64 (PI.f64) #s(literal 2 binary64)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (*.f64 (cbrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))))
(fma.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))))
(fma.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))))) (-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 3 binary64))) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))))))
(/.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))))
(/.f64 (neg.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)))))))
(/.f64 (neg.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 2 binary64)))) (neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)))))
(/.f64 (+.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))) #s(literal 3 binary64))) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (-.f64 (*.f64 (-.f64 #s(literal 0 binary64) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))) (-.f64 #s(literal 0 binary64) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)))) (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)))))))
(/.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))) (-.f64 #s(literal 0 binary64) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))))) (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)))))
(pow.f64 (/.f64 (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))))) (-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 2 binary64)))) #s(literal -1 binary64))
(*.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)))))))
(*.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)))))
(exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 y (*.f64 #s(literal 1/18 binary64) (*.f64 x (sqrt.f64 t)))) z)) #s(literal -1 binary64)))
(neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 x (/.f64 z (sqrt.f64 t)))) (/.f64 #s(literal 1/18 binary64) y)))
(neg.f64 (*.f64 (neg.f64 (/.f64 x (*.f64 y (/.f64 z (sqrt.f64 t))))) #s(literal 1/18 binary64)))
(neg.f64 (*.f64 #s(literal 1/18 binary64) (neg.f64 (/.f64 x (*.f64 y (/.f64 z (sqrt.f64 t)))))))
(neg.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) (-.f64 #s(literal 0 binary64) y)))
(neg.f64 (/.f64 (/.f64 #s(literal -1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))
(/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 y (*.f64 #s(literal 1/18 binary64) (*.f64 x (sqrt.f64 t)))) z))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 y (*.f64 #s(literal 1/18 binary64) (*.f64 x (sqrt.f64 t)))) z) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 z y) (*.f64 #s(literal 1/18 binary64) (*.f64 x (sqrt.f64 t)))))
(/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (/.f64 y (*.f64 #s(literal 1/18 binary64) (*.f64 x (sqrt.f64 t)))) z)))
(/.f64 (/.f64 #s(literal -1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) (-.f64 #s(literal 0 binary64) y))
(/.f64 (*.f64 #s(literal 1/18 binary64) (*.f64 x (sqrt.f64 t))) (*.f64 z y))
(/.f64 (/.f64 #s(literal 1/18 binary64) y) (/.f64 (/.f64 z (sqrt.f64 t)) x))
(/.f64 (*.f64 #s(literal -1/18 binary64) (*.f64 x (sqrt.f64 t))) (-.f64 #s(literal 0 binary64) (*.f64 z y)))
(/.f64 #s(literal -1/18 binary64) (/.f64 y (-.f64 #s(literal 0 binary64) (/.f64 x (/.f64 z (sqrt.f64 t))))))
(/.f64 #s(literal -1/18 binary64) (*.f64 (/.f64 (/.f64 z (sqrt.f64 t)) x) (-.f64 #s(literal 0 binary64) y)))
(/.f64 (*.f64 (*.f64 #s(literal 1/18 binary64) (*.f64 x (sqrt.f64 t))) #s(literal 1 binary64)) (*.f64 z y))
(/.f64 (*.f64 (*.f64 #s(literal 1/18 binary64) (*.f64 x (sqrt.f64 t))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 z y)))
(/.f64 (*.f64 (*.f64 #s(literal -1/18 binary64) (*.f64 x (sqrt.f64 t))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 z y)))
(/.f64 (*.f64 (*.f64 #s(literal -1/18 binary64) (*.f64 x (sqrt.f64 t))) #s(literal -1 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) z) (-.f64 #s(literal 0 binary64) y)))
(/.f64 (*.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) #s(literal 1 binary64)) y)
(/.f64 (*.f64 (*.f64 x (sqrt.f64 t)) (/.f64 #s(literal 1/18 binary64) y)) z)
(/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 x (sqrt.f64 t)) y)) z)
(/.f64 (*.f64 #s(literal 1/18 binary64) (neg.f64 (/.f64 (*.f64 x (sqrt.f64 t)) y))) (-.f64 #s(literal 0 binary64) z))
(/.f64 (*.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) y))
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(*.f64 #s(literal 1/9 binary64) (*.f64 (/.f64 x y) #s(literal 1 binary64)))
(*.f64 #s(literal 1/27 binary64) (/.f64 #s(literal 3 binary64) (/.f64 y x)))
(*.f64 (/.f64 #s(literal 1/9 binary64) y) x)
(*.f64 (/.f64 #s(literal 3 binary64) (/.f64 y x)) #s(literal 1/27 binary64))
(*.f64 (*.f64 x #s(literal 1/9 binary64)) (/.f64 #s(literal 1 binary64) y))
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(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal 1/9 binary64) y))
(*.f64 (*.f64 #s(literal 1/9 binary64) x) (/.f64 #s(literal 1 binary64) y))
(*.f64 (/.f64 #s(literal 3 binary64) (*.f64 y #s(literal -27 binary64))) (-.f64 #s(literal 0 binary64) x))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1/27 binary64) y))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal -3 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal -1/27 binary64) y))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3 binary64) (/.f64 y x))) #s(literal -1 binary64)) #s(literal 1/27 binary64))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/9 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) y))

simplify267.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
3426×*-lowering-*.f32
3426×*-lowering-*.f64
1870×/-lowering-/.f32
1870×/-lowering-/.f64
1482×times-frac
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0354316
1794252
22764236
310384236
424134236
549884236
671024236
081614236
Stop Event
1×iter limit
1×node limit
Counts
432 → 432
Calls
Call 1
Inputs
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(* -1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* 1/18 (/ x (* y z)))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* -1 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))
(* -1 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))
(* -1 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))
(* -1 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
(* 1/9 (/ x y))
Outputs
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (/.f64 (*.f64 x (*.f64 (sqrt.f64 t) #s(literal -1/18 binary64))) y) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (/.f64 (*.f64 x (*.f64 (sqrt.f64 t) #s(literal -1/18 binary64))) y) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (/.f64 (*.f64 x (*.f64 (sqrt.f64 t) #s(literal -1/18 binary64))) y) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (/.f64 (*.f64 x (*.f64 (sqrt.f64 t) #s(literal -1/18 binary64))) y) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y)))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z)))))
(acos.f64 (/.f64 (/.f64 (*.f64 x (*.f64 (sqrt.f64 t) #s(literal -1/18 binary64))) y) z))
(acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z)))))
(acos.f64 (/.f64 (/.f64 (*.f64 x (*.f64 (sqrt.f64 t) #s(literal -1/18 binary64))) y) z))
(acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z)))))
(acos.f64 (/.f64 (/.f64 (*.f64 x (*.f64 (sqrt.f64 t) #s(literal -1/18 binary64))) y) z))
(acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z)))))
(acos.f64 (/.f64 (/.f64 (*.f64 x (*.f64 (sqrt.f64 t) #s(literal -1/18 binary64))) y) z))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (sqrt.f64 t)) z) x) y))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
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(/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) x) y) z)
(* 1/18 (/ x (* y z)))
(/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) x) y) z)
(* 1/18 (/ x (* y z)))
(/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) x) y) z)
(* 1/18 (/ x (* y z)))
(/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) x) y) z)
(* 1/18 (/ x (* y z)))
(/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) x) y) z)
(* 1/18 (/ x (* y z)))
(/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) x) y) z)
(* 1/18 (/ x (* y z)))
(/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) x) y) z)
(* 1/18 (/ x (* y z)))
(/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) x) y) z)
(* 1/18 (/ x (* y z)))
(/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) x) y) z)
(* 1/18 (/ x (* y z)))
(/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) x) y) z)
(* 1/18 (/ x (* y z)))
(/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) x) y) z)
(* 1/18 (/ x (* y z)))
(/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) x) y) z)
(* 1/18 (/ x (* y z)))
(/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) x) y) z)
(* 1/18 (/ x (* y z)))
(/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) x) y) z)
(* 1/18 (/ x (* y z)))
(/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) x) y) z)
(* 1/18 (/ x (* y z)))
(/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) x) y) z)
(* 1/18 (/ x (* y z)))
(/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) x) y) z)
(* 1/18 (/ x (* y z)))
(/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) x) y) z)
(* 1/18 (/ x (* y z)))
(/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) x) y) z)
(* 1/18 (/ x (* y z)))
(/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) x) y) z)
(* 1/18 (/ x (* y z)))
(/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) x) y) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* -1 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* -1 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* -1 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* -1 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) (/ x z))
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)
(* 1/9 (/ x y))
(/.f64 (*.f64 x #s(literal 1/9 binary64)) y)

eval186.0ms (1%)

Compiler

Compiled 21821 to 3750 computations (82.8% saved)

prune172.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New124221244
Fresh000
Picked112
Done000
Total124331246
Accuracy
98.5%
Counts
1246 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶97.9%
(*.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 2 binary64))))))
▶98.1%
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 (sqrt.f64 t) (*.f64 (/.f64 x z) (/.f64 #s(literal 1/18 binary64) y)))))
✓98.1%
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y))))
Compiler

Compiled 77 to 51 computations (33.8% saved)

simplify180.0ms (1%)

Algorithm
1×egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)))
✓cost-diff0
(/.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 2 binary64))))
✓cost-diff128
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 2 binary64)))))
✓cost-diff128
(*.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 2 binary64))))))
✓cost-diff0
(sqrt.f64 t)
✓cost-diff0
(*.f64 (sqrt.f64 t) (*.f64 (/.f64 x z) (/.f64 #s(literal 1/18 binary64) y)))
✓cost-diff0
(acos.f64 (*.f64 (sqrt.f64 t) (*.f64 (/.f64 x z) (/.f64 #s(literal 1/18 binary64) y))))
✓cost-diff0
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 (sqrt.f64 t) (*.f64 (/.f64 x z) (/.f64 #s(literal 1/18 binary64) y)))))
Rules
2176×*-lowering-*.f32
2176×*-lowering-*.f64
1802×fma-lowering-fma.f32
1802×fma-lowering-fma.f64
1678×sum3-define
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
031266
161261
2135260
3332260
4726260
51404256
62240252
73375252
85957252
08135252
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* 1/3 (acos (* (sqrt t) (* (/ x z) (/ 1/18 y)))))
1/3
(acos (* (sqrt t) (* (/ x z) (/ 1/18 y))))
(* (sqrt t) (* (/ x z) (/ 1/18 y)))
(sqrt t)
t
(* (/ x z) (/ 1/18 y))
(/ x z)
x
z
(/ 1/18 y)
1/18
y
(* 1/3 (/ 1 (/ (+ (/ (PI) 2) (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y))) (- (/ (* (PI) (PI)) 4) (pow (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)) 2)))))
1/3
(/ 1 (/ (+ (/ (PI) 2) (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y))) (- (/ (* (PI) (PI)) 4) (pow (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)) 2))))
1
(/ (+ (/ (PI) 2) (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y))) (- (/ (* (PI) (PI)) 4) (pow (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)) 2)))
(+ (/ (PI) 2) (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)))
(/ (PI) 2)
(PI)
2
(asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y))
(/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)
(/ 1/18 (/ (/ z (sqrt t)) x))
1/18
(/ (/ z (sqrt t)) x)
(/ z (sqrt t))
z
(sqrt t)
t
x
y
(- (/ (* (PI) (PI)) 4) (pow (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)) 2))
(/ (* (PI) (PI)) 4)
(* (PI) (PI))
4
(pow (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)) 2)
Outputs
(* 1/3 (acos (* (sqrt t) (* (/ x z) (/ 1/18 y)))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 #s(literal 1/18 binary64) (*.f64 y (/.f64 z (*.f64 (sqrt.f64 t) x))))))
1/3
#s(literal 1/3 binary64)
(acos (* (sqrt t) (* (/ x z) (/ 1/18 y))))
(acos.f64 (/.f64 #s(literal 1/18 binary64) (*.f64 y (/.f64 z (*.f64 (sqrt.f64 t) x)))))
(* (sqrt t) (* (/ x z) (/ 1/18 y)))
(/.f64 #s(literal 1/18 binary64) (*.f64 y (/.f64 z (*.f64 (sqrt.f64 t) x))))
(sqrt t)
(sqrt.f64 t)
t
(* (/ x z) (/ 1/18 y))
(/.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 z y) x))
(/ x z)
(/.f64 x z)
x
z
(/ 1/18 y)
(/.f64 #s(literal 1/18 binary64) y)
1/18
#s(literal 1/18 binary64)
y
(* 1/3 (/ 1 (/ (+ (/ (PI) 2) (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y))) (- (/ (* (PI) (PI)) 4) (pow (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)) 2)))))
(/.f64 (*.f64 #s(literal 1/3 binary64) (+.f64 (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (*.f64 y (/.f64 z (*.f64 (sqrt.f64 t) x))))) #s(literal 2 binary64)) (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal -4 binary64)))) (-.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (*.f64 y (/.f64 z (*.f64 (sqrt.f64 t) x)))))))
1/3
#s(literal 1/3 binary64)
(/ 1 (/ (+ (/ (PI) 2) (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y))) (- (/ (* (PI) (PI)) 4) (pow (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)) 2))))
(/.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (*.f64 y (/.f64 z (*.f64 (sqrt.f64 t) x))))) #s(literal 2 binary64))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (*.f64 y (/.f64 z (*.f64 (sqrt.f64 t) x)))))))
1
#s(literal 1 binary64)
(/ (+ (/ (PI) 2) (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y))) (- (/ (* (PI) (PI)) 4) (pow (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)) 2)))
(/.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (*.f64 y (/.f64 z (*.f64 (sqrt.f64 t) x)))))) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (*.f64 y (/.f64 z (*.f64 (sqrt.f64 t) x))))) #s(literal 2 binary64))))
(+ (/ (PI) 2) (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (*.f64 y (/.f64 z (*.f64 (sqrt.f64 t) x))))))
(/ (PI) 2)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI)
(PI.f64)
2
#s(literal 2 binary64)
(asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y))
(asin.f64 (/.f64 #s(literal 1/18 binary64) (*.f64 y (/.f64 z (*.f64 (sqrt.f64 t) x)))))
(/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)
(/.f64 #s(literal 1/18 binary64) (*.f64 y (/.f64 z (*.f64 (sqrt.f64 t) x))))
(/ 1/18 (/ (/ z (sqrt t)) x))
(*.f64 x (*.f64 #s(literal 1/18 binary64) (/.f64 (sqrt.f64 t) z)))
1/18
#s(literal 1/18 binary64)
(/ (/ z (sqrt t)) x)
(/.f64 z (*.f64 (sqrt.f64 t) x))
(/ z (sqrt t))
(/.f64 z (sqrt.f64 t))
z
(sqrt t)
(sqrt.f64 t)
t
x
y
(- (/ (* (PI) (PI)) 4) (pow (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)) 2))
(-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (*.f64 y (/.f64 z (*.f64 (sqrt.f64 t) x))))) #s(literal 2 binary64)))
(/ (* (PI) (PI)) 4)
(/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64))
(* (PI) (PI))
(*.f64 (PI.f64) (PI.f64))
4
#s(literal 4 binary64)
(pow (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)) 2)
(pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (*.f64 y (/.f64 z (*.f64 (sqrt.f64 t) x))))) #s(literal 2 binary64))

localize177.0ms (1%)

Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓accuracy99.1%
(/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x))
✓accuracy98.5%
(*.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 2 binary64))))))
✓accuracy95.3%
(/.f64 (/.f64 z (sqrt.f64 t)) x)
✓accuracy92.2%
(/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)
✓accuracy99.5%
(/.f64 #s(literal 1/18 binary64) y)
✓accuracy98.5%
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 (sqrt.f64 t) (*.f64 (/.f64 x z) (/.f64 #s(literal 1/18 binary64) y)))))
✓accuracy95.0%
(*.f64 (sqrt.f64 t) (*.f64 (/.f64 x z) (/.f64 #s(literal 1/18 binary64) y)))
✓accuracy93.3%
(*.f64 (/.f64 x z) (/.f64 #s(literal 1/18 binary64) y))
Results
121.0ms256×0valid
Compiler

Compiled 280 to 32 computations (88.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 49.0ms
ival-div: 18.0ms (36.5% of total)
ival-mult: 8.0ms (16.2% of total)
...c/correct-round.rkt:119:19: 8.0ms (16.2% of total)
ival-pow: 4.0ms (8.1% of total)
ival-acos: 3.0ms (6.1% of total)
ival-asin: 2.0ms (4.1% of total)
ival-sqrt: 2.0ms (4.1% of total)
ival-pi: 1.0ms (2% of total)
ival-add: 1.0ms (2% of total)
ival-sub: 1.0ms (2% of total)
const: 1.0ms (2% of total)
backward-pass: 0.0ms (0% of total)

series70.0ms (0.4%)

Counts
13 → 516
Calls
Call 1
Inputs
#<alt (* 1/3 (acos (* (sqrt t) (* (/ x z) (/ 1/18 y)))))>
#<alt (acos (* (sqrt t) (* (/ x z) (/ 1/18 y))))>
#<alt (* (sqrt t) (* (/ x z) (/ 1/18 y)))>
#<alt (sqrt t)>
#<alt (* 1/3 (/ 1 (/ (+ (/ (PI) 2) (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y))) (- (/ (* (PI) (PI)) 4) (pow (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)) 2)))))>
#<alt (/ 1 (/ (+ (/ (PI) 2) (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y))) (- (/ (* (PI) (PI)) 4) (pow (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)) 2))))>
#<alt (/ (+ (/ (PI) 2) (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y))) (- (/ (* (PI) (PI)) 4) (pow (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)) 2)))>
#<alt (+ (/ (PI) 2) (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)))>
#<alt (* (/ x z) (/ 1/18 y))>
#<alt (/ 1/18 y)>
#<alt (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)>
#<alt (/ (/ z (sqrt t)) x)>
#<alt (/ 1/18 (/ (/ z (sqrt t)) x))>
Outputs
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
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#<alt (* 1/18 (/ x (* y z)))>
#<alt (* 1/18 (/ x (* y z)))>
#<alt (* 1/18 (/ x (* y z)))>
#<alt (* 1/18 (/ x (* y z)))>
#<alt (* 1/18 (/ x (* y z)))>
#<alt (* 1/18 (/ x (* y z)))>
#<alt (* 1/18 (/ x (* y z)))>
#<alt (* 1/18 (/ x (* y z)))>
#<alt (* 1/18 (/ x (* y z)))>
#<alt (* 1/18 (/ x (* y z)))>
#<alt (* 1/18 (/ x (* y z)))>
#<alt (* 1/18 (/ x (* y z)))>
#<alt (* 1/18 (/ x (* y z)))>
#<alt (* 1/18 (/ x (* y z)))>
#<alt (* 1/18 (/ x (* y z)))>
#<alt (* 1/18 (/ x (* y z)))>
#<alt (/ 1/18 y)>
#<alt (/ 1/18 y)>
#<alt (/ 1/18 y)>
#<alt (/ 1/18 y)>
#<alt (/ 1/18 y)>
#<alt (/ 1/18 y)>
#<alt (/ 1/18 y)>
#<alt (/ 1/18 y)>
#<alt (/ 1/18 y)>
#<alt (/ 1/18 y)>
#<alt (/ 1/18 y)>
#<alt (/ 1/18 y)>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* -1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))>
#<alt (* -1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))>
#<alt (* -1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))>
#<alt (* -1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* -1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))>
#<alt (* -1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))>
#<alt (* -1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))>
#<alt (* -1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
#<alt (* 1/18 (* (sqrt t) (/ x z)))>
Calls

129 calls:

TimeVariablePointExpression
17.0ms
x
@inf
(* 1/3 (/ 1 (/ (+ (/ (PI) 2) (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y))) (- (/ (* (PI) (PI)) 4) (pow (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)) 2)))))
9.0ms
x
@-inf
(/ (+ (/ (PI) 2) (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y))) (- (/ (* (PI) (PI)) 4) (pow (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)) 2)))
3.0ms
z
@inf
(/ (/ z (sqrt t)) x)
2.0ms
z
@0
(* 1/3 (/ 1 (/ (+ (/ (PI) 2) (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y))) (- (/ (* (PI) (PI)) 4) (pow (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)) 2)))))
2.0ms
y
@-inf
(* 1/3 (/ 1 (/ (+ (/ (PI) 2) (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y))) (- (/ (* (PI) (PI)) 4) (pow (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)) 2)))))

rewrite441.0ms (2.4%)

Algorithm
1×batch-egg-rewrite
Rules
4286×/-lowering-/.f32
4286×/-lowering-/.f64
4186×*-lowering-*.f32
4186×*-lowering-*.f64
1276×+-lowering-+.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
031143
1188120
21457120
08540120
Stop Event
1×iter limit
1×node limit
Counts
13 → 842
Calls
Call 1
Inputs
(* 1/3 (acos (* (sqrt t) (* (/ x z) (/ 1/18 y)))))
(acos (* (sqrt t) (* (/ x z) (/ 1/18 y))))
(* (sqrt t) (* (/ x z) (/ 1/18 y)))
(sqrt t)
(* 1/3 (/ 1 (/ (+ (/ (PI) 2) (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y))) (- (/ (* (PI) (PI)) 4) (pow (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)) 2)))))
(/ 1 (/ (+ (/ (PI) 2) (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y))) (- (/ (* (PI) (PI)) 4) (pow (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)) 2))))
(/ (+ (/ (PI) 2) (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y))) (- (/ (* (PI) (PI)) 4) (pow (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)) 2)))
(+ (/ (PI) 2) (asin (/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)))
(* (/ x z) (/ 1/18 y))
(/ 1/18 y)
(/ (/ 1/18 (/ (/ z (sqrt t)) x)) y)
(/ (/ z (sqrt t)) x)
(/ 1/18 (/ (/ z (sqrt t)) x))
Outputs
(/.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))) #s(literal 1/3 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))) #s(literal 1/3 binary64))))
(/.f64 #s(literal -1/3 binary64) (/.f64 #s(literal -1 binary64) (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))))
(/.f64 (/.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))))) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (/.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))))) (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 2 binary64))))))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))) #s(literal 1/3 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))))
(*.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))))
(*.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 1/3 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))))) (*.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 2 binary64))) #s(literal 1/3 binary64)))
(*.f64 (*.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))))) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))))) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1/3 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))))) (-.f64 #s(literal 0 binary64) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 2 binary64)))))
(acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (neg.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))))
(+.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) (fma.f64 (neg.f64 (sqrt.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))))) (sqrt.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))))) (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))))) (-.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 2 binary64)))))
(+.f64 (*.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))))))
(+.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 2 binary64) (PI.f64))) (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))))) #s(literal -1 binary64)))
(-.f64 (PI.f64) (acos.f64 (*.f64 #s(literal -1/18 binary64) (/.f64 (/.f64 x (/.f64 z (sqrt.f64 t))) y))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))))
(-.f64 (/.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))))) (/.f64 (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 2 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))))))
(-.f64 (/.f64 (/.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64)))) #s(literal 64 binary64)) (+.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) #s(literal 16 binary64)) (+.f64 (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 4 binary64)) (pow.f64 (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))) #s(literal 2 binary64))))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))))) (/.f64 (/.f64 (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 6 binary64)) (+.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) #s(literal 16 binary64)) (+.f64 (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 4 binary64)) (pow.f64 (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))) #s(literal 2 binary64))))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))))))
(-.f64 (/.f64 (/.f64 (/.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (*.f64 (PI.f64) (PI.f64))) #s(literal 16 binary64)) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 2 binary64)))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))))) (/.f64 (/.f64 (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 4 binary64)) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 2 binary64)))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))))) (/.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))))))
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(*.f64 (/.f64 x (pow.f64 t #s(literal -1/2 binary64))) (/.f64 #s(literal 1/18 binary64) z))
(*.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) z) #s(literal 1 binary64)) (/.f64 (sqrt.f64 t) (/.f64 #s(literal 1 binary64) x)))
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simplify327.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
3554×*-lowering-*.f32
3554×*-lowering-*.f64
1996×/-lowering-/.f32
1996×/-lowering-/.f64
1828×fnmsub-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0608856
11378232
23598196
310698196
424268196
553328196
675108196
088388196
Stop Event
1×iter limit
1×node limit
Counts
516 → 516
Calls
Call 1
Inputs
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(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))
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(/ (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))) (- (* 1/4 (pow (PI) 2)) (pow (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) 2)))
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(/ (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))) (- (* 1/4 (pow (PI) 2)) (pow (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) 2)))
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(/ (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))) (- (* 1/4 (pow (PI) 2)) (pow (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) 2)))
(/ (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))) (- (* 1/4 (pow (PI) 2)) (pow (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) 2)))
(/ (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))) (- (* 1/4 (pow (PI) 2)) (pow (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) 2)))
(/ (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))) (- (* 1/4 (pow (PI) 2)) (pow (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) 2)))
(/ (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))) (- (* 1/4 (pow (PI) 2)) (pow (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) 2)))
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(/ 1/18 y)
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(/ 1/18 y)
(/ 1/18 y)
(/ 1/18 y)
(/ 1/18 y)
(/ 1/18 y)
(/ 1/18 y)
(/ 1/18 y)
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Outputs
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 (sqrt.f64 t) x) z) y))))
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(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
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(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
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(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
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(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
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(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
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eval313.0ms (1.7%)

Compiler

Compiled 67698 to 4781 computations (92.9% saved)

prune278.0ms (1.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New171321715
Fresh000
Picked022
Done011
Total171351718
Accuracy
100.0%
Counts
1718 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.3%
(*.f64 (*.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))))) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 2 binary64))))
▶97.0%
(*.f64 #s(literal 1/3 binary64) (pow.f64 (pow.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
✓97.9%
(*.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 2 binary64))))))
✓98.1%
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 (sqrt.f64 t) (*.f64 (/.f64 x z) (/.f64 #s(literal 1/18 binary64) y)))))
✓98.1%
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y))))
Compiler

Compiled 141 to 93 computations (34% saved)

simplify186.0ms (1%)

Algorithm
1×egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))))
✓cost-diff0
(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))))
✓cost-diff128
(*.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))))))
✓cost-diff128
(*.f64 (*.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))))) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 2 binary64))))
✓cost-diff0
(acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))
✓cost-diff64
(pow.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 1/2 binary64))
✓cost-diff12928
(pow.f64 (pow.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
✓cost-diff12928
(*.f64 #s(literal 1/3 binary64) (pow.f64 (pow.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
Rules
2404×*-lowering-*.f32
2404×*-lowering-*.f64
1736×sum5-define
1536×fnmadd-define
1394×fma-define
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
030269
155257
2120257
3312257
4783256
51479255
62357251
73852251
87007251
08040251
Stop Event
1×iter limit
1×node limit
Calls
Call 1
Inputs
(* 1/3 (pow (pow (acos (/ 1/18 (/ y (/ x (/ z (sqrt t)))))) 1/2) 2))
1/3
(pow (pow (acos (/ 1/18 (/ y (/ x (/ z (sqrt t)))))) 1/2) 2)
(pow (acos (/ 1/18 (/ y (/ x (/ z (sqrt t)))))) 1/2)
(acos (/ 1/18 (/ y (/ x (/ z (sqrt t))))))
(/ 1/18 (/ y (/ x (/ z (sqrt t)))))
1/18
(/ y (/ x (/ z (sqrt t))))
y
(/ x (/ z (sqrt t)))
x
(/ z (sqrt t))
z
(sqrt t)
t
1/2
2
(* (* 1/3 (/ 1 (+ (/ (PI) 2) (asin (/ 1/18 (/ y (/ x (/ z (sqrt t))))))))) (- (/ (* (PI) (PI)) 4) (pow (asin (/ 1/18 (/ y (/ x (/ z (sqrt t)))))) 2)))
(* 1/3 (/ 1 (+ (/ (PI) 2) (asin (/ 1/18 (/ y (/ x (/ z (sqrt t)))))))))
1/3
(/ 1 (+ (/ (PI) 2) (asin (/ 1/18 (/ y (/ x (/ z (sqrt t))))))))
1
(+ (/ (PI) 2) (asin (/ 1/18 (/ y (/ x (/ z (sqrt t)))))))
(/ (PI) 2)
(PI)
2
(asin (/ 1/18 (/ y (/ x (/ z (sqrt t))))))
(/ 1/18 (/ y (/ x (/ z (sqrt t)))))
1/18
(/ y (/ x (/ z (sqrt t))))
y
(/ x (/ z (sqrt t)))
x
(/ z (sqrt t))
z
(sqrt t)
t
(- (/ (* (PI) (PI)) 4) (pow (asin (/ 1/18 (/ y (/ x (/ z (sqrt t)))))) 2))
(/ (* (PI) (PI)) 4)
(* (PI) (PI))
4
(pow (asin (/ 1/18 (/ y (/ x (/ z (sqrt t)))))) 2)
Outputs
(* 1/3 (pow (pow (acos (/ 1/18 (/ y (/ x (/ z (sqrt t)))))) 1/2) 2))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 x (/.f64 #s(literal 1/18 binary64) (/.f64 z (sqrt.f64 t)))) y)))
1/3
#s(literal 1/3 binary64)
(pow (pow (acos (/ 1/18 (/ y (/ x (/ z (sqrt t)))))) 1/2) 2)
(acos.f64 (/.f64 (*.f64 x (/.f64 #s(literal 1/18 binary64) (/.f64 z (sqrt.f64 t)))) y))
(pow (acos (/ 1/18 (/ y (/ x (/ z (sqrt t)))))) 1/2)
(sqrt.f64 (acos.f64 (/.f64 (*.f64 x (/.f64 #s(literal 1/18 binary64) (/.f64 z (sqrt.f64 t)))) y)))
(acos (/ 1/18 (/ y (/ x (/ z (sqrt t))))))
(acos.f64 (/.f64 (*.f64 x (/.f64 #s(literal 1/18 binary64) (/.f64 z (sqrt.f64 t)))) y))
(/ 1/18 (/ y (/ x (/ z (sqrt t)))))
(/.f64 (*.f64 x (/.f64 #s(literal 1/18 binary64) (/.f64 z (sqrt.f64 t)))) y)
1/18
#s(literal 1/18 binary64)
(/ y (/ x (/ z (sqrt t))))
(/.f64 (/.f64 y (/.f64 (sqrt.f64 t) z)) x)
y
(/ x (/ z (sqrt t)))
(/.f64 x (/.f64 z (sqrt.f64 t)))
x
(/ z (sqrt t))
(/.f64 z (sqrt.f64 t))
z
(sqrt t)
(sqrt.f64 t)
t
1/2
#s(literal 1/2 binary64)
2
#s(literal 2 binary64)
(* (* 1/3 (/ 1 (+ (/ (PI) 2) (asin (/ 1/18 (/ y (/ x (/ z (sqrt t))))))))) (- (/ (* (PI) (PI)) 4) (pow (asin (/ 1/18 (/ y (/ x (/ z (sqrt t)))))) 2)))
(/.f64 (*.f64 #s(literal 1/3 binary64) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 (*.f64 x (/.f64 #s(literal 1/18 binary64) (/.f64 z (sqrt.f64 t)))) y)) #s(literal 2 binary64)))) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (*.f64 x (/.f64 #s(literal 1/18 binary64) (/.f64 z (sqrt.f64 t)))) y))))
(* 1/3 (/ 1 (+ (/ (PI) 2) (asin (/ 1/18 (/ y (/ x (/ z (sqrt t)))))))))
(/.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (*.f64 x (/.f64 #s(literal 1/18 binary64) (/.f64 z (sqrt.f64 t)))) y))))
1/3
#s(literal 1/3 binary64)
(/ 1 (+ (/ (PI) 2) (asin (/ 1/18 (/ y (/ x (/ z (sqrt t))))))))
(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (*.f64 x (/.f64 #s(literal 1/18 binary64) (/.f64 z (sqrt.f64 t)))) y))))
1
#s(literal 1 binary64)
(+ (/ (PI) 2) (asin (/ 1/18 (/ y (/ x (/ z (sqrt t)))))))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (*.f64 x (/.f64 #s(literal 1/18 binary64) (/.f64 z (sqrt.f64 t)))) y)))
(/ (PI) 2)
(/.f64 (PI.f64) #s(literal 2 binary64))
(PI)
(PI.f64)
2
#s(literal 2 binary64)
(asin (/ 1/18 (/ y (/ x (/ z (sqrt t))))))
(asin.f64 (/.f64 (*.f64 x (/.f64 #s(literal 1/18 binary64) (/.f64 z (sqrt.f64 t)))) y))
(/ 1/18 (/ y (/ x (/ z (sqrt t)))))
(/.f64 (*.f64 x (/.f64 #s(literal 1/18 binary64) (/.f64 z (sqrt.f64 t)))) y)
1/18
#s(literal 1/18 binary64)
(/ y (/ x (/ z (sqrt t))))
(/.f64 (/.f64 y (/.f64 (sqrt.f64 t) z)) x)
y
(/ x (/ z (sqrt t)))
(/.f64 x (/.f64 z (sqrt.f64 t)))
x
(/ z (sqrt t))
(/.f64 z (sqrt.f64 t))
z
(sqrt t)
(sqrt.f64 t)
t
(- (/ (* (PI) (PI)) 4) (pow (asin (/ 1/18 (/ y (/ x (/ z (sqrt t)))))) 2))
(-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 (*.f64 x (/.f64 #s(literal 1/18 binary64) (/.f64 z (sqrt.f64 t)))) y)) #s(literal 2 binary64)))
(/ (* (PI) (PI)) 4)
(/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64))
(* (PI) (PI))
(*.f64 (PI.f64) (PI.f64))
4
#s(literal 4 binary64)
(pow (asin (/ 1/18 (/ y (/ x (/ z (sqrt t)))))) 2)
(pow.f64 (asin.f64 (/.f64 (*.f64 x (/.f64 #s(literal 1/18 binary64) (/.f64 z (sqrt.f64 t)))) y)) #s(literal 2 binary64))

localize208.0ms (1.1%)

Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓accuracy99.7%
(/.f64 z (sqrt.f64 t))
✓accuracy98.8%
(/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))
✓accuracy95.1%
(/.f64 x (/.f64 z (sqrt.f64 t)))
✓accuracy92.3%
(/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))
✓accuracy98.5%
(*.f64 #s(literal 1/3 binary64) (pow.f64 (pow.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
✓accuracy98.4%
(pow.f64 (pow.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
✓accuracy95.1%
(/.f64 x (/.f64 z (sqrt.f64 t)))
✓accuracy92.3%
(/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))
Results
127.0ms256×0valid
Compiler

Compiled 283 to 31 computations (89% saved)

Precisions
Click to see histograms. Total time spent on operations: 52.0ms
ival-pow: 13.0ms (25.1% of total)
ival-div: 12.0ms (23.2% of total)
...c/correct-round.rkt:119:19: 7.0ms (13.5% of total)
ival-mult: 6.0ms (11.6% of total)
ival-add: 3.0ms (5.8% of total)
ival-acos: 3.0ms (5.8% of total)
ival-asin: 2.0ms (3.9% of total)
ival-sqrt: 2.0ms (3.9% of total)
ival-pi: 1.0ms (1.9% of total)
ival-sub: 1.0ms (1.9% of total)
const: 1.0ms (1.9% of total)
backward-pass: 0.0ms (0% of total)

series47.0ms (0.3%)

Counts
12 → 540
Calls
Call 1
Inputs
#<alt (* 1/3 (pow (pow (acos (/ 1/18 (/ y (/ x (/ z (sqrt t)))))) 1/2) 2))>
#<alt (pow (pow (acos (/ 1/18 (/ y (/ x (/ z (sqrt t)))))) 1/2) 2)>
#<alt (pow (acos (/ 1/18 (/ y (/ x (/ z (sqrt t)))))) 1/2)>
#<alt (acos (/ 1/18 (/ y (/ x (/ z (sqrt t))))))>
#<alt (* (* 1/3 (/ 1 (+ (/ (PI) 2) (asin (/ 1/18 (/ y (/ x (/ z (sqrt t))))))))) (- (/ (* (PI) (PI)) 4) (pow (asin (/ 1/18 (/ y (/ x (/ z (sqrt t)))))) 2)))>
#<alt (* 1/3 (/ 1 (+ (/ (PI) 2) (asin (/ 1/18 (/ y (/ x (/ z (sqrt t)))))))))>
#<alt (/ 1 (+ (/ (PI) 2) (asin (/ 1/18 (/ y (/ x (/ z (sqrt t))))))))>
#<alt (+ (/ (PI) 2) (asin (/ 1/18 (/ y (/ x (/ z (sqrt t)))))))>
#<alt (/ y (/ x (/ z (sqrt t))))>
#<alt (/ x (/ z (sqrt t)))>
#<alt (/ 1/18 (/ y (/ x (/ z (sqrt t)))))>
#<alt (/ z (sqrt t))>
Outputs
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z)))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
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#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))) (* 1/2 (PI))))>
#<alt (/ 1 (+ (asin (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))) (* 1/2 (PI))))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ x (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))) (* 1/2 (PI)))>
#<alt (+ (asin (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))) (* 1/2 (PI)))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* y z) x))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* -1 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))>
#<alt (* -1 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))>
#<alt (* -1 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))>
#<alt (* -1 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* -1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))>
#<alt (* -1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))>
#<alt (* -1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))>
#<alt (* -1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
#<alt (* (sqrt (/ 1 t)) z)>
Calls

135 calls:

TimeVariablePointExpression
10.0ms
t
@inf
(* 1/3 (/ 1 (+ (/ (PI) 2) (asin (/ 1/18 (/ y (/ x (/ z (sqrt t)))))))))
1.0ms
t
@-inf
(/ y (/ x (/ z (sqrt t))))
1.0ms
t
@-inf
(/ z (sqrt t))
1.0ms
t
@-inf
(* 1/3 (/ 1 (+ (/ (PI) 2) (asin (/ 1/18 (/ y (/ x (/ z (sqrt t)))))))))
1.0ms
y
@0
(/ y (/ x (/ z (sqrt t))))

rewrite729.0ms (4%)

Algorithm
1×batch-egg-rewrite
Rules
3698×/-lowering-/.f32
3698×/-lowering-/.f64
3580×*-lowering-*.f32
3580×*-lowering-*.f64
1370×+-lowering-+.f64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
030144
1172133
21244133
08264133
Stop Event
1×iter limit
1×node limit
Counts
12 → 718
Calls
Call 1
Inputs
(* 1/3 (pow (pow (acos (/ 1/18 (/ y (/ x (/ z (sqrt t)))))) 1/2) 2))
(pow (pow (acos (/ 1/18 (/ y (/ x (/ z (sqrt t)))))) 1/2) 2)
(pow (acos (/ 1/18 (/ y (/ x (/ z (sqrt t)))))) 1/2)
(acos (/ 1/18 (/ y (/ x (/ z (sqrt t))))))
(* (* 1/3 (/ 1 (+ (/ (PI) 2) (asin (/ 1/18 (/ y (/ x (/ z (sqrt t))))))))) (- (/ (* (PI) (PI)) 4) (pow (asin (/ 1/18 (/ y (/ x (/ z (sqrt t)))))) 2)))
(* 1/3 (/ 1 (+ (/ (PI) 2) (asin (/ 1/18 (/ y (/ x (/ z (sqrt t)))))))))
(/ 1 (+ (/ (PI) 2) (asin (/ 1/18 (/ y (/ x (/ z (sqrt t))))))))
(+ (/ (PI) 2) (asin (/ 1/18 (/ y (/ x (/ z (sqrt t)))))))
(/ y (/ x (/ z (sqrt t))))
(/ x (/ z (sqrt t)))
(/ 1/18 (/ y (/ x (/ z (sqrt t)))))
(/ z (sqrt t))
Outputs
(+.f64 (/.f64 (/.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 z (pow.f64 t #s(literal -1/2 binary64))) x)) y)))) (/.f64 (/.f64 #s(literal 4 binary64) (PI.f64)) (PI.f64))) (*.f64 (/.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 z (pow.f64 t #s(literal -1/2 binary64))) x)) y)))) (-.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 z (pow.f64 t #s(literal -1/2 binary64))) x)) y)) #s(literal 2 binary64)))))
(+.f64 (/.f64 (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (/.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 z (pow.f64 t #s(literal -1/2 binary64))) x)) y))) #s(literal 1/3 binary64))) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 z (pow.f64 t #s(literal -1/2 binary64))) x)) y)) #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 z (pow.f64 t #s(literal -1/2 binary64))) x)) y))) #s(literal 1/3 binary64))))
(fma.f64 (/.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 z (pow.f64 t #s(literal -1/2 binary64))) x)) y)))) (/.f64 (PI.f64) (/.f64 #s(literal 4 binary64) (PI.f64))) (*.f64 (/.f64 #s(literal 1/3 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 z (pow.f64 t #s(literal -1/2 binary64))) x)) y)))) (-.f64 #s(literal 0 binary64) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 z (pow.f64 t #s(literal -1/2 binary64))) x)) y)) #s(literal 2 binary64)))))
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simplify481.0ms (2.7%)

Algorithm
1×egg-herbie
Rules
3642×*-lowering-*.f32
3642×*-lowering-*.f64
1592×fma-define
1584×/-lowering-/.f32
1584×/-lowering-/.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0607716
11347284
23517248
311207248
424057248
552297248
084697248
Stop Event
1×iter limit
1×node limit
Counts
540 → 540
Calls
Call 1
Inputs
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
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(*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) t)))
(* (sqrt (/ 1 t)) z)
(*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) t)))
(* (sqrt (/ 1 t)) z)
(*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) t)))
(* (sqrt (/ 1 t)) z)
(*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) t)))
(* (sqrt (/ 1 t)) z)
(*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) t)))
(* (sqrt (/ 1 t)) z)
(*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) t)))
(* (sqrt (/ 1 t)) z)
(*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) t)))
(* (sqrt (/ 1 t)) z)
(*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) t)))
(* (sqrt (/ 1 t)) z)
(*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) t)))
(* (sqrt (/ 1 t)) z)
(*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) t)))
(* (sqrt (/ 1 t)) z)
(*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) t)))
(* (sqrt (/ 1 t)) z)
(*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) t)))
(* (sqrt (/ 1 t)) z)
(*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) t)))
(* (sqrt (/ 1 t)) z)
(*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) t)))
(* (sqrt (/ 1 t)) z)
(*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) t)))
(* (sqrt (/ 1 t)) z)
(*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) t)))
(* (sqrt (/ 1 t)) z)
(*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) t)))
(* (sqrt (/ 1 t)) z)
(*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) t)))
(* (sqrt (/ 1 t)) z)
(*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) t)))
(* (sqrt (/ 1 t)) z)
(*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) t)))
(* (sqrt (/ 1 t)) z)
(*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) t)))
(* (sqrt (/ 1 t)) z)
(*.f64 z (sqrt.f64 (/.f64 #s(literal 1 binary64) t)))

eval320.0ms (1.8%)

Compiler

Compiled 82682 to 5086 computations (93.8% saved)

prune188.0ms (1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New202222024
Fresh000
Picked202
Done033
Total202452029
Accuracy
100.0%
Counts
2029 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.3%
(*.f64 #s(literal 1/3 binary64) (pow.f64 (pow.f64 (acos.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 z (pow.f64 t #s(literal -1/2 binary64))) x)) y)) #s(literal 1/4 binary64)) #s(literal 4 binary64)))
▶97.2%
(*.f64 #s(literal 1/3 binary64) (pow.f64 (sqrt.f64 (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 (sqrt.f64 t) x) z) y)))) #s(literal 2 binary64)))
✓97.9%
(*.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 2 binary64))))))
✓98.1%
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 (sqrt.f64 t) (*.f64 (/.f64 x z) (/.f64 #s(literal 1/18 binary64) y)))))
✓98.1%
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y))))
Compiler

Compiled 119 to 85 computations (28.6% saved)

simplify26.0ms (0.1%)

Algorithm
1×egg-herbie
Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(acos.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 z (pow.f64 t #s(literal -1/2 binary64))) x)) y))
✓cost-diff0
(pow.f64 (acos.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 z (pow.f64 t #s(literal -1/2 binary64))) x)) y)) #s(literal 1/4 binary64))
✓cost-diff0
(pow.f64 (pow.f64 (acos.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 z (pow.f64 t #s(literal -1/2 binary64))) x)) y)) #s(literal 1/4 binary64)) #s(literal 4 binary64))
✓cost-diff0
(*.f64 #s(literal 1/3 binary64) (pow.f64 (pow.f64 (acos.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 z (pow.f64 t #s(literal -1/2 binary64))) x)) y)) #s(literal 1/4 binary64)) #s(literal 4 binary64)))
✓cost-diff0
(acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 (sqrt.f64 t) x) z) y)))
✓cost-diff0
(sqrt.f64 (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 (sqrt.f64 t) x) z) y))))
✓cost-diff12864
(pow.f64 (sqrt.f64 (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 (sqrt.f64 t) x) z) y)))) #s(literal 2 binary64))
✓cost-diff12864
(*.f64 #s(literal 1/3 binary64) (pow.f64 (sqrt.f64 (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 (sqrt.f64 t) x) z) y)))) #s(literal 2 binary64)))
Rules
378×*-lowering-*.f32
378×*-lowering-*.f64
226×/-lowering-/.f32
226×/-lowering-/.f64
120×associate-/r*
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
028197
146188
295188
3215188
4395188
5456188
6471188
7489188
8499188
0499188
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(* 1/3 (pow (sqrt (acos (* 1/18 (/ (/ (* (sqrt t) x) z) y)))) 2))
1/3
(pow (sqrt (acos (* 1/18 (/ (/ (* (sqrt t) x) z) y)))) 2)
(sqrt (acos (* 1/18 (/ (/ (* (sqrt t) x) z) y))))
(acos (* 1/18 (/ (/ (* (sqrt t) x) z) y)))
(* 1/18 (/ (/ (* (sqrt t) x) z) y))
1/18
(/ (/ (* (sqrt t) x) z) y)
(/ (* (sqrt t) x) z)
(* (sqrt t) x)
(sqrt t)
t
x
z
y
2
(* 1/3 (pow (pow (acos (/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y)) 1/4) 4))
1/3
(pow (pow (acos (/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y)) 1/4) 4)
(pow (acos (/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y)) 1/4)
(acos (/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y))
(/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y)
(/ 1/18 (/ (* z (pow t -1/2)) x))
1/18
(/ (* z (pow t -1/2)) x)
(* z (pow t -1/2))
z
(pow t -1/2)
t
-1/2
x
y
1/4
4
Outputs
(* 1/3 (pow (sqrt (acos (* 1/18 (/ (/ (* (sqrt t) x) z) y)))) 2))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (*.f64 (sqrt.f64 t) x)) z) y)))
1/3
#s(literal 1/3 binary64)
(pow (sqrt (acos (* 1/18 (/ (/ (* (sqrt t) x) z) y)))) 2)
(acos.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (*.f64 (sqrt.f64 t) x)) z) y))
(sqrt (acos (* 1/18 (/ (/ (* (sqrt t) x) z) y))))
(sqrt.f64 (acos.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (*.f64 (sqrt.f64 t) x)) z) y)))
(acos (* 1/18 (/ (/ (* (sqrt t) x) z) y)))
(acos.f64 (/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (*.f64 (sqrt.f64 t) x)) z) y))
(* 1/18 (/ (/ (* (sqrt t) x) z) y))
(/.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (*.f64 (sqrt.f64 t) x)) z) y)
1/18
#s(literal 1/18 binary64)
(/ (/ (* (sqrt t) x) z) y)
(/.f64 (sqrt.f64 t) (*.f64 z (/.f64 y x)))
(/ (* (sqrt t) x) z)
(/.f64 (*.f64 (sqrt.f64 t) x) z)
(* (sqrt t) x)
(*.f64 (sqrt.f64 t) x)
(sqrt t)
(sqrt.f64 t)
t
x
z
y
2
#s(literal 2 binary64)
(* 1/3 (pow (pow (acos (/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y)) 1/4) 4))
(*.f64 #s(literal 1/3 binary64) (pow.f64 (pow.f64 (acos.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) z) (pow.f64 t #s(literal -1/2 binary64))) (/.f64 y x))) #s(literal 1/4 binary64)) #s(literal 4 binary64)))
1/3
#s(literal 1/3 binary64)
(pow (pow (acos (/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y)) 1/4) 4)
(pow.f64 (pow.f64 (acos.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) z) (pow.f64 t #s(literal -1/2 binary64))) (/.f64 y x))) #s(literal 1/4 binary64)) #s(literal 4 binary64))
(pow (acos (/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y)) 1/4)
(pow.f64 (acos.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) z) (pow.f64 t #s(literal -1/2 binary64))) (/.f64 y x))) #s(literal 1/4 binary64))
(acos (/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y))
(acos.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) z) (pow.f64 t #s(literal -1/2 binary64))) (/.f64 y x)))
(/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y)
(/.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) z) (pow.f64 t #s(literal -1/2 binary64))) (/.f64 y x))
(/ 1/18 (/ (* z (pow t -1/2)) x))
(/.f64 (*.f64 #s(literal 1/18 binary64) x) (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))
1/18
#s(literal 1/18 binary64)
(/ (* z (pow t -1/2)) x)
(*.f64 z (/.f64 (pow.f64 t #s(literal -1/2 binary64)) x))
(* z (pow t -1/2))
(*.f64 z (pow.f64 t #s(literal -1/2 binary64)))
z
(pow t -1/2)
(pow.f64 t #s(literal -1/2 binary64))
t
-1/2
#s(literal -1/2 binary64)
x
y
1/4
#s(literal 1/4 binary64)
4
#s(literal 4 binary64)

localize167.0ms (0.9%)

Localize:

Found 8 expressions of interest:

NewMetricScoreProgram
✓accuracy98.5%
(*.f64 #s(literal 1/3 binary64) (pow.f64 (pow.f64 (acos.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 z (pow.f64 t #s(literal -1/2 binary64))) x)) y)) #s(literal 1/4 binary64)) #s(literal 4 binary64)))
✓accuracy97.5%
(pow.f64 (pow.f64 (acos.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 z (pow.f64 t #s(literal -1/2 binary64))) x)) y)) #s(literal 1/4 binary64)) #s(literal 4 binary64))
✓accuracy95.3%
(/.f64 (*.f64 z (pow.f64 t #s(literal -1/2 binary64))) x)
✓accuracy92.2%
(/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 z (pow.f64 t #s(literal -1/2 binary64))) x)) y)
✓accuracy98.5%
(sqrt.f64 (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 (sqrt.f64 t) x) z) y))))
✓accuracy98.4%
(pow.f64 (sqrt.f64 (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 (sqrt.f64 t) x) z) y)))) #s(literal 2 binary64))
✓accuracy96.4%
(/.f64 (*.f64 (sqrt.f64 t) x) z)
✓accuracy92.2%
(/.f64 (/.f64 (*.f64 (sqrt.f64 t) x) z) y)
Results
122.0ms256×0valid
Compiler

Compiled 199 to 29 computations (85.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 62.0ms
ival-pow: 24.0ms (38.6% of total)
ival-div: 11.0ms (17.7% of total)
ival-mult: 9.0ms (14.5% of total)
...c/correct-round.rkt:119:19: 7.0ms (11.2% of total)
ival-acos: 5.0ms (8% of total)
ival-sqrt: 4.0ms (6.4% of total)
const: 1.0ms (1.6% of total)
backward-pass: 0.0ms (0% of total)

series387.0ms (2.1%)

Counts
12 → 552
Calls
Call 1
Inputs
#<alt (* 1/3 (pow (sqrt (acos (* 1/18 (/ (/ (* (sqrt t) x) z) y)))) 2))>
#<alt (pow (sqrt (acos (* 1/18 (/ (/ (* (sqrt t) x) z) y)))) 2)>
#<alt (sqrt (acos (* 1/18 (/ (/ (* (sqrt t) x) z) y))))>
#<alt (acos (* 1/18 (/ (/ (* (sqrt t) x) z) y)))>
#<alt (* 1/3 (pow (pow (acos (/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y)) 1/4) 4))>
#<alt (pow (pow (acos (/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y)) 1/4) 4)>
#<alt (pow (acos (/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y)) 1/4)>
#<alt (acos (/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y))>
#<alt (/ (/ (* (sqrt t) x) z) y)>
#<alt (/ (* (sqrt t) x) z)>
#<alt (/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y)>
#<alt (/ (* z (pow t -1/2)) x)>
Outputs
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (acos (* 1/18 (* (sqrt t) (/ x (* y z)))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))>
#<alt (sqrt (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))>
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#<alt (* (sqrt t) (/ x (* y z)))>
#<alt (* (sqrt t) (/ x (* y z)))>
#<alt (* (sqrt t) (/ x (* y z)))>
#<alt (* (sqrt t) (/ x (* y z)))>
#<alt (* (sqrt t) (/ x (* y z)))>
#<alt (* (sqrt t) (/ x (* y z)))>
#<alt (* (sqrt t) (/ x (* y z)))>
#<alt (* (sqrt t) (/ x (* y z)))>
#<alt (* (sqrt t) (/ x (* y z)))>
#<alt (* (sqrt t) (/ x (* y z)))>
#<alt (* (sqrt t) (/ x (* y z)))>
#<alt (* (sqrt t) (/ x (* y z)))>
#<alt (* (sqrt t) (/ x (* y z)))>
#<alt (* (sqrt t) (/ x (* y z)))>
#<alt (* (sqrt t) (/ x (* y z)))>
#<alt (* (sqrt t) (/ x (* y z)))>
#<alt (* (sqrt t) (/ x (* y z)))>
#<alt (* (sqrt t) (/ x (* y z)))>
#<alt (* (sqrt t) (/ x (* y z)))>
#<alt (* (sqrt t) (/ x (* y z)))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* -1 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))>
#<alt (* -1 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))>
#<alt (* -1 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))>
#<alt (* -1 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* (sqrt t) (/ x z))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* -1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* -1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* -1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* -1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* 1/18 (* (sqrt t) (/ x (* y z))))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ (* z (pow (sqrt -1) 2)) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* z (pow (sqrt -1) 2)) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* z (pow (sqrt -1) 2)) x))>
#<alt (* (sqrt (/ 1 t)) (/ (* z (pow (sqrt -1) 2)) x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
#<alt (* (sqrt (/ 1 t)) (/ z x))>
Calls

138 calls:

TimeVariablePointExpression
88.0ms
x
@-inf
(pow (acos (/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y)) 1/4)
84.0ms
z
@0
(pow (acos (/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y)) 1/4)
52.0ms
z
@inf
(pow (acos (/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y)) 1/4)
25.0ms
t
@-inf
(pow (acos (/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y)) 1/4)
20.0ms
y
@-inf
(pow (acos (/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y)) 1/4)

rewrite276.0ms (1.5%)

Algorithm
1×batch-egg-rewrite
Rules
2962×*-lowering-*.f32
2962×*-lowering-*.f64
1984×/-lowering-/.f32
1984×/-lowering-/.f64
1072×pow-lowering-pow.f64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
028140
1119128
2646128
34502125
08557125
Stop Event
1×iter limit
1×node limit
Counts
12 → 857
Calls
Call 1
Inputs
(* 1/3 (pow (sqrt (acos (* 1/18 (/ (/ (* (sqrt t) x) z) y)))) 2))
(pow (sqrt (acos (* 1/18 (/ (/ (* (sqrt t) x) z) y)))) 2)
(sqrt (acos (* 1/18 (/ (/ (* (sqrt t) x) z) y))))
(acos (* 1/18 (/ (/ (* (sqrt t) x) z) y)))
(* 1/3 (pow (pow (acos (/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y)) 1/4) 4))
(pow (pow (acos (/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y)) 1/4) 4)
(pow (acos (/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y)) 1/4)
(acos (/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y))
(/ (/ (* (sqrt t) x) z) y)
(/ (* (sqrt t) x) z)
(/ (/ 1/18 (/ (* z (pow t -1/2)) x)) y)
(/ (* z (pow t -1/2)) x)
Outputs
(+.f64 (*.f64 #s(literal 1/3 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 #s(literal 1/3 binary64) (asin.f64 (/.f64 (*.f64 x (/.f64 #s(literal -1/18 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))) y))))
(+.f64 (*.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (*.f64 (asin.f64 (/.f64 (*.f64 x (/.f64 #s(literal -1/18 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))) y)) #s(literal 1/3 binary64)))
(fma.f64 #s(literal 1/3 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)) (*.f64 #s(literal 1/3 binary64) (asin.f64 (/.f64 (*.f64 x (/.f64 #s(literal -1/18 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))) y))))
(fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1/3 binary64) (*.f64 (asin.f64 (/.f64 (*.f64 x (/.f64 #s(literal -1/18 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))) y)) #s(literal 1/3 binary64)))
(/.f64 (*.f64 #s(literal 1/3 binary64) (-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))) #s(literal 3 binary64)))) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))) (acos.f64 (/.f64 (*.f64 x (/.f64 #s(literal -1/18 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))) y)))))
(/.f64 (*.f64 #s(literal 1/3 binary64) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))) #s(literal 2 binary64)))) (acos.f64 (/.f64 (*.f64 x (/.f64 #s(literal -1/18 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))) y)))
(/.f64 (*.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))) #s(literal 3 binary64))) #s(literal 1/3 binary64)) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))) (acos.f64 (/.f64 (*.f64 x (/.f64 #s(literal -1/18 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))) y)))))
(/.f64 (*.f64 (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (acos.f64 (/.f64 (*.f64 x (/.f64 #s(literal -1/18 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))) y)))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))))
(*.f64 (sqrt.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64)))))))) (*.f64 #s(literal 1/3 binary64) (sqrt.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))))))
(*.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))) #s(literal 1/3 binary64))
(*.f64 (pow.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/3 binary64) (sqrt.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64)))))))))))
(*.f64 (*.f64 #s(literal 1/3 binary64) (sqrt.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))))) (sqrt.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64)))))))))
(*.f64 (*.f64 (*.f64 #s(literal 1/3 binary64) (sqrt.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))))) (pow.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))) #s(literal 1/4 binary64))) (pow.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))) #s(literal 1/4 binary64)))
(acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64)))))))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (*.f64 x (/.f64 #s(literal -1/18 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))) y)))
(+.f64 (asin.f64 (/.f64 (*.f64 x (/.f64 #s(literal -1/18 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))) y)) (/.f64 (PI.f64) #s(literal 2 binary64)))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))) (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))))
(exp.f64 (log.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64)))))))))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (*.f64 (log.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64)))))))) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (*.f64 (log.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64)))))))) #s(literal 1/8 binary64)) #s(literal 8 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 4 binary64))) (*.f64 #s(literal 1/4 binary64) (log.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64)))))))))))
(exp.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))))) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (log.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))))) #s(literal 1 binary64)) #s(literal 4 binary64)))
(exp.f64 (*.f64 (*.f64 (*.f64 (log.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64)))))))) #s(literal 1/8 binary64)) #s(literal 2 binary64)) #s(literal 4 binary64)))
(exp.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))))) #s(literal 1/8 binary64)) #s(literal 4 binary64)))
(exp.f64 (*.f64 (*.f64 (*.f64 (log.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64)))))))) #s(literal 1/8 binary64)) #s(literal 4 binary64)) #s(literal 2 binary64)))
(fabs.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))))
(-.f64 (PI.f64) (acos.f64 (/.f64 (*.f64 x (/.f64 #s(literal -1/18 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))) y)))
(-.f64 (PI.f64) (acos.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) y) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64)))) x))))
(-.f64 (PI.f64) (acos.f64 (/.f64 (/.f64 #s(literal -1/18 binary64) y) (/.f64 z (/.f64 x (pow.f64 t #s(literal -1/2 binary64)))))))
(-.f64 (PI.f64) (acos.f64 (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))) (/.f64 #s(literal 1/18 binary64) y))))
(-.f64 (PI.f64) (acos.f64 (*.f64 (neg.f64 (/.f64 x (*.f64 y (*.f64 z (pow.f64 t #s(literal -1/2 binary64)))))) #s(literal 1/18 binary64))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))))
(-.f64 (/.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (acos.f64 (/.f64 (*.f64 x (/.f64 #s(literal -1/18 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))) y))) (/.f64 (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))) #s(literal 2 binary64)) (acos.f64 (/.f64 (*.f64 x (/.f64 #s(literal -1/18 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))) y))))
(-.f64 (/.f64 (/.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (PI.f64))) #s(literal 8 binary64)) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))) (acos.f64 (/.f64 (*.f64 x (/.f64 #s(literal -1/18 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))) y))))) (/.f64 (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))) #s(literal 3 binary64)) (+.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (*.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))) (acos.f64 (/.f64 (*.f64 x (/.f64 #s(literal -1/18 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))) y))))))
(sqrt.f64 (pow.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))) #s(literal 2 binary64)))
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(exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 z (/.f64 x (pow.f64 t #s(literal -1/2 binary64))))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64)))) x))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64)))) x))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (/.f64 x (pow.f64 t #s(literal -1/2 binary64))))) (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64)))) x))
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(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64)))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))) (-.f64 #s(literal 0 binary64) x))
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(pow.f64 (pow.f64 (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64)))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 z (/.f64 x (pow.f64 t #s(literal -1/2 binary64)))) #s(literal -2 binary64)) #s(literal -1/2 binary64))
(*.f64 z (/.f64 (pow.f64 t #s(literal -1/2 binary64)) x))
(*.f64 z (/.f64 (/.f64 (pow.f64 t #s(literal -1/2 binary64)) x) #s(literal 1 binary64)))
(*.f64 (pow.f64 t #s(literal -1/2 binary64)) (/.f64 z x))
(*.f64 (pow.f64 t #s(literal -1/2 binary64)) (/.f64 (/.f64 z x) #s(literal 1 binary64)))
(*.f64 (pow.f64 t #s(literal -1/2 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) z) (/.f64 #s(literal -1 binary64) x)))
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(*.f64 (/.f64 z (/.f64 x (pow.f64 t #s(literal -1/2 binary64)))) #s(literal 1 binary64))
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(*.f64 (pow.f64 t #s(literal -1/4 binary64)) (*.f64 (pow.f64 t #s(literal -1/4 binary64)) (/.f64 z x)))
(*.f64 (pow.f64 t #s(literal -1/4 binary64)) (*.f64 (*.f64 z (pow.f64 t #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) x)))
(*.f64 (pow.f64 t #s(literal -1/4 binary64)) (*.f64 (/.f64 (pow.f64 t #s(literal -1/4 binary64)) x) z))
(*.f64 (/.f64 (pow.f64 t #s(literal -1/2 binary64)) x) z)
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(*.f64 (pow.f64 (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64)))) #s(literal -1/2 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (pow.f64 t #s(literal -1/2 binary64))) (/.f64 z x))
(*.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))) (/.f64 #s(literal -1 binary64) x))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 t #s(literal -1/4 binary64))) (*.f64 z (pow.f64 t #s(literal -1/4 binary64))))
(*.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 z (pow.f64 t #s(literal -1/4 binary64)))) (pow.f64 t #s(literal -1/4 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))) (/.f64 #s(literal -1 binary64) x))

simplify380.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
3720×*-lowering-*.f32
3720×*-lowering-*.f64
3096×--lowering--.f32
3096×--lowering--.f64
1874×unsub-neg
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0445992
1975916
22885896
39705896
427165896
555035896
081245896
Stop Event
1×iter limit
1×node limit
Counts
552 → 552
Calls
Call 1
Inputs
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
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(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x (* y z)))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* -1 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))
(* -1 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))
(* -1 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))
(* -1 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) z)))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* (sqrt t) (/ x z))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* -1/18 (* (sqrt t) (/ x (* y z))))
(* -1/18 (* (sqrt t) (/ x (* y z))))
(* -1/18 (* (sqrt t) (/ x (* y z))))
(* -1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* 1/18 (* (sqrt t) (/ x (* y z))))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ (* z (pow (sqrt -1) 2)) x))
(* (sqrt (/ 1 t)) (/ (* z (pow (sqrt -1) 2)) x))
(* (sqrt (/ 1 t)) (/ (* z (pow (sqrt -1) 2)) x))
(* (sqrt (/ 1 t)) (/ (* z (pow (sqrt -1) 2)) x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
(* (sqrt (/ 1 t)) (/ z x))
Outputs
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal -1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal -1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal -1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal -1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(* 1/3 (acos (* 1/18 (* (sqrt t) (/ x (* y z))))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z)))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal -1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal -1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal -1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ (* x (pow (sqrt -1) 2)) (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal -1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
(acos (* 1/18 (* (sqrt t) (/ x (* y z)))))
(acos.f64 (/.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 (sqrt.f64 t) x) y)) z))
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(* (sqrt (/ 1 t)) (/ (* z (pow (sqrt -1) 2)) x))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) t)) (/.f64 z (-.f64 #s(literal 0 binary64) x)))
(* (sqrt (/ 1 t)) (/ (* z (pow (sqrt -1) 2)) x))
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(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) t)) (/.f64 z x))
(* (sqrt (/ 1 t)) (/ z x))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) t)) (/.f64 z x))
(* (sqrt (/ 1 t)) (/ z x))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) t)) (/.f64 z x))
(* (sqrt (/ 1 t)) (/ z x))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) t)) (/.f64 z x))
(* (sqrt (/ 1 t)) (/ z x))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) t)) (/.f64 z x))
(* (sqrt (/ 1 t)) (/ z x))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) t)) (/.f64 z x))

eval256.0ms (1.4%)

Compiler

Compiled 29020 to 4046 computations (86.1% saved)

prune4.2s (23.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New140721409
Fresh000
Picked112
Done123
Total140951414
Accuracy
100.0%
Counts
1414 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.3%
(*.f64 #s(literal 1/3 binary64) (pow.f64 (pow.f64 (pow.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))) #s(literal 1/8 binary64)) #s(literal 4 binary64)) #s(literal 2 binary64)))
99.9%
(*.f64 #s(literal 1/3 binary64) (pow.f64 (pow.f64 (acos.f64 (*.f64 (*.f64 #s(literal 1/18 binary64) x) (/.f64 (sqrt.f64 t) (*.f64 z y)))) #s(literal 1/4 binary64)) #s(literal 4 binary64)))
✓97.2%
(*.f64 #s(literal 1/3 binary64) (pow.f64 (sqrt.f64 (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 (sqrt.f64 t) x) z) y)))) #s(literal 2 binary64)))
✓98.1%
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 (sqrt.f64 t) (*.f64 (/.f64 x z) (/.f64 #s(literal 1/18 binary64) y)))))
✓98.1%
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y))))
Compiler

Compiled 314 to 178 computations (43.3% saved)

regimes49.0ms (0.3%)

Counts
10 → 1
Calls
Call 1
Inputs
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 (sqrt.f64 t) (*.f64 (/.f64 x z) (/.f64 #s(literal 1/18 binary64) y)))))
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) (acos.f64 (*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))))
(*.f64 #s(literal 1/3 binary64) (pow.f64 (sqrt.f64 (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 (sqrt.f64 t) x) z) y)))) #s(literal 2 binary64)))
(*.f64 #s(literal 1/3 binary64) (pow.f64 (pow.f64 (acos.f64 (*.f64 (*.f64 #s(literal 1/18 binary64) x) (/.f64 (sqrt.f64 t) (*.f64 z y)))) #s(literal 1/4 binary64)) #s(literal 4 binary64)))
(*.f64 #s(literal 1/3 binary64) (pow.f64 (pow.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(*.f64 #s(literal 1/3 binary64) (pow.f64 (pow.f64 (acos.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (*.f64 z (pow.f64 t #s(literal -1/2 binary64))) x)) y)) #s(literal 1/4 binary64)) #s(literal 4 binary64)))
(*.f64 #s(literal 1/3 binary64) (pow.f64 (pow.f64 (pow.f64 (acos.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (*.f64 z (pow.f64 t #s(literal -1/2 binary64))))))) #s(literal 1/8 binary64)) #s(literal 4 binary64)) #s(literal 2 binary64)))
(*.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y))) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 z (sqrt.f64 t)) x)) y)) #s(literal 2 binary64))))))
(*.f64 (*.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t))))))))) (-.f64 (/.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 4 binary64)) (pow.f64 (asin.f64 (/.f64 #s(literal 1/18 binary64) (/.f64 y (/.f64 x (/.f64 z (sqrt.f64 t)))))) #s(literal 2 binary64))))
Outputs
(*.f64 #s(literal 1/3 binary64) (pow.f64 (pow.f64 (acos.f64 (*.f64 (*.f64 #s(literal 1/18 binary64) x) (/.f64 (sqrt.f64 t) (*.f64 z y)))) #s(literal 1/4 binary64)) #s(literal 4 binary64)))
Calls

13 calls:

5.0ms
y
4.0ms
(sqrt.f64 t)
4.0ms
(acos.f64 (*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t)))
4.0ms
(/.f64 x (*.f64 y #s(literal 27 binary64)))
4.0ms
(*.f64 y #s(literal 27 binary64))
Results
AccuracySegmentsBranch
99.9%1x
99.9%1y
99.9%1z
99.9%1t
99.9%1(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) (acos.f64 (*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))))
99.9%1(acos.f64 (*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t)))
99.9%1(*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))
99.9%1(/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64)))
99.9%1(*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64))))
99.9%1(/.f64 x (*.f64 y #s(literal 27 binary64)))
99.9%1(*.f64 y #s(literal 27 binary64))
99.9%1(*.f64 z #s(literal 2 binary64))
99.9%1(sqrt.f64 t)
Compiler

Compiled 135 to 108 computations (20% saved)

regimes29.0ms (0.2%)

Accuracy

Total -1.2b remaining (-94.8%)

Threshold costs -1.2b (-94.8%)

Counts
4 → 1
Calls
Call 1
Inputs
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y))))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 (sqrt.f64 t) (*.f64 (/.f64 x z) (/.f64 #s(literal 1/18 binary64) y)))))
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) (acos.f64 (*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))))
(*.f64 #s(literal 1/3 binary64) (pow.f64 (sqrt.f64 (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 (sqrt.f64 t) x) z) y)))) #s(literal 2 binary64)))
Outputs
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y))))
Calls

13 calls:

4.0ms
(*.f64 y #s(literal 27 binary64))
4.0ms
t
2.0ms
(*.f64 z #s(literal 2 binary64))
2.0ms
(sqrt.f64 t)
2.0ms
z
Results
AccuracySegmentsBranch
98.1%1x
98.1%1y
98.1%1z
98.1%1t
98.1%1(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 3 binary64)) (acos.f64 (*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))))
98.1%1(acos.f64 (*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t)))
98.1%1(*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))
98.1%1(/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64)))
98.1%1(*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64))))
98.1%1(/.f64 x (*.f64 y #s(literal 27 binary64)))
98.1%1(*.f64 y #s(literal 27 binary64))
98.1%1(*.f64 z #s(literal 2 binary64))
98.1%1(sqrt.f64 t)
Compiler

Compiled 135 to 108 computations (20% saved)

simplify8.0ms (0%)

Algorithm
1×egg-herbie
Rules
14×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02330
13030
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 #s(literal 1/3 binary64) (pow.f64 (pow.f64 (acos.f64 (*.f64 (*.f64 #s(literal 1/18 binary64) x) (/.f64 (sqrt.f64 t) (*.f64 z y)))) #s(literal 1/4 binary64)) #s(literal 4 binary64)))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y))))
Outputs
(*.f64 #s(literal 1/3 binary64) (pow.f64 (pow.f64 (acos.f64 (*.f64 (*.f64 #s(literal 1/18 binary64) x) (/.f64 (sqrt.f64 t) (*.f64 z y)))) #s(literal 1/4 binary64)) #s(literal 4 binary64)))
(*.f64 #s(literal 1/3 binary64) (acos.f64 (*.f64 #s(literal 1/18 binary64) (/.f64 (/.f64 (*.f64 x (sqrt.f64 t)) z) y))))

soundness1.6s (9.1%)

Rules
5482×*-lowering-*.f32
5482×*-lowering-*.f64
4286×/-lowering-/.f32
4286×/-lowering-/.f64
4186×*-lowering-*.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01917
13915
211713
339213
4138613
5314813
6324013
7329013
8329013
9329013
10391313
11395213
12395213
0395213
031143
1188120
21457120
08540120
028140
1119128
2646128
34502125
08557125
030144
1172133
21244133
08264133
026112
191102
259094
3534794
0896194
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×saturated
Compiler

Compiled 84 to 65 computations (22.6% saved)

preprocess39.0ms (0.2%)

Remove

(sort y z)

Compiler

Compiled 240 to 182 computations (24.2% saved)

end0.0ms (0%)

Profiling

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