Falkner and Boettcher, Appendix B, 1

Time bar (total: 9.7s)

analyze737.0ms (7.6%)

Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
0%0%100%0%0%0%0%3
0%0%100%0%0%0%0%4
0%0%100%0%0%0%0%5
0%0%100%0%0%0%0%6
0%0%100%0%0%0%0%7
0%0%100%0%0%0%0%8
0%0%100%0%0%0%0%9
0%0%100%0%0%0%0%10
0%0%100%0%0%0%0%11
0%0%100%0%0%0%0%12
Compiler

Compiled 16 to 10 computations (37.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 448.0ms
ival-sub: 289.0ms (64.5% of total)
ival-mult: 70.0ms (15.6% of total)
ival-acos: 50.0ms (11.2% of total)
ival-div: 31.0ms (6.9% of total)
const: 6.0ms (1.3% of total)
backward-pass: 2.0ms (0.4% of total)

sample5.5s (56.7%)

Results
2.2s3727×3valid
1.1s8406×0invalid
745.0ms2169×1valid
741.0ms2128×2valid
20.0ms232×0valid
Precisions
Click to see histograms. Total time spent on operations: 3.1s
ival-mult: 1.1s (34.8% of total)
ival-acos: 812.0ms (25.9% of total)
ival-div: 406.0ms (13% of total)
ival-sub: 396.0ms (12.6% of total)
backward-pass: 376.0ms (12% of total)
const: 53.0ms (1.7% of total)
Bogosity

preprocess164.0ms (1.7%)

Algorithm
egg-herbie
Rules
2668×fnmadd-define
2218×fma-define
1908×fma-define
1656×fnmadd-define
1110×sum3-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01737
15837
213034
330134
469934
5145134
6430734
7598834
8634034
9634034
0912
12912
25711
311911
424411
540011
669011
7118211
8206311
9446511
10565311
11567311
12567311
0567311
Stop Event
iter limit
saturated
saturated
Calls
Call 1
Inputs
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
Outputs
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v #s(literal -5 binary64)))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
Call 2
Inputs
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
(acos (/ (- 1 (* 5 (* (neg v) (neg v)))) (- (* (neg v) (neg v)) 1)))
(neg (acos (/ (- 1 (* 5 (* (neg v) (neg v)))) (- (* (neg v) (neg v)) 1))))
Outputs
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
(acos (/ (fnmsub 5 (square v) -1) (+ (square v) -1)))
(acos (/ (- 1 (* 5 (* (neg v) (neg v)))) (- (* (neg v) (neg v)) 1)))
(acos (/ (fnmsub 5 (square v) -1) (+ (square v) -1)))
(neg (acos (/ (- 1 (* 5 (* (neg v) (neg v)))) (- (* (neg v) (neg v)) 1))))
(neg (acos (/ (fnmsub 5 (square v) -1) (+ (square v) -1))))
Symmetry

(abs v)

explain345.0ms (3.6%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
6249(1.0750526720992017e-279)0-(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
00-0-(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v)))
00-0-(-.f64 (*.f64 v v) #s(literal 1 binary64))
00-0-v
00-0-(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64)))
00-0-(*.f64 v v)
00-0-#s(literal 5 binary64)
00-0-#s(literal 1 binary64)
01(1.4493921699903596e-162)0-(*.f64 #s(literal 5 binary64) (*.f64 v v))
Results
143.0ms222×3valid
90.0ms134×2valid
42.0ms148×1valid
1.0ms0valid
Compiler

Compiled 119 to 29 computations (75.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 116.0ms
backward-pass: 29.0ms (25% of total)
ival-acos: 29.0ms (25% of total)
ival-mult: 23.0ms (19.8% of total)
ival-sub: 17.0ms (14.6% of total)
ival-div: 16.0ms (13.8% of total)
const: 3.0ms (2.6% of total)

eval0.0ms (0%)

Compiler

Compiled 15 to 11 computations (26.7% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
99.5%
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
Compiler

Compiled 15 to 9 computations (40% saved)

simplify95.0ms (1%)

Algorithm
egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 #s(literal 5 binary64) (*.f64 v v))
cost-diff0
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v)))
cost-diff0
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64)))
cost-diff0
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
Rules
1908×fma-define
1656×fnmadd-define
1110×sum3-define
1034×fmsub-define
956×fnmsub-define
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0942
12942
25739
311939
424439
540039
669039
7118239
8206339
9446539
10565339
11567339
12567339
0567339
Stop Event
iter limit
saturated
Calls
Call 1
Inputs
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
(- 1 (* 5 (* v v)))
1
(* 5 (* v v))
5
(* v v)
v
(- (* v v) 1)
Outputs
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v #s(literal -5 binary64)))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v #s(literal -5 binary64)))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))
(- 1 (* 5 (* v v)))
(+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v #s(literal -5 binary64))))
1
#s(literal 1 binary64)
(* 5 (* v v))
(*.f64 #s(literal 5 binary64) (*.f64 v v))
5
#s(literal 5 binary64)
(* v v)
(*.f64 v v)
v
(- (* v v) 1)
(+.f64 (*.f64 v v) #s(literal -1 binary64))

localize137.0ms (1.4%)

Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy100.0%
(*.f64 v v)
accuracy100.0%
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64)))
accuracy99.7%
(*.f64 #s(literal 5 binary64) (*.f64 v v))
accuracy99.5%
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
Results
66.0ms111×3valid
32.0ms67×2valid
20.0ms74×1valid
0.0ms0valid
Compiler

Compiled 52 to 10 computations (80.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 60.0ms
ival-acos: 15.0ms (24.8% of total)
backward-pass: 14.0ms (23.1% of total)
ival-mult: 12.0ms (19.8% of total)
ival-sub: 10.0ms (16.5% of total)
ival-div: 8.0ms (13.2% of total)
const: 1.0ms (1.7% of total)

series3.0ms (0%)

Counts
5 → 60
Calls
Call 1
Inputs
#<alt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))>
#<alt (/ (- 1 (* 5 (* v v))) (- (* v v) 1))>
#<alt (- 1 (* 5 (* v v)))>
#<alt (* 5 (* v v))>
#<alt (* v v)>
Outputs
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt -1>
#<alt (- (* 4 (pow v 2)) 1)>
#<alt (- (* (pow v 2) (+ 4 (* 4 (pow v 2)))) 1)>
#<alt (- (* (pow v 2) (+ 4 (* (pow v 2) (+ 4 (* 4 (pow v 2)))))) 1)>
#<alt -5>
#<alt (* -1 (+ 5 (* 4 (/ 1 (pow v 2)))))>
#<alt (- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 2))) 5)>
#<alt (- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2)))))>
#<alt -5>
#<alt (* -1 (+ 5 (* 4 (/ 1 (pow v 2)))))>
#<alt (- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 2))) 5)>
#<alt (- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2)))))>
#<alt 1>
#<alt (+ 1 (* -5 (pow v 2)))>
#<alt (+ 1 (* -5 (pow v 2)))>
#<alt (+ 1 (* -5 (pow v 2)))>
#<alt (* -5 (pow v 2))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 5))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 5))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 5))>
#<alt (* -5 (pow v 2))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 5))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 5))>
#<alt (* (pow v 2) (- (/ 1 (pow v 2)) 5))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
Calls

15 calls:

TimeVariablePointExpression
0.0ms
v
@inf
(* 5 (* v v))
0.0ms
v
@inf
(- 1 (* 5 (* v v)))
0.0ms
v
@inf
(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
0.0ms
v
@0
(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
0.0ms
v
@0
(* 5 (* v v))

rewrite290.0ms (3%)

Algorithm
batch-egg-rewrite
Rules
2676×*-lowering-*.f32
2676×*-lowering-*.f64
1410×sum4-define
1354×/-lowering-/.f32
1354×/-lowering-/.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0935
14135
215132
377132
4534432
0802632
Stop Event
iter limit
node limit
Counts
5 → 237
Calls
Call 1
Inputs
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
(- 1 (* 5 (* v v)))
(* 5 (* v v))
(* v v)
Outputs
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(+.f64 (acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))) #s(literal 0 binary64))
(+.f64 (PI.f64) (neg.f64 (acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(+.f64 #s(literal 0 binary64) (acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(+.f64 (asin.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))) (/.f64 (PI.f64) #s(literal 2 binary64)))
(+.f64 (+.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) (asin.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 0 binary64)) (asin.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(-.f64 (PI.f64) (acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))))
(-.f64 #s(literal 0 binary64) (-.f64 (asin.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64))))
(-.f64 (asin.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))) (/.f64 (PI.f64) #s(literal -2 binary64)))
(-.f64 (asin.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))) (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 2 binary64) (PI.f64))))
(-.f64 (+.f64 #s(literal 1 binary64) (PI.f64)) (+.f64 #s(literal 1 binary64) (acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))))
(-.f64 (+.f64 #s(literal 0 binary64) (/.f64 (PI.f64) #s(literal 2 binary64))) (asin.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(-.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 0 binary64)) (asin.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(-.f64 (+.f64 #s(literal 0 binary64) (PI.f64)) (acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(-.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 0 binary64)) (asin.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(fma.f64 #s(literal 1 binary64) (PI.f64) (neg.f64 (acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))))
(fma.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(fma.f64 #s(literal -1 binary64) (asin.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64)))
(fma.f64 (PI.f64) #s(literal 1 binary64) (neg.f64 (acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(fma.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (neg.f64 (acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (PI.f64)) (neg.f64 (acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (asin.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(fma.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (asin.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(fma.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) #s(literal -1/2 binary64) (asin.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(neg.f64 (+.f64 (/.f64 (PI.f64) #s(literal -2 binary64)) (asin.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))))
(neg.f64 (+.f64 (asin.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))) (/.f64 (PI.f64) #s(literal -2 binary64))))
(+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (+.f64 (/.f64 (*.f64 #s(literal 5 binary64) (*.f64 v v)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (/.f64 (*.f64 #s(literal 5 binary64) (*.f64 v v)) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (+.f64 (*.f64 (neg.f64 (/.f64 (*.f64 #s(literal 5 binary64) v) (+.f64 (*.f64 v v) #s(literal -1 binary64)))) v) (/.f64 (*.f64 #s(literal 5 binary64) (*.f64 v v)) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (+.f64 (*.f64 v v) #s(literal -1 binary64))) (*.f64 #s(literal 1 binary64) (+.f64 (/.f64 (*.f64 #s(literal 5 binary64) (*.f64 v v)) (-.f64 #s(literal 1 binary64) (*.f64 v v))) (/.f64 (*.f64 #s(literal 5 binary64) (*.f64 v v)) (+.f64 (*.f64 v v) #s(literal -1 binary64))))))
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(*.f64 (*.f64 #s(literal 5 binary64) (*.f64 v v)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (*.f64 v (*.f64 v #s(literal -5 binary64))))
(*.f64 #s(literal -1 binary64) (/.f64 (*.f64 #s(literal 5 binary64) (*.f64 v v)) #s(literal -1 binary64)))
(*.f64 #s(literal -1 binary64) (*.f64 (*.f64 v (*.f64 v #s(literal -5 binary64))) #s(literal 1 binary64)))
(*.f64 (*.f64 v (*.f64 v #s(literal -5 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal -5 binary64) (-.f64 #s(literal 0 binary64) (*.f64 v v)))
(*.f64 #s(literal -5 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal 1 binary64)))
(*.f64 (*.f64 #s(literal 5 binary64) v) v)
(*.f64 (*.f64 #s(literal 5 binary64) v) (/.f64 (-.f64 #s(literal 0 binary64) v) #s(literal -1 binary64)))
(*.f64 (*.f64 #s(literal 5 binary64) v) (*.f64 v #s(literal 1 binary64)))
(*.f64 (*.f64 #s(literal 5 binary64) v) (*.f64 (-.f64 #s(literal 0 binary64) v) #s(literal -1 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal -5 binary64))
(*.f64 (*.f64 v #s(literal -5 binary64)) (-.f64 #s(literal 0 binary64) v))
(*.f64 (*.f64 v #s(literal -5 binary64)) (/.f64 v #s(literal -1 binary64)))
(*.f64 (*.f64 v #s(literal -5 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) v) #s(literal 1 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) v) (*.f64 v #s(literal -5 binary64)))
(*.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 v v))) #s(literal -5 binary64))
(*.f64 (*.f64 #s(literal 1 binary64) (*.f64 v #s(literal -5 binary64))) (-.f64 #s(literal 0 binary64) v))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 v)))
(exp.f64 (log.f64 (*.f64 v v)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 v)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 v v)))
(neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 v v)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 v v))))
(/.f64 (*.f64 v v) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal -1 binary64))
(pow.f64 v #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 v))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 v v)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 v v))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 v v))
(*.f64 v v)
(*.f64 v (/.f64 v #s(literal 1 binary64)))
(*.f64 v (/.f64 (-.f64 #s(literal 0 binary64) v) #s(literal -1 binary64)))
(*.f64 v (*.f64 v #s(literal 1 binary64)))
(*.f64 (*.f64 v v) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (*.f64 v v)))
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal -1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) v) (-.f64 #s(literal 0 binary64) v))
(*.f64 (-.f64 #s(literal 0 binary64) v) (/.f64 v #s(literal -1 binary64)))

simplify211.0ms (2.2%)

Algorithm
egg-herbie
Rules
2418×fma-lowering-fma.f32
2418×fma-lowering-fma.f64
2002×fmsub-define
1894×fmm-def
1650×*-lowering-*.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
037461
1106356
2301354
3794354
41904354
54496354
08492354
Stop Event
iter limit
node limit
Counts
60 → 60
Calls
Call 1
Inputs
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
-1
(- (* 4 (pow v 2)) 1)
(- (* (pow v 2) (+ 4 (* 4 (pow v 2)))) 1)
(- (* (pow v 2) (+ 4 (* (pow v 2) (+ 4 (* 4 (pow v 2)))))) 1)
-5
(* -1 (+ 5 (* 4 (/ 1 (pow v 2)))))
(- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 2))) 5)
(- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2)))))
-5
(* -1 (+ 5 (* 4 (/ 1 (pow v 2)))))
(- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 2))) 5)
(- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2)))))
1
(+ 1 (* -5 (pow v 2)))
(+ 1 (* -5 (pow v 2)))
(+ 1 (* -5 (pow v 2)))
(* -5 (pow v 2))
(* (pow v 2) (- (/ 1 (pow v 2)) 5))
(* (pow v 2) (- (/ 1 (pow v 2)) 5))
(* (pow v 2) (- (/ 1 (pow v 2)) 5))
(* -5 (pow v 2))
(* (pow v 2) (- (/ 1 (pow v 2)) 5))
(* (pow v 2) (- (/ 1 (pow v 2)) 5))
(* (pow v 2) (- (/ 1 (pow v 2)) 5))
(* 5 (pow v 2))
(* 5 (pow v 2))
(* 5 (pow v 2))
(* 5 (pow v 2))
(* 5 (pow v 2))
(* 5 (pow v 2))
(* 5 (pow v 2))
(* 5 (pow v 2))
(* 5 (pow v 2))
(* 5 (pow v 2))
(* 5 (pow v 2))
(* 5 (pow v 2))
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
Outputs
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
-1
#s(literal -1 binary64)
(- (* 4 (pow v 2)) 1)
(+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64)))
(- (* (pow v 2) (+ 4 (* 4 (pow v 2)))) 1)
(+.f64 #s(literal -1 binary64) (*.f64 v (*.f64 v (*.f64 #s(literal 4 binary64) (+.f64 #s(literal 1 binary64) (*.f64 v v))))))
(- (* (pow v 2) (+ 4 (* (pow v 2) (+ 4 (* 4 (pow v 2)))))) 1)
(+.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal 4 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 1 binary64) (*.f64 v v))))))
-5
#s(literal -5 binary64)
(* -1 (+ 5 (* 4 (/ 1 (pow v 2)))))
(-.f64 #s(literal -5 binary64) (/.f64 #s(literal 4 binary64) (*.f64 v v)))
(- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 2))) 5)
(+.f64 #s(literal -5 binary64) (/.f64 (+.f64 (/.f64 #s(literal -4 binary64) (*.f64 v v)) #s(literal -4 binary64)) (*.f64 v v)))
(- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2)))))
(+.f64 #s(literal -5 binary64) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -4 binary64) (*.f64 v v)) #s(literal -4 binary64)) (*.f64 v (*.f64 v (*.f64 v v)))) (/.f64 #s(literal -4 binary64) (*.f64 v v))))
-5
#s(literal -5 binary64)
(* -1 (+ 5 (* 4 (/ 1 (pow v 2)))))
(-.f64 #s(literal -5 binary64) (/.f64 #s(literal 4 binary64) (*.f64 v v)))
(- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 2))) 5)
(+.f64 #s(literal -5 binary64) (/.f64 (+.f64 (/.f64 #s(literal -4 binary64) (*.f64 v v)) #s(literal -4 binary64)) (*.f64 v v)))
(- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2)))))
(+.f64 #s(literal -5 binary64) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -4 binary64) (*.f64 v v)) #s(literal -4 binary64)) (*.f64 v (*.f64 v (*.f64 v v)))) (/.f64 #s(literal -4 binary64) (*.f64 v v))))
1
#s(literal 1 binary64)
(+ 1 (* -5 (pow v 2)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64)))
(+ 1 (* -5 (pow v 2)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64)))
(+ 1 (* -5 (pow v 2)))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64)))
(* -5 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -5 binary64))
(* (pow v 2) (- (/ 1 (pow v 2)) 5))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64)))
(* (pow v 2) (- (/ 1 (pow v 2)) 5))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64)))
(* (pow v 2) (- (/ 1 (pow v 2)) 5))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64)))
(* -5 (pow v 2))
(*.f64 (*.f64 v v) #s(literal -5 binary64))
(* (pow v 2) (- (/ 1 (pow v 2)) 5))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64)))
(* (pow v 2) (- (/ 1 (pow v 2)) 5))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64)))
(* (pow v 2) (- (/ 1 (pow v 2)) 5))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64)))
(* 5 (pow v 2))
(*.f64 #s(literal 5 binary64) (*.f64 v v))
(* 5 (pow v 2))
(*.f64 #s(literal 5 binary64) (*.f64 v v))
(* 5 (pow v 2))
(*.f64 #s(literal 5 binary64) (*.f64 v v))
(* 5 (pow v 2))
(*.f64 #s(literal 5 binary64) (*.f64 v v))
(* 5 (pow v 2))
(*.f64 #s(literal 5 binary64) (*.f64 v v))
(* 5 (pow v 2))
(*.f64 #s(literal 5 binary64) (*.f64 v v))
(* 5 (pow v 2))
(*.f64 #s(literal 5 binary64) (*.f64 v v))
(* 5 (pow v 2))
(*.f64 #s(literal 5 binary64) (*.f64 v v))
(* 5 (pow v 2))
(*.f64 #s(literal 5 binary64) (*.f64 v v))
(* 5 (pow v 2))
(*.f64 #s(literal 5 binary64) (*.f64 v v))
(* 5 (pow v 2))
(*.f64 #s(literal 5 binary64) (*.f64 v v))
(* 5 (pow v 2))
(*.f64 #s(literal 5 binary64) (*.f64 v v))
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)

eval41.0ms (0.4%)

Compiler

Compiled 6897 to 890 computations (87.1% saved)

prune56.0ms (0.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New3284332
Fresh000
Picked011
Done000
Total3285333
Accuracy
99.5%
Counts
333 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.0%
(fma.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))))
99.5%
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
99.5%
(acos.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 v v) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))))))
99.3%
(acos.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))
99.0%
(acos.f64 #s(literal -1 binary64))
Compiler

Compiled 65 to 43 computations (33.8% saved)

simplify139.0ms (1.4%)

Algorithm
egg-herbie
Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
cost-diff0
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
cost-diff0
(PI.f64)
cost-diff0
(sqrt.f64 (PI.f64))
cost-diff19328
(fma.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))))
cost-diff0
(+.f64 (*.f64 v v) #s(literal -1 binary64))
cost-diff0
(/.f64 (+.f64 (*.f64 v v) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))))
cost-diff0
(acos.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 v v) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))))))
cost-diff128
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 v v) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v)))))
cost-diff0
(*.f64 v v)
cost-diff0
(*.f64 (*.f64 v v) #s(literal 4 binary64))
cost-diff0
(+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64)))
cost-diff0
(acos.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))
cost-diff0
(acos.f64 #s(literal -1 binary64))
Rules
2492×fnmadd-define
2080×fma-define
1562×sum3-define
1252×fma-lowering-fma.f32
1252×fma-lowering-fma.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
024152
161150
2117140
3254140
4667140
51274140
62881140
76327140
87555140
08002140
Stop Event
iter limit
node limit
Calls
Call 1
Inputs
(acos -1)
-1
(acos (+ -1 (* (* v v) 4)))
(+ -1 (* (* v v) 4))
-1
(* (* v v) 4)
(* v v)
v
4
(acos (/ 1 (/ (+ (* v v) -1) (- 1 (* 5 (* v v))))))
(/ 1 (/ (+ (* v v) -1) (- 1 (* 5 (* v v)))))
1
(/ (+ (* v v) -1) (- 1 (* 5 (* v v))))
(+ (* v v) -1)
(* v v)
v
-1
(- 1 (* 5 (* v v)))
(* 5 (* v v))
5
(+ (* (sqrt (PI)) (sqrt (PI))) (neg (acos (/ (- 1 (* 5 (* v v))) (- 1 (* v v))))))
(sqrt (PI))
(PI)
(neg (acos (/ (- 1 (* 5 (* v v))) (- 1 (* v v)))))
(acos (/ (- 1 (* 5 (* v v))) (- 1 (* v v))))
(/ (- 1 (* 5 (* v v))) (- 1 (* v v)))
(- 1 (* 5 (* v v)))
1
(* 5 (* v v))
5
(* v v)
v
(- 1 (* v v))
Outputs
(acos -1)
(acos.f64 #s(literal -1 binary64))
-1
#s(literal -1 binary64)
(acos (+ -1 (* (* v v) 4)))
(acos.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))
(+ -1 (* (* v v) 4))
(+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64)))
-1
#s(literal -1 binary64)
(* (* v v) 4)
(*.f64 (*.f64 v v) #s(literal 4 binary64))
(* v v)
(*.f64 v v)
v
4
#s(literal 4 binary64)
(acos (/ 1 (/ (+ (* v v) -1) (- 1 (* 5 (* v v))))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v #s(literal -5 binary64)))) (+.f64 #s(literal -1 binary64) (*.f64 v v))))
(/ 1 (/ (+ (* v v) -1) (- 1 (* 5 (* v v)))))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v #s(literal -5 binary64)))) (+.f64 #s(literal -1 binary64) (*.f64 v v)))
1
#s(literal 1 binary64)
(/ (+ (* v v) -1) (- 1 (* 5 (* v v))))
(/.f64 (+.f64 #s(literal -1 binary64) (*.f64 v v)) (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v #s(literal -5 binary64)))))
(+ (* v v) -1)
(+.f64 #s(literal -1 binary64) (*.f64 v v))
(* v v)
(*.f64 v v)
v
-1
#s(literal -1 binary64)
(- 1 (* 5 (* v v)))
(+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v #s(literal -5 binary64))))
(* 5 (* v v))
(*.f64 v (*.f64 v #s(literal 5 binary64)))
5
#s(literal 5 binary64)
(+ (* (sqrt (PI)) (sqrt (PI))) (neg (acos (/ (- 1 (* 5 (* v v))) (- 1 (* v v))))))
(-.f64 (PI.f64) (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v #s(literal -5 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(sqrt (PI))
(sqrt.f64 (PI.f64))
(PI)
(PI.f64)
(neg (acos (/ (- 1 (* 5 (* v v))) (- 1 (* v v)))))
(-.f64 #s(literal 0 binary64) (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v #s(literal -5 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(acos (/ (- 1 (* 5 (* v v))) (- 1 (* v v))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v #s(literal -5 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(/ (- 1 (* 5 (* v v))) (- 1 (* v v)))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v #s(literal -5 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))
(- 1 (* 5 (* v v)))
(+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v #s(literal -5 binary64))))
1
#s(literal 1 binary64)
(* 5 (* v v))
(*.f64 v (*.f64 v #s(literal 5 binary64)))
5
#s(literal 5 binary64)
(* v v)
(*.f64 v v)
v
(- 1 (* v v))
(-.f64 #s(literal 1 binary64) (*.f64 v v))

localize785.0ms (8.1%)

Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
accuracy99.1%
(fma.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))))
accuracy99.1%
(sqrt.f64 (PI.f64))
accuracy58.8%
(PI.f64)
accuracy45.6%
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
accuracy100.0%
(/.f64 (+.f64 (*.f64 v v) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))))
accuracy100.0%
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 v v) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v)))))
accuracy99.7%
(*.f64 #s(literal 5 binary64) (*.f64 v v))
accuracy99.5%
(acos.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 v v) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))))))
accuracy100.0%
(+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64)))
accuracy100.0%
(*.f64 v v)
accuracy99.9%
(*.f64 (*.f64 v v) #s(literal 4 binary64))
accuracy99.5%
(acos.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))
accuracy100.0%
(acos.f64 #s(literal -1 binary64))
Results
414.0ms109×5exit
104.0ms64×2valid
66.0ms80×1valid
3.0ms3valid
0.0ms0valid
Compiler

Compiled 187 to 24 computations (87.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 294.0ms
ival-acos: 106.0ms (36.1% of total)
backward-pass: 63.0ms (21.4% of total)
ival-div: 39.0ms (13.3% of total)
ival-mult: 28.0ms (9.5% of total)
compiled-spec: 16.0ms (5.4% of total)
ival-add: 14.0ms (4.8% of total)
ival-sub: 11.0ms (3.7% of total)
ival-neg: 6.0ms (2% of total)
ival-sqrt: 4.0ms (1.4% of total)
const: 3.0ms (1% of total)
ival-pi: 2.0ms (0.7% of total)

series4.0ms (0%)

Counts
14 → 132
Calls
Call 1
Inputs
#<alt (acos -1)>
#<alt (acos (+ -1 (* (* v v) 4)))>
#<alt (+ -1 (* (* v v) 4))>
#<alt (* (* v v) 4)>
#<alt (* v v)>
#<alt (/ 1 (/ (+ (* v v) -1) (- 1 (* 5 (* v v)))))>
#<alt (acos (/ 1 (/ (+ (* v v) -1) (- 1 (* 5 (* v v))))))>
#<alt (/ (+ (* v v) -1) (- 1 (* 5 (* v v))))>
#<alt (+ (* v v) -1)>
#<alt (+ (* (sqrt (PI)) (sqrt (PI))) (neg (acos (/ (- 1 (* 5 (* v v))) (- 1 (* v v))))))>
#<alt (sqrt (PI))>
#<alt (PI)>
#<alt (acos (/ (- 1 (* 5 (* v v))) (- 1 (* v v))))>
#<alt (* 5 (* v v))>
Outputs
#<alt (acos (- (* 4 (pow v 2)) 1))>
#<alt (acos (- (* 4 (pow v 2)) 1))>
#<alt (acos (- (* 4 (pow v 2)) 1))>
#<alt (acos (- (* 4 (pow v 2)) 1))>
#<alt (acos (- (* 4 (pow v 2)) 1))>
#<alt (acos (- (* 4 (pow v 2)) 1))>
#<alt (acos (- (* 4 (pow v 2)) 1))>
#<alt (acos (- (* 4 (pow v 2)) 1))>
#<alt (acos (- (* 4 (pow v 2)) 1))>
#<alt (acos (- (* 4 (pow v 2)) 1))>
#<alt (acos (- (* 4 (pow v 2)) 1))>
#<alt (acos (- (* 4 (pow v 2)) 1))>
#<alt -1>
#<alt (- (* 4 (pow v 2)) 1)>
#<alt (- (* 4 (pow v 2)) 1)>
#<alt (- (* 4 (pow v 2)) 1)>
#<alt (* 4 (pow v 2))>
#<alt (* (pow v 2) (- 4 (/ 1 (pow v 2))))>
#<alt (* (pow v 2) (- 4 (/ 1 (pow v 2))))>
#<alt (* (pow v 2) (- 4 (/ 1 (pow v 2))))>
#<alt (* 4 (pow v 2))>
#<alt (* (pow v 2) (- 4 (/ 1 (pow v 2))))>
#<alt (* (pow v 2) (- 4 (/ 1 (pow v 2))))>
#<alt (* (pow v 2) (- 4 (/ 1 (pow v 2))))>
#<alt (* 4 (pow v 2))>
#<alt (* 4 (pow v 2))>
#<alt (* 4 (pow v 2))>
#<alt (* 4 (pow v 2))>
#<alt (* 4 (pow v 2))>
#<alt (* 4 (pow v 2))>
#<alt (* 4 (pow v 2))>
#<alt (* 4 (pow v 2))>
#<alt (* 4 (pow v 2))>
#<alt (* 4 (pow v 2))>
#<alt (* 4 (pow v 2))>
#<alt (* 4 (pow v 2))>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt (pow v 2)>
#<alt -1>
#<alt (- (* 4 (pow v 2)) 1)>
#<alt (- (* (pow v 2) (+ 4 (* 4 (pow v 2)))) 1)>
#<alt (- (* (pow v 2) (+ 4 (* (pow v 2) (+ 4 (* 4 (pow v 2)))))) 1)>
#<alt -5>
#<alt (* -1 (+ 5 (* 4 (/ 1 (pow v 2)))))>
#<alt (- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 2))) 5)>
#<alt (- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2)))))>
#<alt -5>
#<alt (* -1 (+ 5 (* 4 (/ 1 (pow v 2)))))>
#<alt (- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 2))) 5)>
#<alt (- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2)))))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))>
#<alt -1>
#<alt (- (* -4 (pow v 2)) 1)>
#<alt (- (* (pow v 2) (- (* -20 (pow v 2)) 4)) 1)>
#<alt (- (* (pow v 2) (- (* (pow v 2) (- (* -100 (pow v 2)) 20)) 4)) 1)>
#<alt -1/5>
#<alt (- (* 4/25 (/ 1 (pow v 2))) 1/5)>
#<alt (- (+ (/ 4/125 (pow v 4)) (* 4/25 (/ 1 (pow v 2)))) 1/5)>
#<alt (- (+ (/ 4/125 (pow v 4)) (+ (* 4/25 (/ 1 (pow v 2))) (* 4/625 (/ 1 (pow v 6))))) 1/5)>
#<alt -1/5>
#<alt (- (* 4/25 (/ 1 (pow v 2))) 1/5)>
#<alt (- (+ (/ 4/125 (pow v 4)) (* 4/25 (/ 1 (pow v 2)))) 1/5)>
#<alt (- (+ (/ 4/125 (pow v 4)) (+ (* 4/25 (/ 1 (pow v 2))) (* 4/625 (/ 1 (pow v 6))))) 1/5)>
#<alt -1>
#<alt (- (pow v 2) 1)>
#<alt (- (pow v 2) 1)>
#<alt (- (pow v 2) 1)>
#<alt (pow v 2)>
#<alt (* (pow v 2) (- 1 (/ 1 (pow v 2))))>
#<alt (* (pow v 2) (- 1 (/ 1 (pow v 2))))>
#<alt (* (pow v 2) (- 1 (/ 1 (pow v 2))))>
#<alt (pow v 2)>
#<alt (* (pow v 2) (- 1 (/ 1 (pow v 2))))>
#<alt (* (pow v 2) (- 1 (/ 1 (pow v 2))))>
#<alt (* (pow v 2) (- 1 (/ 1 (pow v 2))))>
#<alt (- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))>
#<alt (- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))>
#<alt (- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))>
#<alt (- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))>
#<alt (- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))>
#<alt (- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))>
#<alt (- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))>
#<alt (- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))>
#<alt (- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))>
#<alt (- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))>
#<alt (- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))>
#<alt (- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))>
#<alt (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
#<alt (* 5 (pow v 2))>
Calls

33 calls:

TimeVariablePointExpression
1.0ms
v
@inf
(+ (* (sqrt (PI)) (sqrt (PI))) (neg (acos (/ (- 1 (* 5 (* v v))) (- 1 (* v v))))))
0.0ms
v
@inf
(* (* v v) 4)
0.0ms
v
@inf
(/ (+ (* v v) -1) (- 1 (* 5 (* v v))))
0.0ms
v
@0
(/ (+ (* v v) -1) (- 1 (* 5 (* v v))))
0.0ms
v
@inf
(+ -1 (* (* v v) 4))

rewrite259.0ms (2.7%)

Algorithm
batch-egg-rewrite
Rules
1798×*-lowering-*.f32
1798×*-lowering-*.f64
1770×sum5-define
1452×fma-lowering-fma.f32
1452×fma-lowering-fma.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02491
111188
244883
3244083
0821383
Stop Event
iter limit
node limit
Counts
14 → 537
Calls
Call 1
Inputs
(acos -1)
(acos (+ -1 (* (* v v) 4)))
(+ -1 (* (* v v) 4))
(* (* v v) 4)
(* v v)
(/ 1 (/ (+ (* v v) -1) (- 1 (* 5 (* v v)))))
(acos (/ 1 (/ (+ (* v v) -1) (- 1 (* 5 (* v v))))))
(/ (+ (* v v) -1) (- 1 (* 5 (* v v))))
(+ (* v v) -1)
(+ (* (sqrt (PI)) (sqrt (PI))) (neg (acos (/ (- 1 (* 5 (* v v))) (- 1 (* v v))))))
(sqrt (PI))
(PI)
(acos (/ (- 1 (* 5 (* v v))) (- 1 (* v v))))
(* 5 (* v v))
Outputs
(acos.f64 #s(literal -1 binary64))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 #s(literal -1 binary64))))
(+.f64 (-.f64 #s(literal 0 binary64) (asin.f64 #s(literal -1 binary64))) (/.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 #s(literal -1 binary64)))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 #s(literal -1 binary64)))
(fma.f64 #s(literal -1 binary64) (asin.f64 #s(literal -1 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 #s(literal -1 binary64))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (asin.f64 #s(literal -1 binary64))))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 #s(literal -1 binary64))))
(fma.f64 (sqrt.f64 (PI.f64)) (-.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (asin.f64 #s(literal -1 binary64))))
(fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (asin.f64 #s(literal -1 binary64))))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (-.f64 #s(literal 0 binary64) (asin.f64 #s(literal -1 binary64))))
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 #s(literal -1 binary64))))
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (asin.f64 #s(literal -1 binary64))))
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (asin.f64 #s(literal -1 binary64))))
(fma.f64 (cbrt.f64 (PI.f64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 #s(literal -1 binary64))))
(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 #s(literal -1 binary64))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (-.f64 (cbrt.f64 (PI.f64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (asin.f64 #s(literal -1 binary64))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (asin.f64 #s(literal -1 binary64))))
(fma.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (asin.f64 #s(literal -1 binary64))))
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (-.f64 #s(literal 0 binary64) (asin.f64 #s(literal -1 binary64))))
(fma.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 #s(literal -1 binary64))))
(acos.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))
(+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))))
(+.f64 (-.f64 #s(literal 0 binary64) (asin.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))) (/.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 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64)))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64)))))
(fma.f64 #s(literal -1 binary64) (asin.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64)))) (/.f64 (PI.f64) #s(literal 2 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (asin.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))))
(fma.f64 (sqrt.f64 (PI.f64)) (-.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (asin.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))))
(fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (asin.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (-.f64 #s(literal 0 binary64) (asin.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))))
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))))
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (asin.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))))
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (asin.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))))
(fma.f64 (cbrt.f64 (PI.f64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))))
(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 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (-.f64 (cbrt.f64 (PI.f64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (asin.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (asin.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))))
(fma.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (asin.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))))
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (-.f64 #s(literal 0 binary64) (asin.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))))
(fma.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (-.f64 #s(literal 0 binary64) (asin.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))))
(+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64)))
(+.f64 (*.f64 (*.f64 v v) #s(literal 4 binary64)) #s(literal -1 binary64))
(fma.f64 v (*.f64 v #s(literal 4 binary64)) #s(literal -1 binary64))
(fma.f64 (*.f64 v v) #s(literal 4 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 4 binary64) (*.f64 v v) #s(literal -1 binary64))
(fma.f64 (*.f64 v #s(literal 4 binary64)) v #s(literal -1 binary64))
(*.f64 v (*.f64 v #s(literal 4 binary64)))
(*.f64 (*.f64 v v) #s(literal 4 binary64))
(*.f64 #s(literal 4 binary64) (*.f64 v v))
(*.f64 (*.f64 v #s(literal 4 binary64)) v)
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(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))) (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(-.f64 (PI.f64) (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v)))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(fma.f64 #s(literal -1 binary64) (asin.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))) (/.f64 (PI.f64) #s(literal 2 binary64)))
(fma.f64 #s(literal 1 binary64) (PI.f64) (neg.f64 (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v))))))
(fma.f64 #s(literal 1 binary64) (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v)))))
(fma.f64 (PI.f64) #s(literal 1 binary64) (neg.f64 (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v))))))
(fma.f64 (PI.f64) #s(literal 1/2 binary64) (asin.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v)))))
(fma.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v))))))
(fma.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (asin.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v)))))
(fma.f64 (sqrt.f64 (PI.f64)) (-.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))) (asin.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v)))))
(fma.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 1 binary64) (asin.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v)))))
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (asin.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v)))))
(fma.f64 (cbrt.f64 (PI.f64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (neg.f64 (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v))))))
(fma.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)))) (neg.f64 (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v))))))
(fma.f64 (cbrt.f64 (PI.f64)) (fabs.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (neg.f64 (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v))))))
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 1/2 binary64)) (asin.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v)))))
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))) (asin.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v)))))
(fma.f64 (cbrt.f64 (PI.f64)) (*.f64 (cbrt.f64 (PI.f64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (asin.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v)))))
(fma.f64 (cbrt.f64 (PI.f64)) (/.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 2 binary64)) (asin.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v)))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (cbrt.f64 (PI.f64)) (neg.f64 (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v))))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (asin.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v)))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (-.f64 (cbrt.f64 (PI.f64)) (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) (asin.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v)))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (pow.f64 (PI.f64) #s(literal 3/4 binary64)) (neg.f64 (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v))))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))) (asin.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v)))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (pow.f64 (PI.f64) #s(literal 5/6 binary64)) (neg.f64 (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v))))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 2/9 binary64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 7/3 binary64)) (neg.f64 (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v))))))
(fma.f64 (-.f64 #s(literal 0 binary64) (PI.f64)) #s(literal -1/2 binary64) (asin.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v)))))
(fma.f64 (/.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64)) (sqrt.f64 (PI.f64)) (asin.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v)))))
(fma.f64 (/.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (PI.f64) #s(literal 2/3 binary64)) (asin.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v)))))
(fma.f64 (exp.f64 (*.f64 #s(literal 2/3 binary64) (log.f64 (PI.f64)))) (exp.f64 (*.f64 #s(literal 1/3 binary64) (log.f64 (PI.f64)))) (neg.f64 (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v))))))
(fma.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64)) #s(literal 4/3 binary64)) (pow.f64 (PI.f64) #s(literal 1/9 binary64)) (neg.f64 (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v))))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 3/4 binary64)) (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (neg.f64 (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v))))))
(fma.f64 (pow.f64 (PI.f64) #s(literal 5/6 binary64)) (pow.f64 (PI.f64) #s(literal 1/6 binary64)) (neg.f64 (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v))))))
(fma.f64 (fabs.f64 (pow.f64 (PI.f64) #s(literal 2/3 binary64))) (cbrt.f64 (PI.f64)) (neg.f64 (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 #s(literal -1 binary64) (*.f64 v v))))))
(-.f64 #s(literal 0 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64)))
(neg.f64 (*.f64 (*.f64 v v) #s(literal -5 binary64)))
(*.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64)))
(*.f64 v (*.f64 v #s(literal 5 binary64)))
(*.f64 (*.f64 v v) #s(literal 5 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal 5 binary64)))
(*.f64 #s(literal 5 binary64) (*.f64 v v))
(*.f64 (-.f64 #s(literal 0 binary64) (*.f64 v v)) #s(literal -5 binary64))
(*.f64 #s(literal -5 binary64) (-.f64 #s(literal 0 binary64) (*.f64 v v)))
(*.f64 (*.f64 v #s(literal 5 binary64)) v)
(*.f64 (*.f64 v #s(literal 5 binary64)) (neg.f64 (-.f64 #s(literal 0 binary64) v)))
(*.f64 (*.f64 v #s(literal -5 binary64)) (-.f64 #s(literal 0 binary64) v))
(*.f64 (neg.f64 (*.f64 v #s(literal -5 binary64))) v)

simplify232.0ms (2.4%)

Algorithm
egg-herbie
Rules
2286×*-lowering-*.f32
2286×*-lowering-*.f64
1472×sum3-define
1448×fma-lowering-fma.f32
1448×fma-lowering-fma.f64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0761122
1202939
2517899
31340899
43357899
56709899
08300899
Stop Event
iter limit
node limit
Counts
132 → 132
Calls
Call 1
Inputs
(acos (- (* 4 (pow v 2)) 1))
(acos (- (* 4 (pow v 2)) 1))
(acos (- (* 4 (pow v 2)) 1))
(acos (- (* 4 (pow v 2)) 1))
(acos (- (* 4 (pow v 2)) 1))
(acos (- (* 4 (pow v 2)) 1))
(acos (- (* 4 (pow v 2)) 1))
(acos (- (* 4 (pow v 2)) 1))
(acos (- (* 4 (pow v 2)) 1))
(acos (- (* 4 (pow v 2)) 1))
(acos (- (* 4 (pow v 2)) 1))
(acos (- (* 4 (pow v 2)) 1))
-1
(- (* 4 (pow v 2)) 1)
(- (* 4 (pow v 2)) 1)
(- (* 4 (pow v 2)) 1)
(* 4 (pow v 2))
(* (pow v 2) (- 4 (/ 1 (pow v 2))))
(* (pow v 2) (- 4 (/ 1 (pow v 2))))
(* (pow v 2) (- 4 (/ 1 (pow v 2))))
(* 4 (pow v 2))
(* (pow v 2) (- 4 (/ 1 (pow v 2))))
(* (pow v 2) (- 4 (/ 1 (pow v 2))))
(* (pow v 2) (- 4 (/ 1 (pow v 2))))
(* 4 (pow v 2))
(* 4 (pow v 2))
(* 4 (pow v 2))
(* 4 (pow v 2))
(* 4 (pow v 2))
(* 4 (pow v 2))
(* 4 (pow v 2))
(* 4 (pow v 2))
(* 4 (pow v 2))
(* 4 (pow v 2))
(* 4 (pow v 2))
(* 4 (pow v 2))
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
(pow v 2)
-1
(- (* 4 (pow v 2)) 1)
(- (* (pow v 2) (+ 4 (* 4 (pow v 2)))) 1)
(- (* (pow v 2) (+ 4 (* (pow v 2) (+ 4 (* 4 (pow v 2)))))) 1)
-5
(* -1 (+ 5 (* 4 (/ 1 (pow v 2)))))
(- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 2))) 5)
(- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2)))))
-5
(* -1 (+ 5 (* 4 (/ 1 (pow v 2)))))
(- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 2))) 5)
(- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2)))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
-1
(- (* -4 (pow v 2)) 1)
(- (* (pow v 2) (- (* -20 (pow v 2)) 4)) 1)
(- (* (pow v 2) (- (* (pow v 2) (- (* -100 (pow v 2)) 20)) 4)) 1)
-1/5
(- (* 4/25 (/ 1 (pow v 2))) 1/5)
(- (+ (/ 4/125 (pow v 4)) (* 4/25 (/ 1 (pow v 2)))) 1/5)
(- (+ (/ 4/125 (pow v 4)) (+ (* 4/25 (/ 1 (pow v 2))) (* 4/625 (/ 1 (pow v 6))))) 1/5)
-1/5
(- (* 4/25 (/ 1 (pow v 2))) 1/5)
(- (+ (/ 4/125 (pow v 4)) (* 4/25 (/ 1 (pow v 2)))) 1/5)
(- (+ (/ 4/125 (pow v 4)) (+ (* 4/25 (/ 1 (pow v 2))) (* 4/625 (/ 1 (pow v 6))))) 1/5)
-1
(- (pow v 2) 1)
(- (pow v 2) 1)
(- (pow v 2) 1)
(pow v 2)
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
(pow v 2)
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(* 5 (pow v 2))
(* 5 (pow v 2))
(* 5 (pow v 2))
(* 5 (pow v 2))
(* 5 (pow v 2))
(* 5 (pow v 2))
(* 5 (pow v 2))
(* 5 (pow v 2))
(* 5 (pow v 2))
(* 5 (pow v 2))
(* 5 (pow v 2))
(* 5 (pow v 2))
Outputs
(acos (- (* 4 (pow v 2)) 1))
(acos.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64)))
(acos (- (* 4 (pow v 2)) 1))
(acos.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64)))
(acos (- (* 4 (pow v 2)) 1))
(acos.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64)))
(acos (- (* 4 (pow v 2)) 1))
(acos.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64)))
(acos (- (* 4 (pow v 2)) 1))
(acos.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64)))
(acos (- (* 4 (pow v 2)) 1))
(acos.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64)))
(acos (- (* 4 (pow v 2)) 1))
(acos.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64)))
(acos (- (* 4 (pow v 2)) 1))
(acos.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64)))
(acos (- (* 4 (pow v 2)) 1))
(acos.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64)))
(acos (- (* 4 (pow v 2)) 1))
(acos.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64)))
(acos (- (* 4 (pow v 2)) 1))
(acos.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64)))
(acos (- (* 4 (pow v 2)) 1))
(acos.f64 (+.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64)))
-1
#s(literal -1 binary64)
(- (* 4 (pow v 2)) 1)
(+.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64))
(- (* 4 (pow v 2)) 1)
(+.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64))
(- (* 4 (pow v 2)) 1)
(+.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64))
(* 4 (pow v 2))
(*.f64 #s(literal 4 binary64) (*.f64 v v))
(* (pow v 2) (- 4 (/ 1 (pow v 2))))
(+.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64))
(* (pow v 2) (- 4 (/ 1 (pow v 2))))
(+.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64))
(* (pow v 2) (- 4 (/ 1 (pow v 2))))
(+.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64))
(* 4 (pow v 2))
(*.f64 #s(literal 4 binary64) (*.f64 v v))
(* (pow v 2) (- 4 (/ 1 (pow v 2))))
(+.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64))
(* (pow v 2) (- 4 (/ 1 (pow v 2))))
(+.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64))
(* (pow v 2) (- 4 (/ 1 (pow v 2))))
(+.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64))
(* 4 (pow v 2))
(*.f64 #s(literal 4 binary64) (*.f64 v v))
(* 4 (pow v 2))
(*.f64 #s(literal 4 binary64) (*.f64 v v))
(* 4 (pow v 2))
(*.f64 #s(literal 4 binary64) (*.f64 v v))
(* 4 (pow v 2))
(*.f64 #s(literal 4 binary64) (*.f64 v v))
(* 4 (pow v 2))
(*.f64 #s(literal 4 binary64) (*.f64 v v))
(* 4 (pow v 2))
(*.f64 #s(literal 4 binary64) (*.f64 v v))
(* 4 (pow v 2))
(*.f64 #s(literal 4 binary64) (*.f64 v v))
(* 4 (pow v 2))
(*.f64 #s(literal 4 binary64) (*.f64 v v))
(* 4 (pow v 2))
(*.f64 #s(literal 4 binary64) (*.f64 v v))
(* 4 (pow v 2))
(*.f64 #s(literal 4 binary64) (*.f64 v v))
(* 4 (pow v 2))
(*.f64 #s(literal 4 binary64) (*.f64 v v))
(* 4 (pow v 2))
(*.f64 #s(literal 4 binary64) (*.f64 v v))
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
(pow v 2)
(*.f64 v v)
-1
#s(literal -1 binary64)
(- (* 4 (pow v 2)) 1)
(+.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) #s(literal -1 binary64))
(- (* (pow v 2) (+ 4 (* 4 (pow v 2)))) 1)
(+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal 4 binary64) (*.f64 #s(literal 4 binary64) (*.f64 v v)))))
(- (* (pow v 2) (+ 4 (* (pow v 2) (+ 4 (* 4 (pow v 2)))))) 1)
(+.f64 #s(literal -1 binary64) (*.f64 (*.f64 #s(literal 4 binary64) (*.f64 v v)) (+.f64 #s(literal 1 binary64) (*.f64 v (*.f64 v (+.f64 (*.f64 v v) #s(literal 1 binary64)))))))
-5
#s(literal -5 binary64)
(* -1 (+ 5 (* 4 (/ 1 (pow v 2)))))
(+.f64 #s(literal -5 binary64) (/.f64 #s(literal -4 binary64) (*.f64 v v)))
(- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 2))) 5)
(+.f64 (/.f64 (+.f64 #s(literal -4 binary64) (/.f64 #s(literal -4 binary64) (*.f64 v v))) (*.f64 v v)) #s(literal -5 binary64))
(- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2)))))
(+.f64 (/.f64 (+.f64 #s(literal -4 binary64) (/.f64 #s(literal -4 binary64) (*.f64 v v))) (*.f64 v (*.f64 v (*.f64 v v)))) (+.f64 #s(literal -5 binary64) (/.f64 #s(literal -4 binary64) (*.f64 v v))))
-5
#s(literal -5 binary64)
(* -1 (+ 5 (* 4 (/ 1 (pow v 2)))))
(+.f64 #s(literal -5 binary64) (/.f64 #s(literal -4 binary64) (*.f64 v v)))
(- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 2))) 5)
(+.f64 (/.f64 (+.f64 #s(literal -4 binary64) (/.f64 #s(literal -4 binary64) (*.f64 v v))) (*.f64 v v)) #s(literal -5 binary64))
(- (* -1 (/ (+ 4 (* 4 (/ 1 (pow v 2)))) (pow v 4))) (+ 5 (* 4 (/ 1 (pow v 2)))))
(+.f64 (/.f64 (+.f64 #s(literal -4 binary64) (/.f64 #s(literal -4 binary64) (*.f64 v v))) (*.f64 v (*.f64 v (*.f64 v v)))) (+.f64 #s(literal -5 binary64) (/.f64 #s(literal -4 binary64) (*.f64 v v))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos (/ (- 1 (* 5 (pow v 2))) (- (pow v 2) 1)))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
-1
#s(literal -1 binary64)
(- (* -4 (pow v 2)) 1)
(+.f64 #s(literal -1 binary64) (*.f64 v (*.f64 v #s(literal -4 binary64))))
(- (* (pow v 2) (- (* -20 (pow v 2)) 4)) 1)
(+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal -4 binary64) (*.f64 (*.f64 v v) #s(literal -20 binary64)))))
(- (* (pow v 2) (- (* (pow v 2) (- (* -100 (pow v 2)) 20)) 4)) 1)
(+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) (+.f64 #s(literal -4 binary64) (*.f64 v (*.f64 v (+.f64 #s(literal -20 binary64) (*.f64 (*.f64 v v) #s(literal -100 binary64))))))))
-1/5
#s(literal -1/5 binary64)
(- (* 4/25 (/ 1 (pow v 2))) 1/5)
(+.f64 (/.f64 #s(literal 4/25 binary64) (*.f64 v v)) #s(literal -1/5 binary64))
(- (+ (/ 4/125 (pow v 4)) (* 4/25 (/ 1 (pow v 2)))) 1/5)
(+.f64 (/.f64 #s(literal 4/25 binary64) (*.f64 v v)) (+.f64 (/.f64 #s(literal 4/125 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -1/5 binary64)))
(- (+ (/ 4/125 (pow v 4)) (+ (* 4/25 (/ 1 (pow v 2))) (* 4/625 (/ 1 (pow v 6))))) 1/5)
(+.f64 (+.f64 (/.f64 #s(literal 4/25 binary64) (*.f64 v v)) #s(literal -1/5 binary64)) (+.f64 (/.f64 #s(literal 4/125 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) (/.f64 #s(literal 4/625 binary64) (pow.f64 v #s(literal 6 binary64)))))
-1/5
#s(literal -1/5 binary64)
(- (* 4/25 (/ 1 (pow v 2))) 1/5)
(+.f64 (/.f64 #s(literal 4/25 binary64) (*.f64 v v)) #s(literal -1/5 binary64))
(- (+ (/ 4/125 (pow v 4)) (* 4/25 (/ 1 (pow v 2)))) 1/5)
(+.f64 (/.f64 #s(literal 4/25 binary64) (*.f64 v v)) (+.f64 (/.f64 #s(literal 4/125 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) #s(literal -1/5 binary64)))
(- (+ (/ 4/125 (pow v 4)) (+ (* 4/25 (/ 1 (pow v 2))) (* 4/625 (/ 1 (pow v 6))))) 1/5)
(+.f64 (+.f64 (/.f64 #s(literal 4/25 binary64) (*.f64 v v)) #s(literal -1/5 binary64)) (+.f64 (/.f64 #s(literal 4/125 binary64) (*.f64 v (*.f64 v (*.f64 v v)))) (/.f64 #s(literal 4/625 binary64) (pow.f64 v #s(literal 6 binary64)))))
-1
#s(literal -1 binary64)
(- (pow v 2) 1)
(+.f64 (*.f64 v v) #s(literal -1 binary64))
(- (pow v 2) 1)
(+.f64 (*.f64 v v) #s(literal -1 binary64))
(- (pow v 2) 1)
(+.f64 (*.f64 v v) #s(literal -1 binary64))
(pow v 2)
(*.f64 v v)
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
(+.f64 (*.f64 v v) #s(literal -1 binary64))
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
(+.f64 (*.f64 v v) #s(literal -1 binary64))
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
(+.f64 (*.f64 v v) #s(literal -1 binary64))
(pow v 2)
(*.f64 v v)
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
(+.f64 (*.f64 v v) #s(literal -1 binary64))
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
(+.f64 (*.f64 v v) #s(literal -1 binary64))
(* (pow v 2) (- 1 (/ 1 (pow v 2))))
(+.f64 (*.f64 v v) #s(literal -1 binary64))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(-.f64 (PI.f64) (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(-.f64 (PI.f64) (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(-.f64 (PI.f64) (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(-.f64 (PI.f64) (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(-.f64 (PI.f64) (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(-.f64 (PI.f64) (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(-.f64 (PI.f64) (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(-.f64 (PI.f64) (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(-.f64 (PI.f64) (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(-.f64 (PI.f64) (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(-.f64 (PI.f64) (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(- (PI) (acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2)))))
(-.f64 (PI.f64) (acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(acos (/ (- 1 (* 5 (pow v 2))) (- 1 (pow v 2))))
(acos.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal -5 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(* 5 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 5 binary64))
(* 5 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 5 binary64))
(* 5 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 5 binary64))
(* 5 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 5 binary64))
(* 5 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 5 binary64))
(* 5 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 5 binary64))
(* 5 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 5 binary64))
(* 5 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 5 binary64))
(* 5 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 5 binary64))
(* 5 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 5 binary64))
(* 5 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 5 binary64))
(* 5 (pow v 2))
(*.f64 (*.f64 v v) #s(literal 5 binary64))

eval215.0ms (2.2%)

Compiler

Compiled 19373 to 1956 computations (89.9% saved)

prune85.0ms (0.9%)

Pruning

5 alts after pruning (0 fresh and 5 done)

PrunedKeptTotal
New9430943
Fresh000
Picked044
Done011
Total9435948
Accuracy
99.5%
Counts
948 → 5
Alt Table
Click to see full alt table
StatusAccuracyProgram
98.0%
(fma.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))))
99.5%
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
99.5%
(acos.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 v v) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))))))
99.3%
(acos.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))
99.0%
(acos.f64 #s(literal -1 binary64))
Compiler

Compiled 126 to 69 computations (45.2% saved)

regimes9.0ms (0.1%)

Counts
5 → 1
Calls
Call 1
Inputs
(acos.f64 #s(literal -1 binary64))
(acos.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
(acos.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 v v) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))))))
(fma.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)) (neg.f64 (acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))))
Outputs
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
Calls

4 calls:

2.0ms
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
2.0ms
v
2.0ms
(*.f64 v v)
2.0ms
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64)))
Results
AccuracySegmentsBranch
99.5%1v
99.5%1(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
99.5%1(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64)))
99.5%1(*.f64 v v)
Compiler

Compiled 35 to 20 computations (42.9% saved)

regimes3.0ms (0%)

Counts
2 → 1
Calls
Call 1
Inputs
(acos.f64 #s(literal -1 binary64))
(acos.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))
Outputs
(acos.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))
Calls

2 calls:

1.0ms
v
1.0ms
(*.f64 v v)
Results
AccuracySegmentsBranch
99.3%1v
99.3%1(*.f64 v v)
Compiler

Compiled 6 to 3 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
(acos.f64 #s(literal -1 binary64))
Outputs
(acos.f64 #s(literal -1 binary64))
Calls

1 calls:

1.0ms
v
Results
AccuracySegmentsBranch
99.0%1v
Compiler

Compiled 2 to 1 computations (50% saved)

simplify9.0ms (0.1%)

Algorithm
egg-herbie
Rules
16×+-commutative_binary64
14×*-commutative_binary64
14×sub-neg_binary64
10×neg-sub0_binary64
10×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01524
12824
24124
35524
46124
56424
66524
Stop Event
saturated
Calls
Call 1
Inputs
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
(acos.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))
(acos.f64 #s(literal -1 binary64))
Outputs
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (-.f64 (*.f64 v v) #s(literal 1 binary64))))
(acos.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (+.f64 (*.f64 v v) #s(literal -1 binary64))))
(acos.f64 (+.f64 #s(literal -1 binary64) (*.f64 (*.f64 v v) #s(literal 4 binary64))))
(acos.f64 #s(literal -1 binary64))

soundness352.0ms (3.6%)

Rules
2418×fma-lowering-fma.f32
2418×fma-lowering-fma.f64
2002×fmsub-define
1894×fmm-def
1650×*-lowering-*.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
037461
1106356
2301354
3794354
41904354
54496354
08492354
Stop Event
done
iter limit
node limit
Compiler

Compiled 37 to 25 computations (32.4% saved)

preprocess29.0ms (0.3%)

Remove

(abs v)

Compiler

Compiled 140 to 88 computations (37.1% saved)

end0.0ms (0%)

Profiling

Loading profile data...