Numeric.Integration.TanhSinh:everywhere from integration-0.2.1

Time bar (total: 6.5s)

analyze0.0ms (0%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
100%99.9%0%0.1%0%0%0%1
Compiler

Compiled 10 to 7 computations (30% saved)

Precisions
Click to see histograms. Total time spent on operations: 0.0ms
ival-add: 0.0ms (0% of total)
ival-mult: 0.0ms (0% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

sample645.0ms (9.9%)

Results
430.0ms8256×0valid
Precisions
Click to see histograms. Total time spent on operations: 222.0ms
ival-mult: 141.0ms (63.5% of total)
ival-add: 68.0ms (30.6% of total)
const: 11.0ms (5% of total)
backward-pass: 3.0ms (1.4% of total)
Bogosity

preprocess105.0ms (1.6%)

Algorithm
2×egg-herbie
Rules
164×associate-*r*
132×distribute-lft-in
112×unsub-neg
90×associate-*l*
80×distribute-rgt-in
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01744
16544
219442
347142
464742
577642
680342
067
1167
2247
3457
4457
0456
Stop Event
1×iter limit
1×saturated
1×saturated
Calls
Call 1
Inputs
(* x (+ 1 (* y y)))
Outputs
(* x (+ 1 (* y y)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
Call 2
Inputs
(* x (+ 1 (* y y)))
(* (neg x) (+ 1 (* y y)))
(* x (+ 1 (* (neg y) (neg y))))
(neg (* (neg x) (+ 1 (* y y))))
(neg (* x (+ 1 (* (neg y) (neg y)))))
(* y (+ 1 (* x x)))
Outputs
(* x (+ 1 (* y y)))
(+ x (* x (* y y)))
(* (neg x) (+ 1 (* y y)))
(* x (- -1 (* y y)))
(* x (+ 1 (* (neg y) (neg y))))
(+ x (* x (* y y)))
(neg (* (neg x) (+ 1 (* y y))))
(+ x (* x (* y y)))
(neg (* x (+ 1 (* (neg y) (neg y)))))
(* x (- -1 (* y y)))
(* y (+ 1 (* x x)))
Symmetry

(abs y)

(negabs x)

explain61.0ms (0.9%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
130-0-(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
00-0-x
00-0-(+.f64 #s(literal 1 binary64) (*.f64 y y))
00-0-(*.f64 y y)
00-0-#s(literal 1 binary64)
00-0-y
Results
29.0ms512×0valid
Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-mult: 8.0ms (70.4% of total)
ival-add: 3.0ms (26.4% of total)
const: 1.0ms (8.8% of total)
backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler

Compiled 9 to 6 computations (33.3% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
▶95.1%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
Compiler

Compiled 9 to 6 computations (33.3% saved)

localize38.0ms (0.6%)

Algorithm
1×egg-herbie
Localize:

Found 7 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
#s(literal 1 binary64)
✓cost-diff0
(+.f64 #s(literal 1 binary64) (*.f64 y y))
✓cost-diff0
x
✓cost-diff0
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
✓accuracy100.0%
(+.f64 #s(literal 1 binary64) (*.f64 y y))
✓accuracy100.0%
(*.f64 y y)
✓accuracy95.1%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
Rules
46×*-lowering-*.f32
46×*-lowering-*.f64
22×accelerator-lowering-fma.f32
22×accelerator-lowering-fma.f64
14×associate-*r*
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0618
11618
22418
34518
44518
04516
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(* x (+ 1 (* y y)))
x
(+ 1 (* y y))
1
(* y y)
y
Outputs
(* x (+ 1 (* y y)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
x
(+ 1 (* y y))
(+.f64 #s(literal 1 binary64) (*.f64 y y))
1
#s(literal 1 binary64)
(* y y)
(*.f64 y y)
y
Results
18.0ms256×0valid
Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 9.0ms
ival-mult: 7.0ms (76.9% of total)
ival-add: 1.0ms (11% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

series10.0ms (0.2%)

Counts
5 → 60
Calls
Call 1
Inputs
#<alt (* x (+ 1 (* y y)))>
#<alt (* y y)>
#<alt (+ 1 (* y y))>
#<alt x>
#<alt 1>
Outputs
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt x>
#<alt (+ x (* x (pow y 2)))>
#<alt (+ x (* x (pow y 2)))>
#<alt (+ x (* x (pow y 2)))>
#<alt (* x (pow y 2))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* x (pow y 2))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt 1>
#<alt (+ 1 (pow y 2))>
#<alt (+ 1 (pow y 2))>
#<alt (+ 1 (pow y 2))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (/ 1 (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ 1 (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ 1 (pow y 2))))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (/ 1 (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ 1 (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ 1 (pow y 2))))>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
Calls

15 calls:

TimeVariablePointExpression
3.0ms
y
@0
(* y y)
1.0ms
x
@0
(* x (+ 1 (* y y)))
1.0ms
y
@inf
(* x (+ 1 (* y y)))
0.0ms
x
@inf
(* x (+ 1 (* y y)))
0.0ms
y
@inf
(* y y)

rewrite437.0ms (6.7%)

Algorithm
1×batch-egg-rewrite
Rules
5242×accelerator-lowering-fma.f32
5242×accelerator-lowering-fma.f64
4884×/-lowering-/.f32
4884×/-lowering-/.f64
4162×*-lowering-*.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0617
13117
220617
3140417
0825915
Stop Event
1×iter limit
1×node limit
Counts
5 → 368
Calls
Call 1
Inputs
(* x (+ 1 (* y y)))
(* y y)
(+ 1 (* y y))
x
1
Outputs
(+.f64 x (*.f64 x (*.f64 y y)))
(+.f64 (*.f64 x (*.f64 y y)) x)
(+.f64 (/.f64 (*.f64 x x) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y)))) (neg.f64 (*.f64 (/.f64 (*.f64 y y) x) (/.f64 (*.f64 x (*.f64 x (*.f64 y y))) (-.f64 #s(literal 1 binary64) (*.f64 y y))))))
(-.f64 (/.f64 (*.f64 x x) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y)))) (*.f64 (/.f64 (*.f64 y y) x) (/.f64 (*.f64 x (*.f64 x (*.f64 y y))) (-.f64 #s(literal 1 binary64) (*.f64 y y)))))
(-.f64 (/.f64 (*.f64 (*.f64 y y) (*.f64 x (*.f64 x (*.f64 y y)))) (-.f64 (*.f64 x (*.f64 y y)) x)) (/.f64 (*.f64 x x) (-.f64 (*.f64 x (*.f64 y y)) x)))
(fma.f64 x #s(literal 1 binary64) (*.f64 x (*.f64 y y)))
(fma.f64 x (*.f64 y y) x)
(fma.f64 #s(literal 1 binary64) x (*.f64 x (*.f64 y y)))
(fma.f64 #s(literal 1 binary64) (*.f64 x (*.f64 y y)) x)
(fma.f64 y (*.f64 x y) x)
(fma.f64 (*.f64 y y) x x)
(fma.f64 (*.f64 x (*.f64 y y)) #s(literal 1 binary64) x)
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y)))) (neg.f64 (*.f64 (/.f64 (*.f64 y y) x) (/.f64 (*.f64 x (*.f64 x (*.f64 y y))) (-.f64 #s(literal 1 binary64) (*.f64 y y))))))
(fma.f64 (*.f64 x y) y x)
(fma.f64 (/.f64 x x) (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (neg.f64 (*.f64 (/.f64 (*.f64 y y) x) (/.f64 (*.f64 x (*.f64 x (*.f64 y y))) (-.f64 #s(literal 1 binary64) (*.f64 y y))))))
(fma.f64 (/.f64 (*.f64 x x) x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y y))) (neg.f64 (*.f64 (/.f64 (*.f64 y y) x) (/.f64 (*.f64 x (*.f64 x (*.f64 y y))) (-.f64 #s(literal 1 binary64) (*.f64 y y))))))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 y y))) (neg.f64 (*.f64 (/.f64 (*.f64 y y) x) (/.f64 (*.f64 x (*.f64 x (*.f64 y y))) (-.f64 #s(literal 1 binary64) (*.f64 y y))))))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 y y))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 y y))) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 (*.f64 y y) (*.f64 x (*.f64 x (*.f64 y y)))) (-.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 y y))))) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 y y)) (*.f64 (*.f64 y y) (*.f64 x (*.f64 x (*.f64 y y))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (*.f64 x (*.f64 y y)) x) (-.f64 (*.f64 (*.f64 y y) (*.f64 x (*.f64 x (*.f64 y y)))) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64))))) (*.f64 x (-.f64 #s(literal -1 binary64) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y y))) (*.f64 x (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 y y) #s(literal -1 binary64)) (*.f64 x (+.f64 (*.f64 y (*.f64 y (*.f64 y y))) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64))))) (*.f64 (-.f64 #s(literal -1 binary64) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y)))))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y y))) (*.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (*.f64 y y) #s(literal -1 binary64)) (*.f64 (+.f64 (*.f64 y (*.f64 y (*.f64 y y))) #s(literal -1 binary64)) x)))
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 y y)) (*.f64 (*.f64 y y) (*.f64 x (*.f64 x (*.f64 y y)))))) (+.f64 (*.f64 (*.f64 x (*.f64 y y)) (-.f64 (*.f64 x (*.f64 y y)) x)) (*.f64 x x)))
(/.f64 (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 y y)) (*.f64 (*.f64 y y) (*.f64 x (*.f64 x (*.f64 y y)))))) (+.f64 (*.f64 (*.f64 y y) (*.f64 x (*.f64 x (*.f64 y y)))) (-.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 y y))))))
(/.f64 (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y)))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))))))
(/.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))) (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(/.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))) (-.f64 #s(literal 1 binary64) (*.f64 y y)))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 y y)) (*.f64 (*.f64 y y) (*.f64 x (*.f64 x (*.f64 y y))))))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 (*.f64 x (*.f64 y y)) (-.f64 (*.f64 x (*.f64 y y)) x)) (*.f64 x x))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 y y)) (*.f64 (*.f64 y y) (*.f64 x (*.f64 x (*.f64 y y))))))) (neg.f64 (+.f64 (*.f64 (*.f64 y y) (*.f64 x (*.f64 x (*.f64 y y)))) (-.f64 (*.f64 x x) (*.f64 x (*.f64 x (*.f64 y y)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))))) (-.f64 #s(literal 0 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y)))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y)))))))) (-.f64 #s(literal -1 binary64) (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y y))))
(/.f64 (-.f64 (*.f64 (*.f64 y y) (*.f64 x (*.f64 x (*.f64 y y)))) (*.f64 x x)) (-.f64 (*.f64 x (*.f64 y y)) x))
(/.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 y y)))))
(/.f64 (*.f64 x (-.f64 #s(literal -1 binary64) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))) (-.f64 #s(literal -1 binary64) (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(/.f64 (*.f64 x (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y y))))
(/.f64 (*.f64 x (+.f64 (*.f64 y (*.f64 y (*.f64 y y))) #s(literal -1 binary64))) (+.f64 (*.f64 y y) #s(literal -1 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal -1 binary64) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y)))))) x) (-.f64 #s(literal -1 binary64) (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))) x) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y y))))
(/.f64 (*.f64 (+.f64 (*.f64 y (*.f64 y (*.f64 y y))) #s(literal -1 binary64)) x) (+.f64 (*.f64 y y) #s(literal -1 binary64)))
(/.f64 (/.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))) (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 y y))))
(/.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y)))) (*.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (*.f64 (*.f64 y y) (*.f64 x (*.f64 x (*.f64 y y)))))) (*.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x (*.f64 x x)) (*.f64 (*.f64 x (*.f64 y y)) (*.f64 (*.f64 y y) (*.f64 x (*.f64 x (*.f64 y y)))))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 (*.f64 x (*.f64 y y)) (-.f64 (*.f64 x (*.f64 y y)) x)) (*.f64 x x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y)))))) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y y)))))
(/.f64 (neg.f64 (-.f64 (*.f64 (*.f64 y y) (*.f64 x (*.f64 x (*.f64 y y)))) (*.f64 x x))) (neg.f64 (-.f64 (*.f64 x (*.f64 y y)) x)))
(/.f64 (neg.f64 (*.f64 x (-.f64 #s(literal -1 binary64) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y)))))))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64)))))))
(/.f64 (neg.f64 (*.f64 x (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y y)))))
(/.f64 (neg.f64 (*.f64 x (+.f64 (*.f64 y (*.f64 y (*.f64 y y))) #s(literal -1 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 y y) #s(literal -1 binary64))))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal -1 binary64) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y)))))) x)) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64)))))))
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(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 y (*.f64 y (*.f64 y y))))))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64)))) (*.f64 (*.f64 y y) (*.f64 (+.f64 (*.f64 y y) #s(literal -1 binary64)) (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64))))))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))) (+.f64 (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))) #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64)))) (+.f64 (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64)))) #s(literal -1 binary64)))))))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 y (*.f64 y (*.f64 y y))))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (*.f64 (+.f64 (*.f64 y y) #s(literal -1 binary64)) (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64)))))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))) (+.f64 (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))) #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64))))))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 y (*.f64 y (*.f64 y y)))))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64)))) (*.f64 (*.f64 y y) (*.f64 (+.f64 (*.f64 y y) #s(literal -1 binary64)) (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64))))))))) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64)))) (+.f64 (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64)))) #s(literal -1 binary64)))))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 y (*.f64 y (*.f64 y y)))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (*.f64 (+.f64 (*.f64 y y) #s(literal -1 binary64)) (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64)))))))) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64))))))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 y (*.f64 y (*.f64 y y)))))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))) (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y)))))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))))) (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64)))))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 y (*.f64 y (*.f64 y y)))))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))) (-.f64 #s(literal -1 binary64) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y)))))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))))) (-.f64 #s(literal -1 binary64) (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64)))))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 y (*.f64 y (*.f64 y y)))))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y y)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 y (*.f64 y (*.f64 y y)))))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))) (+.f64 (*.f64 y (*.f64 y (*.f64 y y))) #s(literal -1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))))) (+.f64 (*.f64 y y) #s(literal -1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 y (*.f64 y (*.f64 y y))))) (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y))))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (+.f64 #s(literal 1 binary64) (*.f64 y y)))))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 y (*.f64 y (*.f64 y y))))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))) (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y)))))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))) (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64)))))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 y (*.f64 y (*.f64 y y))))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))) (-.f64 #s(literal -1 binary64) (*.f64 y (*.f64 y (*.f64 y (*.f64 y (*.f64 y y)))))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))) (-.f64 #s(literal -1 binary64) (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64)))))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 y (*.f64 y (*.f64 y y))))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y y)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 y (*.f64 y (*.f64 y y))))) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))) (+.f64 (*.f64 y (*.f64 y (*.f64 y y))) #s(literal -1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))) (+.f64 (*.f64 y y) #s(literal -1 binary64))))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 y y)) (+.f64 y #s(literal 1 binary64))) (/.f64 (+.f64 (*.f64 y y) #s(literal -1 binary64)) (+.f64 y #s(literal -1 binary64))))
x
(*.f64 x #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)

simplify493.0ms (7.6%)

Algorithm
1×egg-herbie
Rules
9064×accelerator-lowering-fma.f32
9064×accelerator-lowering-fma.f64
6574×*-lowering-*.f32
6574×*-lowering-*.f64
2468×cube-prod
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
015258
142258
274258
3213258
4707258
51980258
62707258
73799258
85144258
96027258
107003258
117346258
127464258
137541258
147610258
157757258
08295228
Stop Event
1×iter limit
1×node limit
Counts
60 → 60
Calls
Call 1
Inputs
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
1
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
x
x
x
x
x
x
x
x
x
x
x
x
Outputs
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
x
(+ x (* x (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(+ x (* x (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(+ x (* x (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
1
#s(literal 1 binary64)
(+ 1 (pow y 2))
(+.f64 #s(literal 1 binary64) (*.f64 y y))
(+ 1 (pow y 2))
(+.f64 #s(literal 1 binary64) (*.f64 y y))
(+ 1 (pow y 2))
(+.f64 #s(literal 1 binary64) (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(+.f64 #s(literal 1 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(+.f64 #s(literal 1 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(+.f64 #s(literal 1 binary64) (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(+.f64 #s(literal 1 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(+.f64 #s(literal 1 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(+.f64 #s(literal 1 binary64) (*.f64 y y))
x
x
x
x
x
x
x
x
x
x
x
x

eval66.0ms (1%)

Compiler

Compiled 16237 to 1113 computations (93.1% saved)

prune60.0ms (0.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New4217428
Fresh000
Picked011
Done000
Total4218429
Accuracy
100.0%
Counts
429 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.9%
(fma.f64 (*.f64 x y) y x)
▶95.2%
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 y y))))
94.9%
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 y y))) x))
▶95.1%
(+.f64 (*.f64 x (*.f64 y y)) x)
63.4%
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))))
✓95.1%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
▶49.1%
(*.f64 x (*.f64 y y))
▶50.2%
x
Compiler

Compiled 149 to 86 computations (42.3% saved)

localize102.0ms (1.6%)

Algorithm
1×egg-herbie
Localize:

Found 28 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
#s(literal 1 binary64)
✓cost-diff0
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 y y)))
✓cost-diff0
x
✓cost-diff128
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 y y))))
✓cost-diff0
(*.f64 y y)
✓cost-diff0
x
✓cost-diff0
(*.f64 x (*.f64 y y))
✓cost-diff0
(+.f64 (*.f64 x (*.f64 y y)) x)
✓cost-diff0
y
✓cost-diff0
(*.f64 y y)
✓cost-diff0
x
✓cost-diff0
(*.f64 x (*.f64 y y))
✓cost-diff0
x
✓cost-diff0
y
✓cost-diff0
x
✓cost-diff0
(*.f64 x y)
✓cost-diff6272
(fma.f64 (*.f64 x y) y x)
✓accuracy100.0%
(+.f64 #s(literal 1 binary64) (*.f64 y y))
✓accuracy100.0%
(*.f64 y y)
✓accuracy99.9%
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 y y)))
✓accuracy95.2%
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 y y))))
✓accuracy100.0%
(+.f64 (*.f64 x (*.f64 y y)) x)
✓accuracy100.0%
(*.f64 y y)
✓accuracy88.0%
(*.f64 x (*.f64 y y))
✓accuracy100.0%
(*.f64 y y)
✓accuracy88.0%
(*.f64 x (*.f64 y y))
✓accuracy100.0%
(*.f64 x y)
✓accuracy99.9%
(fma.f64 (*.f64 x y) y x)
Rules
50×*-lowering-*.f32
50×*-lowering-*.f64
22×/-lowering-/.f32
22×/-lowering-/.f64
22×accelerator-lowering-fma.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01247
12147
23047
33947
46647
56647
66747
06742
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(+ (* (* x y) y) x)
(* x y)
x
y
(* x (* y y))
(* y y)
(+ (* x (* y y)) x)
(/ x (/ 1 (+ 1 (* y y))))
(/ 1 (+ 1 (* y y)))
1
(+ 1 (* y y))
Outputs
(+ (* (* x y) y) x)
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(* x y)
(*.f64 x y)
x
y
(* x (* y y))
(*.f64 x (*.f64 y y))
(* y y)
(*.f64 y y)
(+ (* x (* y y)) x)
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(/ x (/ 1 (+ 1 (* y y))))
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(/ 1 (+ 1 (* y y)))
(/.f64 #s(literal 1 binary64) (+.f64 (*.f64 y y) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* y y))
(+.f64 (*.f64 y y) #s(literal 1 binary64))
Results
59.0ms256×0valid
Compiler

Compiled 69 to 12 computations (82.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 19.0ms
ival-mult: 7.0ms (36.9% of total)
<compiled-spec>: 4.0ms (21.1% of total)
ival-add: 4.0ms (21.1% of total)
ival-div: 3.0ms (15.8% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

series17.0ms (0.3%)

Counts
11 → 180
Calls
Call 1
Inputs
#<alt (+ (* (* x y) y) x)>
#<alt (* x y)>
#<alt (* x (* y y))>
#<alt (* y y)>
#<alt (+ (* x (* y y)) x)>
#<alt (/ x (/ 1 (+ 1 (* y y))))>
#<alt (/ 1 (+ 1 (* y y)))>
#<alt (+ 1 (* y y))>
#<alt x>
#<alt y>
#<alt 1>
Outputs
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* -1 (* x (- (* -1 (pow y 2)) 1)))>
#<alt (* -1 (* x (- (* -1 (pow y 2)) 1)))>
#<alt (* -1 (* x (- (* -1 (pow y 2)) 1)))>
#<alt (* -1 (* x (- (* -1 (pow y 2)) 1)))>
#<alt x>
#<alt (+ x (* x (pow y 2)))>
#<alt (+ x (* x (pow y 2)))>
#<alt (+ x (* x (pow y 2)))>
#<alt (* x (pow y 2))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* x (pow y 2))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* -1 (* x (- (* -1 (pow y 2)) 1)))>
#<alt (* -1 (* x (- (* -1 (pow y 2)) 1)))>
#<alt (* -1 (* x (- (* -1 (pow y 2)) 1)))>
#<alt (* -1 (* x (- (* -1 (pow y 2)) 1)))>
#<alt x>
#<alt (+ x (* x (pow y 2)))>
#<alt (+ x (* x (pow y 2)))>
#<alt (+ x (* x (pow y 2)))>
#<alt (* x (pow y 2))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* x (pow y 2))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt x>
#<alt (+ x (* x (pow y 2)))>
#<alt (+ x (* x (pow y 2)))>
#<alt (+ x (* x (pow y 2)))>
#<alt (* x (pow y 2))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* x (pow y 2))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt 1>
#<alt (+ 1 (* -1 (pow y 2)))>
#<alt (+ 1 (* (pow y 2) (- (pow y 2) 1)))>
#<alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1)))>
#<alt (/ 1 (pow y 2))>
#<alt (/ (- 1 (/ 1 (pow y 2))) (pow y 2))>
#<alt (/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))>
#<alt (/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))>
#<alt (/ 1 (pow y 2))>
#<alt (/ (- 1 (/ 1 (pow y 2))) (pow y 2))>
#<alt (/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))>
#<alt (/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))>
#<alt 1>
#<alt (+ 1 (pow y 2))>
#<alt (+ 1 (pow y 2))>
#<alt (+ 1 (pow y 2))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (/ 1 (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ 1 (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ 1 (pow y 2))))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (/ 1 (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ 1 (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ 1 (pow y 2))))>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
Calls

45 calls:

TimeVariablePointExpression
1.0ms
y
@inf
(+ (* (* x y) y) x)
0.0ms
x
@0
(+ (* (* x y) y) x)
0.0ms
x
@inf
(+ (* (* x y) y) x)
0.0ms
x
@-inf
(+ (* (* x y) y) x)
0.0ms
x
@inf
(* x y)

rewrite481.0ms (7.4%)

Algorithm
1×batch-egg-rewrite
Rules
5314×accelerator-lowering-fma.f32
5314×accelerator-lowering-fma.f64
3918×*-lowering-*.f32
3918×*-lowering-*.f64
2290×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01247
17647
243247
3405147
0810542
Stop Event
1×iter limit
1×node limit
Counts
11 → 824
Calls
Call 1
Inputs
(+ (* (* x y) y) x)
(* x y)
(* x (* y y))
(* y y)
(+ (* x (* y y)) x)
(/ x (/ 1 (+ 1 (* y y))))
(/ 1 (+ 1 (* y y)))
(+ 1 (* y y))
x
y
1
Outputs
(+.f64 x (*.f64 x (*.f64 y y)))
(+.f64 x (*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (*.f64 y y))))
(+.f64 x (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 y y)) (-.f64 #s(literal 0 binary64) x)))
(+.f64 (*.f64 x (*.f64 y y)) x)
(+.f64 (/.f64 (*.f64 x (*.f64 y (*.f64 x (*.f64 y (*.f64 y y))))) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(+.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (*.f64 y y))) x)
(+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 y y)) (-.f64 #s(literal 0 binary64) x)) x)
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 y y) #s(literal 1 binary64))) x)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x (-.f64 #s(literal -1 binary64) (*.f64 y y))))
(-.f64 (/.f64 (*.f64 x (*.f64 y (*.f64 x (*.f64 y (*.f64 y y))))) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64)))) (/.f64 (*.f64 x x) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64)))))
(-.f64 (/.f64 (/.f64 (*.f64 x (*.f64 y (*.f64 x (*.f64 y (*.f64 y y))))) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64)))) #s(literal 1 binary64)) (/.f64 (/.f64 (*.f64 x x) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64)))) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (*.f64 y y) #s(literal 1 binary64)))) (*.f64 x (-.f64 #s(literal -1 binary64) (*.f64 y y))))
(-.f64 (/.f64 (*.f64 x x) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y)))) (/.f64 (*.f64 x (*.f64 y (*.f64 x (*.f64 y (*.f64 y y))))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y)))))
(fma.f64 x (*.f64 y y) x)
(fma.f64 x #s(literal 1 binary64) (*.f64 x (*.f64 y y)))
(fma.f64 x #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (*.f64 y y))))
(fma.f64 x #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 y y)) (-.f64 #s(literal 0 binary64) x)))
(fma.f64 x (/.f64 (*.f64 y (*.f64 x (*.f64 y (*.f64 y y)))) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(fma.f64 y (*.f64 x y) x)
(fma.f64 y (/.f64 (*.f64 x (*.f64 x (*.f64 y (*.f64 y y)))) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(fma.f64 y (exp.f64 (log.f64 (*.f64 x y))) x)
(fma.f64 (*.f64 x y) y x)
(fma.f64 (*.f64 x y) (/.f64 (*.f64 x (*.f64 y (*.f64 y y))) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(fma.f64 (*.f64 y y) x x)
(fma.f64 (*.f64 y y) (/.f64 (*.f64 x (*.f64 x (*.f64 y y))) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(fma.f64 (*.f64 x (*.f64 y y)) #s(literal 1 binary64) x)
(fma.f64 (*.f64 x (*.f64 y y)) (/.f64 (*.f64 x (*.f64 y y)) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(fma.f64 #s(literal 1 binary64) x (*.f64 x (*.f64 y y)))
(fma.f64 #s(literal 1 binary64) x (*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (*.f64 y y))))
(fma.f64 #s(literal 1 binary64) x (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 y y)) (-.f64 #s(literal 0 binary64) x)))
(fma.f64 #s(literal 1 binary64) (*.f64 x (*.f64 y y)) x)
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x) (*.f64 x (*.f64 y y)))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x) (*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (*.f64 y y))))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 y y)) (-.f64 #s(literal 0 binary64) x)))
(fma.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64) (*.f64 x (*.f64 y y)))
(fma.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (*.f64 y y))))
(fma.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (*.f64 y y)) (-.f64 #s(literal 0 binary64) x)))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) (*.f64 y y)) x)
(fma.f64 (*.f64 x x) (/.f64 (*.f64 y (*.f64 y (*.f64 y y))) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(fma.f64 (*.f64 y (*.f64 y (*.f64 y y))) (/.f64 (*.f64 x x) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(fma.f64 (*.f64 x (*.f64 y (*.f64 x (*.f64 y (*.f64 y y))))) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(fma.f64 (*.f64 x (*.f64 x (*.f64 y y))) (/.f64 (*.f64 y y) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(fma.f64 (-.f64 #s(literal 0 binary64) (*.f64 y y)) (-.f64 #s(literal 0 binary64) x) x)
(fma.f64 (*.f64 x (*.f64 y (*.f64 y y))) (/.f64 (*.f64 x y) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(fma.f64 (*.f64 x (*.f64 x (*.f64 y (*.f64 y y)))) (/.f64 y (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(fma.f64 (*.f64 y (*.f64 x (*.f64 y (*.f64 y y)))) (/.f64 x (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(fma.f64 (/.f64 (*.f64 x (*.f64 y (*.f64 x (*.f64 y (*.f64 y y))))) (*.f64 x (-.f64 (*.f64 y (*.f64 x (*.f64 y (*.f64 y y)))) x))) (*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(fma.f64 (/.f64 (*.f64 x (*.f64 y (*.f64 x (*.f64 y (*.f64 y y))))) (-.f64 (*.f64 (*.f64 x (*.f64 x (*.f64 y y))) (*.f64 y (*.f64 x (*.f64 y (*.f64 y y))))) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x (*.f64 y (*.f64 x (*.f64 y (*.f64 y y))))) (*.f64 x (*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64))))) (neg.f64 (/.f64 (*.f64 x x) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(fma.f64 (exp.f64 (log.f64 (*.f64 x y))) y x)
(neg.f64 (*.f64 x (-.f64 #s(literal -1 binary64) (*.f64 y y))))
(neg.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)))) (*.f64 x (*.f64 x x))) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 y y)) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64))))))))
(neg.f64 (/.f64 (*.f64 x (-.f64 (*.f64 y (*.f64 x (*.f64 y (*.f64 y y)))) x)) (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 y y) #s(literal 1 binary64))) x)))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)))) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 y y)) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64)))))))
(neg.f64 (/.f64 (*.f64 (*.f64 x (-.f64 #s(literal -1 binary64) (*.f64 y y))) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64)))) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64)))))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 y y) #s(literal 1 binary64))))
(/.f64 (*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 y y) #s(literal 1 binary64))) x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (+.f64 (*.f64 y y) #s(literal -1 binary64)))) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (*.f64 x (-.f64 x (*.f64 y (*.f64 x (*.f64 y (*.f64 y y))))))))
(/.f64 (+.f64 (*.f64 y y) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (+.f64 (*.f64 y y) #s(literal 1 binary64))) x))
(/.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -1 binary64) (+.f64 (*.f64 y y) #s(literal 1 binary64))))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)))) (*.f64 x (*.f64 x x))) (+.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 y y)) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)))) (*.f64 x (*.f64 x x))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 y y)) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64))))))))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)))) (*.f64 x (*.f64 x x))) (*.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) (*.f64 (*.f64 x (*.f64 y y)) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64)))))))
(/.f64 (*.f64 x (-.f64 (*.f64 y (*.f64 x (*.f64 y (*.f64 y y)))) x)) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64))))
(/.f64 (*.f64 x (-.f64 (*.f64 y (*.f64 x (*.f64 y (*.f64 y y)))) x)) (*.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (*.f64 y y) #s(literal -1 binary64)))))
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(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y))) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (+.f64 (*.f64 y y) #s(literal -1 binary64)))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y))) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y y)))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y (*.f64 y y))) (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))))))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y y)))) (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))))
(/.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) (exp.f64 (log.f64 (/.f64 #s(literal -1 binary64) (+.f64 (*.f64 y y) #s(literal 1 binary64))))))
(/.f64 (exp.f64 (log.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)))) (exp.f64 (log.f64 #s(literal -1 binary64))))
(/.f64 (exp.f64 (log1p.f64 (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y))))) (exp.f64 (log1p.f64 (*.f64 (*.f64 y y) (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(/.f64 (exp.f64 (log.f64 (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))))) (exp.f64 (log.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)))))
(/.f64 (exp.f64 (log.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y))))))) (exp.f64 (log.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (+.f64 (*.f64 y y) #s(literal -1 binary64))))))))
(/.f64 (exp.f64 (log.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))))) (exp.f64 (log.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y y))))))
(/.f64 (exp.f64 (log.f64 (+.f64 (*.f64 y (*.f64 y (*.f64 y y))) #s(literal -1 binary64)))) (exp.f64 (log.f64 (+.f64 (*.f64 y y) #s(literal -1 binary64)))))
(pow.f64 (+.f64 (*.f64 y y) #s(literal 1 binary64)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 y y) #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 (*.f64 y y) #s(literal 1 binary64)) #s(literal -1/2 binary64)) #s(literal -2 binary64))
(pow.f64 (*.f64 (+.f64 (*.f64 y y) #s(literal 1 binary64)) (+.f64 (*.f64 y y) #s(literal 1 binary64))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 y y) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 y y) #s(literal 1 binary64)))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (+.f64 (*.f64 y y) #s(literal -1 binary64)) (+.f64 (*.f64 y (*.f64 y (*.f64 y y))) #s(literal -1 binary64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 (*.f64 y y) #s(literal 1 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (log1p.f64 (*.f64 y y))))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log1p.f64 (*.f64 y y)))
(*.f64 #s(literal 1 binary64) (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(*.f64 (+.f64 (*.f64 y y) #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (*.f64 y y)))
(*.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)) #s(literal -1 binary64))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (+.f64 (*.f64 y y) #s(literal -1 binary64))))) #s(literal 1 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (+.f64 (*.f64 y y) #s(literal -1 binary64))))) #s(literal 1 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y y))))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y y))) #s(literal 1 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y y))) #s(literal 1 binary64)))
(*.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (+.f64 (*.f64 y y) #s(literal -1 binary64)))))))
(*.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y y)))))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (+.f64 (*.f64 y y) #s(literal -1 binary64))))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)))))
(*.f64 (+.f64 (*.f64 y (*.f64 y (*.f64 y y))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 y y) #s(literal -1 binary64))))
(*.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (+.f64 (*.f64 y y) #s(literal -1 binary64))))))
(*.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y y))))
(*.f64 (pow.f64 (+.f64 (*.f64 y y) #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (+.f64 (*.f64 y y) #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))) (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y))))) (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y))) (*.f64 (+.f64 (*.f64 y y) #s(literal -1 binary64)) (*.f64 (+.f64 (*.f64 y y) #s(literal -1 binary64)) (+.f64 (*.f64 y y) #s(literal -1 binary64))))))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 (*.f64 y y) (+.f64 (*.f64 y y) #s(literal -1 binary64))) (-.f64 (*.f64 (*.f64 y y) (+.f64 (*.f64 y y) #s(literal -1 binary64))) #s(literal 1 binary64)))))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y)))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (*.f64 (+.f64 (*.f64 y y) #s(literal -1 binary64)) (*.f64 (*.f64 y y) (+.f64 (*.f64 y y) #s(literal -1 binary64))))))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (+.f64 (*.f64 y y) #s(literal -1 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y))))) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 y y) (+.f64 (*.f64 y y) #s(literal 1 binary64)))))
(*.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) (exp.f64 (log.f64 (-.f64 #s(literal -1 binary64) (*.f64 y y)))))
(*.f64 (exp.f64 (log1p.f64 (*.f64 (*.f64 y (*.f64 y y)) (*.f64 y (*.f64 y y))))) (exp.f64 (-.f64 #s(literal 0 binary64) (log1p.f64 (*.f64 (*.f64 y y) (+.f64 (*.f64 y y) #s(literal -1 binary64)))))))
(*.f64 (exp.f64 (log.f64 (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))))) (exp.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 y y))))))
x
(exp.f64 (log.f64 x))
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x))
(neg.f64 (-.f64 #s(literal 0 binary64) x))
(/.f64 x #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (exp.f64 (-.f64 #s(literal 0 binary64) (log.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) #s(literal -1 binary64))
(/.f64 (exp.f64 (log.f64 (-.f64 #s(literal 0 binary64) x))) (exp.f64 (log.f64 #s(literal -1 binary64))))
(pow.f64 x #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
(*.f64 x #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) x)
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x))
(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64))
y
(exp.f64 (log.f64 y))
(pow.f64 y #s(literal 1 binary64))
(pow.f64 (*.f64 y y) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 y) #s(literal 2 binary64))
(*.f64 y #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) y)
(*.f64 (sqrt.f64 y) (sqrt.f64 y))
#s(literal 1 binary64)

simplify451.0ms (6.9%)

Algorithm
1×egg-herbie
Rules
10220×accelerator-lowering-fma.f32
10220×accelerator-lowering-fma.f64
2984×*-lowering-*.f32
2984×*-lowering-*.f64
1546×+-lowering-+.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
043926
1110924
2259920
3773916
42592916
56400916
08200842
Stop Event
1×iter limit
1×node limit
Counts
180 → 180
Calls
Call 1
Inputs
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
1
(+ 1 (* -1 (pow y 2)))
(+ 1 (* (pow y 2) (- (pow y 2) 1)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1)))
(/ 1 (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/ 1 (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
1
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
x
x
x
x
x
x
x
x
x
x
x
x
y
y
y
y
y
y
y
y
y
y
y
y
Outputs
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
x
(+ x (* x (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(+ x (* x (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(+ x (* x (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
x
(+ x (* x (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(+ x (* x (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(+ x (* x (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
x
(+ x (* x (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(+ x (* x (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(+ x (* x (pow y 2)))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow y 2)))
(-.f64 #s(literal 1 binary64) (*.f64 y y))
(+ 1 (* (pow y 2) (- (pow y 2) 1)))
(+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (+.f64 (*.f64 y y) #s(literal -1 binary64)))))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (*.f64 y y)) (+.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 y y))) (*.f64 y y))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) (*.f64 y y))) (*.f64 y y))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 y y))) (*.f64 y y))) (*.f64 y y))) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 y y))) (*.f64 y y))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) (*.f64 y y))) (*.f64 y y))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (*.f64 y y))) (*.f64 y y))) (*.f64 y y))) (*.f64 y y))
1
#s(literal 1 binary64)
(+ 1 (pow y 2))
(+.f64 #s(literal 1 binary64) (*.f64 y y))
(+ 1 (pow y 2))
(+.f64 #s(literal 1 binary64) (*.f64 y y))
(+ 1 (pow y 2))
(+.f64 #s(literal 1 binary64) (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(+.f64 #s(literal 1 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(+.f64 #s(literal 1 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(+.f64 #s(literal 1 binary64) (*.f64 y y))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(+.f64 #s(literal 1 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(+.f64 #s(literal 1 binary64) (*.f64 y y))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(+.f64 #s(literal 1 binary64) (*.f64 y y))
x
x
x
x
x
x
x
x
x
x
x
x
y
y
y
y
y
y
y
y
y
y
y
y

eval306.0ms (4.7%)

Compiler

Compiled 27745 to 1483 computations (94.7% saved)

prune122.0ms (1.9%)

Pruning

7 alts after pruning (3 fresh and 4 done)

PrunedKeptTotal
New140631409
Fresh202
Picked235
Done011
Total141071417
Accuracy
100.0%
Counts
1417 → 7
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.8%
(fma.f64 (*.f64 x y) (pow.f64 (sqrt.f64 y) #s(literal 2 binary64)) x)
▶49.1%
(/.f64 (*.f64 y y) (/.f64 #s(literal 1 binary64) x))
✓95.1%
(+.f64 (*.f64 x (*.f64 y y)) x)
▶53.9%
(*.f64 (*.f64 x y) y)
✓95.1%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
✓49.1%
(*.f64 x (*.f64 y y))
✓50.2%
x
Compiler

Compiled 55 to 34 computations (38.2% saved)

localize132.0ms (2%)

Algorithm
1×egg-herbie
Localize:

Found 21 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
x
✓cost-diff0
(*.f64 x y)
✓cost-diff12864
(pow.f64 (sqrt.f64 y) #s(literal 2 binary64))
✓cost-diff19136
(fma.f64 (*.f64 x y) (pow.f64 (sqrt.f64 y) #s(literal 2 binary64)) x)
✓cost-diff0
(/.f64 #s(literal 1 binary64) x)
✓cost-diff0
y
✓cost-diff0
(*.f64 y y)
✓cost-diff128
(/.f64 (*.f64 y y) (/.f64 #s(literal 1 binary64) x))
✓cost-diff0
y
✓cost-diff0
x
✓cost-diff0
(*.f64 x y)
✓cost-diff0
(*.f64 (*.f64 x y) y)
✓accuracy100.0%
(*.f64 x y)
✓accuracy100.0%
(sqrt.f64 y)
✓accuracy99.9%
(fma.f64 (*.f64 x y) (pow.f64 (sqrt.f64 y) #s(literal 2 binary64)) x)
✓accuracy99.2%
(pow.f64 (sqrt.f64 y) #s(literal 2 binary64))
✓accuracy100.0%
(/.f64 #s(literal 1 binary64) x)
✓accuracy100.0%
(*.f64 y y)
✓accuracy88.0%
(/.f64 (*.f64 y y) (/.f64 #s(literal 1 binary64) x))
✓accuracy100.0%
(*.f64 x y)
✓accuracy99.8%
(*.f64 (*.f64 x y) y)
Rules
104×*-lowering-*.f32
104×*-lowering-*.f64
52×associate-*r*
48×associate-*l*
38×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01336
12733
24133
39033
412933
513833
614033
717233
817233
918133
1018133
1118233
018232
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(* (* x y) y)
(* x y)
x
y
(/ (* y y) (/ 1 x))
(* y y)
(/ 1 x)
1
(+ (* (* x y) (pow (sqrt y) 2)) x)
(pow (sqrt y) 2)
(sqrt y)
2
Outputs
(* (* x y) y)
(*.f64 x (*.f64 y y))
(* x y)
(*.f64 x y)
x
y
(/ (* y y) (/ 1 x))
(*.f64 x (*.f64 y y))
(* y y)
(*.f64 y y)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
(+ (* (* x y) (pow (sqrt y) 2)) x)
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(pow (sqrt y) 2)
y
(sqrt y)
(sqrt.f64 y)
2
#s(literal 2 binary64)
Results
37.0ms256×0valid
Compiler

Compiled 50 to 13 computations (74% saved)

Precisions
Click to see histograms. Total time spent on operations: 21.0ms
ival-mult: 7.0ms (33% of total)
<compiled-spec>: 4.0ms (18.9% of total)
ival-div: 3.0ms (14.2% of total)
ival-pow: 3.0ms (14.2% of total)
ival-sqrt: 2.0ms (9.4% of total)
ival-add: 1.0ms (4.7% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

series13.0ms (0.2%)

Counts
10 → 168
Calls
Call 1
Inputs
#<alt (* (* x y) y)>
#<alt (* x y)>
#<alt (/ (* y y) (/ 1 x))>
#<alt (* y y)>
#<alt (/ 1 x)>
#<alt (pow (sqrt y) 2)>
#<alt (+ (* (* x y) (pow (sqrt y) 2)) x)>
#<alt (sqrt y)>
#<alt x>
#<alt y>
Outputs
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt (* -1 (* y (pow (sqrt -1) 2)))>
#<alt (* -1 (* y (pow (sqrt -1) 2)))>
#<alt (* -1 (* y (pow (sqrt -1) 2)))>
#<alt (* -1 (* y (pow (sqrt -1) 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* x (+ 1 (pow y 2)))>
#<alt (* -1 (* x (- (* -1 (pow y 2)) 1)))>
#<alt (* -1 (* x (- (* -1 (pow y 2)) 1)))>
#<alt (* -1 (* x (- (* -1 (pow y 2)) 1)))>
#<alt (* -1 (* x (- (* -1 (pow y 2)) 1)))>
#<alt x>
#<alt (+ x (* x (pow y 2)))>
#<alt (+ x (* x (pow y 2)))>
#<alt (+ x (* x (pow y 2)))>
#<alt (* x (pow y 2))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* (pow y 2) (+ x (/ x (pow y 2))))>
#<alt (* -1 (* x (* (pow y 2) (pow (sqrt -1) 2))))>
#<alt (* (pow y 2) (+ (* -1 (* x (pow (sqrt -1) 2))) (/ x (pow y 2))))>
#<alt (* (pow y 2) (+ (* -1 (* x (pow (sqrt -1) 2))) (/ x (pow y 2))))>
#<alt (* (pow y 2) (+ (* -1 (* x (pow (sqrt -1) 2))) (/ x (pow y 2))))>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
Calls

42 calls:

TimeVariablePointExpression
2.0ms
y
@-inf
(+ (* (* x y) (pow (sqrt y) 2)) x)
1.0ms
y
@-inf
(pow (sqrt y) 2)
0.0ms
y
@-inf
(sqrt y)
0.0ms
x
@-inf
(/ 1 x)
0.0ms
y
@0
(sqrt y)

rewrite437.0ms (6.7%)

Algorithm
1×batch-egg-rewrite
Rules
6386×accelerator-lowering-fma.f32
6386×accelerator-lowering-fma.f64
3750×*-lowering-*.f32
3750×*-lowering-*.f64
2112×/-lowering-/.f32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01337
16531
234431
3371331
0840130
Stop Event
1×iter limit
1×node limit
Counts
10 → 477
Calls
Call 1
Inputs
(* (* x y) y)
(* x y)
(/ (* y y) (/ 1 x))
(* y y)
(/ 1 x)
(pow (sqrt y) 2)
(+ (* (* x y) (pow (sqrt y) 2)) x)
(sqrt y)
x
y
Outputs
(exp.f64 (log.f64 (*.f64 x (*.f64 y y))))
(exp.f64 (*.f64 (log.f64 (*.f64 x (*.f64 y y))) #s(literal 1 binary64)))
(exp.f64 (-.f64 (log.f64 x) (neg.f64 (*.f64 #s(literal 2 binary64) (log.f64 y)))))
(exp.f64 (-.f64 (log.f64 y) (-.f64 (log.f64 (/.f64 #s(literal 1 binary64) x)) (log.f64 y))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 y y))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) x)) (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 y y))))
(neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (*.f64 y y))))
(/.f64 x (/.f64 #s(literal 1 binary64) (*.f64 y y)))
(/.f64 y (/.f64 #s(literal 1 binary64) (*.f64 x y)))
(/.f64 (*.f64 y y) (/.f64 #s(literal 1 binary64) x))
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(*.f64 (/.f64 (*.f64 (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (*.f64 x (-.f64 (*.f64 y y) #s(literal 1 binary64)))) (-.f64 (*.f64 (*.f64 x (*.f64 y y)) (*.f64 (*.f64 y y) (*.f64 x (*.f64 x (*.f64 y y))))) (*.f64 x (*.f64 x x)))) (+.f64 (*.f64 (*.f64 y y) (*.f64 x (*.f64 x (*.f64 y y)))) (*.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 y)))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 y)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 y) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 1/2 binary64))) (log.f64 y)))
(fabs.f64 (sqrt.f64 y))
(sqrt.f64 y)
(pow.f64 y #s(literal 1/2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 y) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 y y)) #s(literal -1/4 binary64))
(pow.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 y (*.f64 y (*.f64 y y))) #s(literal 1/8 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 y))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.f64 y) #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64)) (log.f64 y))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 y)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 y)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 y)))
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (pow.f64 y #s(literal 1/4 binary64)))
x
(exp.f64 (log.f64 x))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x))
(neg.f64 (-.f64 #s(literal 0 binary64) x))
(/.f64 x #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64))
(/.f64 (sqrt.f64 x) (pow.f64 x #s(literal -1/2 binary64)))
(/.f64 (exp.f64 (log.f64 (-.f64 #s(literal 0 binary64) x))) (exp.f64 (log.f64 #s(literal -1 binary64))))
(/.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) (exp.f64 (log.f64 (/.f64 #s(literal -1 binary64) x))))
(pow.f64 x #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (/.f64 #s(literal 1 binary64) x)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 x))
(*.f64 x #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) x)
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x))
(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64))
(*.f64 (sqrt.f64 x) (sqrt.f64 x))
(*.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) (exp.f64 (log.f64 (-.f64 #s(literal 0 binary64) x))))
y
(exp.f64 (log.f64 y))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (*.f64 #s(literal 1/2 binary64) (log.f64 y))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal -1 binary64)))
(fabs.f64 y)
(sqrt.f64 (*.f64 y y))
(/.f64 y #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) y))
(/.f64 (-.f64 #s(literal 0 binary64) y) #s(literal -1 binary64))
(/.f64 (pow.f64 (-.f64 #s(literal 0 binary64) (*.f64 y y)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64)))
(pow.f64 y #s(literal 1 binary64))
(pow.f64 (*.f64 y y) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 y) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 y y)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 4 binary64))
(pow.f64 (*.f64 y (*.f64 y (*.f64 y y))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 y)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 y)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 y)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (log.f64 y))
(pow.f64 (*.f64 (exp.f64 #s(literal 1/2 binary64)) (exp.f64 #s(literal 1/2 binary64))) (log.f64 y))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 y))
(*.f64 y #s(literal 1 binary64))
(*.f64 (sqrt.f64 y) (sqrt.f64 y))
(*.f64 (sqrt.f64 y) (/.f64 (sqrt.f64 y) #s(literal 1 binary64)))
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (pow.f64 y #s(literal 3/4 binary64)))
(*.f64 (pow.f64 y #s(literal 3/4 binary64)) (pow.f64 y #s(literal 1/4 binary64)))

simplify291.0ms (4.5%)

Algorithm
1×egg-herbie
Rules
4674×accelerator-lowering-fma.f32
4674×accelerator-lowering-fma.f64
3148×*-lowering-*.f32
3148×*-lowering-*.f64
1386×div-sub
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033602
189602
2242602
3690602
42298602
55205602
67225602
08135581
Stop Event
1×iter limit
1×node limit
Counts
168 → 168
Calls
Call 1
Inputs
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
y
y
y
y
y
y
y
y
(* -1 (* y (pow (sqrt -1) 2)))
(* -1 (* y (pow (sqrt -1) 2)))
(* -1 (* y (pow (sqrt -1) 2)))
(* -1 (* y (pow (sqrt -1) 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* -1 (* x (* (pow y 2) (pow (sqrt -1) 2))))
(* (pow y 2) (+ (* -1 (* x (pow (sqrt -1) 2))) (/ x (pow y 2))))
(* (pow y 2) (+ (* -1 (* x (pow (sqrt -1) 2))) (/ x (pow y 2))))
(* (pow y 2) (+ (* -1 (* x (pow (sqrt -1) 2))) (/ x (pow y 2))))
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
x
x
x
x
x
x
x
x
x
x
x
x
y
y
y
y
y
y
y
y
y
y
y
y
Outputs
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
y
y
y
y
y
y
y
y
(* -1 (* y (pow (sqrt -1) 2)))
y
(* -1 (* y (pow (sqrt -1) 2)))
y
(* -1 (* y (pow (sqrt -1) 2)))
y
(* -1 (* y (pow (sqrt -1) 2)))
y
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
x
(+ x (* x (pow y 2)))
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(+ x (* x (pow y 2)))
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(+ x (* x (pow y 2)))
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(* x (pow y 2))
(*.f64 x (*.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(* -1 (* x (* (pow y 2) (pow (sqrt -1) 2))))
(*.f64 x (*.f64 y y))
(* (pow y 2) (+ (* -1 (* x (pow (sqrt -1) 2))) (/ x (pow y 2))))
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(* (pow y 2) (+ (* -1 (* x (pow (sqrt -1) 2))) (/ x (pow y 2))))
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(* (pow y 2) (+ (* -1 (* x (pow (sqrt -1) 2))) (/ x (pow y 2))))
(*.f64 x (+.f64 (*.f64 y y) #s(literal 1 binary64)))
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(sqrt y)
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(sqrt.f64 y)
x
x
x
x
x
x
x
x
x
x
x
x
y
y
y
y
y
y
y
y
y
y
y
y

eval115.0ms (1.8%)

Compiler

Compiled 12844 to 1367 computations (89.4% saved)

prune131.0ms (2%)

Pruning

10 alts after pruning (4 fresh and 6 done)

PrunedKeptTotal
New101741021
Fresh000
Picked123
Done044
Total1018101028
Accuracy
100.0%
Counts
1028 → 10
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶53.7%
(pow.f64 (/.f64 y (pow.f64 x #s(literal -1/2 binary64))) #s(literal 2 binary64))
✓49.1%
(/.f64 (*.f64 y y) (/.f64 #s(literal 1 binary64) x))
▶53.8%
(/.f64 y (/.f64 #s(literal 1 binary64) (*.f64 x y)))
✓95.1%
(+.f64 (*.f64 x (*.f64 y y)) x)
▶51.7%
(*.f64 (pow.f64 y #s(literal 3/2 binary64)) (/.f64 (sqrt.f64 y) (/.f64 #s(literal 1 binary64) x)))
▶51.7%
(*.f64 (*.f64 x (pow.f64 y #s(literal 3/2 binary64))) (sqrt.f64 y))
✓53.9%
(*.f64 (*.f64 x y) y)
✓95.1%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
✓49.1%
(*.f64 x (*.f64 y y))
✓50.2%
x
Compiler

Compiled 84 to 56 computations (33.3% saved)

localize131.0ms (2%)

Algorithm
1×egg-herbie
Localize:

Found 30 expressions of interest:

NewMetricScoreProgram
✓cost-diff0
(pow.f64 x #s(literal -1/2 binary64))
✓cost-diff0
y
✓cost-diff0
(/.f64 y (pow.f64 x #s(literal -1/2 binary64)))
✓cost-diff12800
(pow.f64 (/.f64 y (pow.f64 x #s(literal -1/2 binary64))) #s(literal 2 binary64))
✓cost-diff0
#s(literal 1 binary64)
✓cost-diff0
(/.f64 #s(literal 1 binary64) (*.f64 x y))
✓cost-diff0
y
✓cost-diff128
(/.f64 y (/.f64 #s(literal 1 binary64) (*.f64 x y)))
✓cost-diff0
y
✓cost-diff0
(pow.f64 y #s(literal 3/2 binary64))
✓cost-diff128
(/.f64 (sqrt.f64 y) (/.f64 #s(literal 1 binary64) x))
✓cost-diff128
(*.f64 (pow.f64 y #s(literal 3/2 binary64)) (/.f64 (sqrt.f64 y) (/.f64 #s(literal 1 binary64) x)))
✓cost-diff0
(pow.f64 y #s(literal 3/2 binary64))
✓cost-diff0
x
✓cost-diff0
(*.f64 x (pow.f64 y #s(literal 3/2 binary64)))
✓cost-diff0
(*.f64 (*.f64 x (pow.f64 y #s(literal 3/2 binary64))) (sqrt.f64 y))
✓accuracy100.0%
(pow.f64 x #s(literal -1/2 binary64))
✓accuracy99.6%
(/.f64 y (pow.f64 x #s(literal -1/2 binary64)))
✓accuracy99.6%
(pow.f64 (/.f64 y (pow.f64 x #s(literal -1/2 binary64))) #s(literal 2 binary64))
✓accuracy100.0%
(*.f64 x y)
✓accuracy99.8%
(/.f64 y (/.f64 #s(literal 1 binary64) (*.f64 x y)))
✓accuracy99.6%
(/.f64 #s(literal 1 binary64) (*.f64 x y))
✓accuracy100.0%
(sqrt.f64 y)
✓accuracy100.0%
(pow.f64 y #s(literal 3/2 binary64))
✓accuracy99.5%
(/.f64 (sqrt.f64 y) (/.f64 #s(literal 1 binary64) x))
✓accuracy93.4%
(*.f64 (pow.f64 y #s(literal 3/2 binary64)) (/.f64 (sqrt.f64 y) (/.f64 #s(literal 1 binary64) x)))
✓accuracy100.0%
(sqrt.f64 y)
✓accuracy100.0%
(pow.f64 y #s(literal 3/2 binary64))
✓accuracy99.7%
(*.f64 (*.f64 x (pow.f64 y #s(literal 3/2 binary64))) (sqrt.f64 y))
✓accuracy84.0%
(*.f64 x (pow.f64 y #s(literal 3/2 binary64)))
Rules
98×/-lowering-/.f32
98×/-lowering-/.f64
96×*-lowering-*.f32
96×*-lowering-*.f64
30×associate-/l/
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01971
13465
25965
38965
410465
511965
613065
714465
816165
916265
016265
Stop Event
1×iter limit
1×saturated
Calls
Call 1
Inputs
(* (* x (pow y 3/2)) (sqrt y))
(* x (pow y 3/2))
x
(pow y 3/2)
y
3/2
(sqrt y)
(* (pow y 3/2) (/ (sqrt y) (/ 1 x)))
(/ (sqrt y) (/ 1 x))
(/ 1 x)
1
(/ y (/ 1 (* x y)))
(/ 1 (* x y))
(* x y)
(pow (/ y (pow x -1/2)) 2)
(/ y (pow x -1/2))
(pow x -1/2)
-1/2
2
Outputs
(* (* x (pow y 3/2)) (sqrt y))
(*.f64 (pow.f64 y #s(literal 3/2 binary64)) (*.f64 x (sqrt.f64 y)))
(* x (pow y 3/2))
(*.f64 x (pow.f64 y #s(literal 3/2 binary64)))
x
(pow y 3/2)
(pow.f64 y #s(literal 3/2 binary64))
y
3/2
#s(literal 3/2 binary64)
(sqrt y)
(sqrt.f64 y)
(* (pow y 3/2) (/ (sqrt y) (/ 1 x)))
(*.f64 (pow.f64 y #s(literal 3/2 binary64)) (*.f64 x (sqrt.f64 y)))
(/ (sqrt y) (/ 1 x))
(*.f64 x (sqrt.f64 y))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
(/ y (/ 1 (* x y)))
(*.f64 x (*.f64 y y))
(/ 1 (* x y))
(/.f64 #s(literal 1 binary64) (*.f64 x y))
(* x y)
(*.f64 x y)
(pow (/ y (pow x -1/2)) 2)
(*.f64 x (*.f64 y y))
(/ y (pow x -1/2))
(/.f64 y (pow.f64 x #s(literal -1/2 binary64)))
(pow x -1/2)
(pow.f64 x #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
2
#s(literal 2 binary64)
Results
68.0ms256×0valid
Compiler

Compiled 89 to 20 computations (77.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 41.0ms
ival-pow: 22.0ms (53.4% of total)
ival-div: 8.0ms (19.4% of total)
ival-mult: 7.0ms (17% of total)
ival-sqrt: 2.0ms (4.9% of total)
const: 1.0ms (2.4% of total)
backward-pass: 0.0ms (0% of total)

series30.0ms (0.5%)

Counts
15 → 276
Calls
Call 1
Inputs
#<alt (* x (pow y 3/2))>
#<alt (* (* x (pow y 3/2)) (sqrt y))>
#<alt (pow y 3/2)>
#<alt (sqrt y)>
#<alt (* (pow y 3/2) (/ (sqrt y) (/ 1 x)))>
#<alt (/ (sqrt y) (/ 1 x))>
#<alt (/ 1 (* x y))>
#<alt (/ y (/ 1 (* x y)))>
#<alt (* x y)>
#<alt (pow (/ y (pow x -1/2)) 2)>
#<alt (/ y (pow x -1/2))>
#<alt (pow x -1/2)>
#<alt x>
#<alt y>
#<alt 1>
Outputs
#<alt (* x (sqrt (pow y 3)))>
#<alt (* x (sqrt (pow y 3)))>
#<alt (* x (sqrt (pow y 3)))>
#<alt (* x (sqrt (pow y 3)))>
#<alt (* x (sqrt (pow y 3)))>
#<alt (* x (sqrt (pow y 3)))>
#<alt (* x (sqrt (pow y 3)))>
#<alt (* x (sqrt (pow y 3)))>
#<alt (* x (sqrt (pow y 3)))>
#<alt (* x (sqrt (pow y 3)))>
#<alt (* x (sqrt (pow y 3)))>
#<alt (* x (sqrt (pow y 3)))>
#<alt (* x (sqrt (pow y 3)))>
#<alt (* x (sqrt (pow y 3)))>
#<alt (* x (sqrt (pow y 3)))>
#<alt (* x (sqrt (pow y 3)))>
#<alt (* x (sqrt (pow y 3)))>
#<alt (* x (sqrt (pow y 3)))>
#<alt (* x (sqrt (pow y 3)))>
#<alt (* x (sqrt (pow y 3)))>
#<alt (* (* x (pow (sqrt -1) 2)) (sqrt (pow y 3)))>
#<alt (* (* x (pow (sqrt -1) 2)) (sqrt (pow y 3)))>
#<alt (* (* x (pow (sqrt -1) 2)) (sqrt (pow y 3)))>
#<alt (* (* x (pow (sqrt -1) 2)) (sqrt (pow y 3)))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (* (pow y 2) (pow (sqrt -1) 2)))>
#<alt (* x (* (pow y 2) (pow (sqrt -1) 2)))>
#<alt (* x (* (pow y 2) (pow (sqrt -1) 2)))>
#<alt (* x (* (pow y 2) (pow (sqrt -1) 2)))>
#<alt (sqrt (pow y 3))>
#<alt (sqrt (pow y 3))>
#<alt (sqrt (pow y 3))>
#<alt (sqrt (pow y 3))>
#<alt (sqrt (pow y 3))>
#<alt (sqrt (pow y 3))>
#<alt (sqrt (pow y 3))>
#<alt (sqrt (pow y 3))>
#<alt (* (sqrt (pow y 3)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (pow y 3)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (pow y 3)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (pow y 3)) (pow (sqrt -1) 2))>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (sqrt y)>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt y) (pow (sqrt -1) 2)))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (* (pow y 2) (pow (sqrt -1) 2)))>
#<alt (* x (* (pow y 2) (pow (sqrt -1) 2)))>
#<alt (* x (* (pow y 2) (pow (sqrt -1) 2)))>
#<alt (* x (* (pow y 2) (pow (sqrt -1) 2)))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (sqrt y))>
#<alt (* x (sqrt y))>
#<alt (* x (sqrt y))>
#<alt (* x (sqrt y))>
#<alt (* x (sqrt y))>
#<alt (* x (sqrt y))>
#<alt (* x (sqrt y))>
#<alt (* x (sqrt y))>
#<alt (* -1 (* (* x (pow (sqrt -1) 2)) (sqrt y)))>
#<alt (* -1 (* (* x (pow (sqrt -1) 2)) (sqrt y)))>
#<alt (* -1 (* (* x (pow (sqrt -1) 2)) (sqrt y)))>
#<alt (* -1 (* (* x (pow (sqrt -1) 2)) (sqrt y)))>
#<alt (* x (sqrt y))>
#<alt (* x (sqrt y))>
#<alt (* x (sqrt y))>
#<alt (* x (sqrt y))>
#<alt (* x (sqrt y))>
#<alt (* x (sqrt y))>
#<alt (* x (sqrt y))>
#<alt (* x (sqrt y))>
#<alt (* x (sqrt y))>
#<alt (* x (sqrt y))>
#<alt (* x (sqrt y))>
#<alt (* x (sqrt y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (/ 1 (* x y))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* -1 (/ (* x (pow y 2)) (pow (sqrt -1) 2)))>
#<alt (* -1 (/ (* x (pow y 2)) (pow (sqrt -1) 2)))>
#<alt (* -1 (/ (* x (pow y 2)) (pow (sqrt -1) 2)))>
#<alt (* -1 (/ (* x (pow y 2)) (pow (sqrt -1) 2)))>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* (sqrt x) y)>
#<alt (* -1 (* (sqrt x) y))>
#<alt (* -1 (* (sqrt x) y))>
#<alt (* -1 (* (sqrt x) y))>
#<alt (* -1 (* (sqrt x) y))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt x>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
#<alt y>
Calls

69 calls:

TimeVariablePointExpression
3.0ms
x
@-inf
(pow x -1/2)
1.0ms
x
@-inf
(pow (/ y (pow x -1/2)) 2)
1.0ms
x
@0
(* x (pow y 3/2))
1.0ms
y
@-inf
(pow y 3/2)
1.0ms
x
@-inf
(/ y (pow x -1/2))

rewrite478.0ms (7.3%)

Algorithm
1×batch-egg-rewrite
Rules
2560×*-lowering-*.f32
2560×*-lowering-*.f64
2082×/-lowering-/.f32
2082×/-lowering-/.f64
1892×accelerator-lowering-fma.f32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01967
19053
243352
3272952
0843852
Stop Event
1×iter limit
1×node limit
Counts
15 → 1451
Calls
Call 1
Inputs
(* x (pow y 3/2))
(* (* x (pow y 3/2)) (sqrt y))
(pow y 3/2)
(sqrt y)
(* (pow y 3/2) (/ (sqrt y) (/ 1 x)))
(/ (sqrt y) (/ 1 x))
(/ 1 (* x y))
(/ y (/ 1 (* x y)))
(* x y)
(pow (/ y (pow x -1/2)) 2)
(/ y (pow x -1/2))
(pow x -1/2)
x
y
1
Outputs
(exp.f64 (+.f64 (log.f64 x) (*.f64 #s(literal 3/2 binary64) (log.f64 y))))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (*.f64 (log.f64 y) #s(literal 3/4 binary64)) #s(literal 2 binary64))))
(exp.f64 (+.f64 (log.f64 x) (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 y)) #s(literal 3/4 binary64))))
(exp.f64 (+.f64 (log.f64 x) (+.f64 (*.f64 (log.f64 y) #s(literal 3/4 binary64)) (*.f64 (log.f64 y) #s(literal 3/4 binary64)))))
(exp.f64 (+.f64 (*.f64 #s(literal 3/2 binary64) (log.f64 y)) (log.f64 x)))
(exp.f64 (+.f64 (*.f64 (*.f64 (log.f64 y) #s(literal 3/4 binary64)) #s(literal 2 binary64)) (log.f64 x)))
(exp.f64 (+.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 y)) #s(literal 3/4 binary64)) (log.f64 x)))
(exp.f64 (+.f64 (+.f64 (*.f64 (log.f64 y) #s(literal 3/4 binary64)) (*.f64 (log.f64 y) #s(literal 3/4 binary64))) (log.f64 x)))
(exp.f64 (-.f64 (*.f64 #s(literal 3/2 binary64) (log.f64 y)) (-.f64 #s(literal 0 binary64) (log.f64 x))))
(exp.f64 (-.f64 (*.f64 (*.f64 (log.f64 y) #s(literal 3/4 binary64)) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) (log.f64 x))))
(exp.f64 (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 y)) #s(literal 3/4 binary64)) (-.f64 #s(literal 0 binary64) (log.f64 x))))
(exp.f64 (-.f64 (+.f64 (*.f64 (log.f64 y) #s(literal 3/4 binary64)) (*.f64 (log.f64 y) #s(literal 3/4 binary64))) (-.f64 #s(literal 0 binary64) (log.f64 x))))
(/.f64 (pow.f64 y #s(literal 3/2 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 x (pow.f64 y #s(literal 3/2 binary64))) #s(literal 1 binary64))
(/.f64 (*.f64 (pow.f64 y #s(literal 3/2 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(/.f64 (neg.f64 (pow.f64 y #s(literal 3/2 binary64))) (/.f64 #s(literal -1 binary64) x))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) (pow.f64 y #s(literal 3/2 binary64))) #s(literal -1 binary64))
(/.f64 (*.f64 (pow.f64 y #s(literal 3/2 binary64)) (-.f64 #s(literal 0 binary64) x)) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 3/2 binary64))) (/.f64 #s(literal -1 binary64) x))
(/.f64 (neg.f64 (*.f64 x (pow.f64 y #s(literal 3/2 binary64)))) #s(literal -1 binary64))
(/.f64 (neg.f64 (*.f64 (pow.f64 y #s(literal 3/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) x) (pow.f64 y #s(literal 3/2 binary64)))) #s(literal 1 binary64))
(/.f64 (neg.f64 (*.f64 (pow.f64 y #s(literal 3/2 binary64)) (-.f64 #s(literal 0 binary64) x))) #s(literal 1 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 3/2 binary64)))) (/.f64 #s(literal 1 binary64) x))
(pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 y #s(literal 3/4 binary64))) #s(literal 2 binary64))
(pow.f64 (*.f64 (pow.f64 y #s(literal 3/4 binary64)) (sqrt.f64 x)) #s(literal 2 binary64))
(*.f64 x (pow.f64 y #s(literal 3/2 binary64)))
(*.f64 (pow.f64 y #s(literal 3/2 binary64)) x)
(*.f64 (*.f64 x (pow.f64 y #s(literal 3/2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (*.f64 x (pow.f64 y #s(literal 3/2 binary64))))
(*.f64 #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) x) (pow.f64 y #s(literal 3/2 binary64))))
(*.f64 (pow.f64 y #s(literal 3/4 binary64)) (*.f64 x (pow.f64 y #s(literal 3/4 binary64))))
(*.f64 (pow.f64 y #s(literal 3/8 binary64)) (*.f64 (pow.f64 y #s(literal 3/8 binary64)) (*.f64 x (pow.f64 y #s(literal 3/4 binary64)))))
(*.f64 (*.f64 (pow.f64 y #s(literal 3/2 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(*.f64 (*.f64 x (pow.f64 y #s(literal 3/4 binary64))) (pow.f64 y #s(literal 3/4 binary64)))
(*.f64 (*.f64 (*.f64 x (pow.f64 y #s(literal 3/4 binary64))) (pow.f64 y #s(literal 3/8 binary64))) (pow.f64 y #s(literal 3/8 binary64)))
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(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64)))) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (*.f64 (-.f64 #s(literal 0 binary64) y) (pow.f64 x #s(literal 1/4 binary64))))) (pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64))) #s(literal 3 binary64)))
(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64)))) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (neg.f64 (/.f64 y (pow.f64 x #s(literal -1/4 binary64)))))) (pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64))) #s(literal 3 binary64)))
(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64)))) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 y (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64)))))) (pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64))) #s(literal 3 binary64)))
(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/8 binary64))) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (/.f64 y (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/8 binary64))))) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/8 binary64))))
(/.f64 (neg.f64 (*.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal -1/4 binary64)) y)))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 y (pow.f64 x #s(literal -1/4 binary64))))) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64))))
(/.f64 (neg.f64 (*.f64 (/.f64 y (pow.f64 x #s(literal -1/4 binary64))) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64))))
(/.f64 (neg.f64 (*.f64 (pow.f64 x #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) y))) (neg.f64 (*.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal -1 binary64))))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) y) (pow.f64 x #s(literal 1/4 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64)))))
(/.f64 (neg.f64 (neg.f64 (/.f64 y (pow.f64 x #s(literal -1/4 binary64))))) (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64)))))
(/.f64 (neg.f64 (/.f64 y (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64))))) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64))))
(/.f64 (neg.f64 (/.f64 y (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64))))) (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64)))))
(/.f64 (neg.f64 (/.f64 (/.f64 y (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/8 binary64)))) (neg.f64 (pow.f64 x #s(literal -1/8 binary64))))
(pow.f64 (/.f64 y (pow.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))
(pow.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) y) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) y) y) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (*.f64 x (*.f64 y y)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x (*.f64 y y)) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 x (*.f64 y y)))) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) y) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 x #s(literal -1/4 binary64)) (/.f64 y (pow.f64 x #s(literal -1/4 binary64)))) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 x (*.f64 y y)))))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 x (*.f64 y y))))))
(*.f64 y (sqrt.f64 x))
(*.f64 #s(literal 1 binary64) (/.f64 y (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (/.f64 y (pow.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 y (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) y) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) y)
(*.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) y))
(*.f64 (pow.f64 (*.f64 x (*.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x (*.f64 y y)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (/.f64 y (pow.f64 x #s(literal -1/4 binary64))))
(*.f64 (/.f64 y (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (/.f64 y (pow.f64 x #s(literal -1/4 binary64))) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1/4 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1/4 binary64))) (/.f64 y (pow.f64 x #s(literal -1/4 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1/4 binary64))) (/.f64 y (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64)))))
(*.f64 (/.f64 y (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64)))) (pow.f64 x #s(literal 1/4 binary64)))
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 x)))
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal -1/2 binary64))) (log.f64 x)))
(exp.f64 (-.f64 (*.f64 (log.f64 x) #s(literal -1/4 binary64)) (*.f64 #s(literal 1/4 binary64) (log.f64 x))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (sqrt.f64 x))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) #s(literal -1 binary64))
(/.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64))) (neg.f64 (pow.f64 x #s(literal 1/4 binary64))))
(/.f64 (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 #s(literal -1 binary64))) (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x))))
(/.f64 (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 (-.f64 #s(literal 0 binary64) x))) (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 #s(literal -1 binary64))))
(pow.f64 x #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -1 binary64))
(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(pow.f64 (pow.f64 x #s(literal -1/8 binary64)) #s(literal 4 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal -1/8 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.f64 x) #s(literal -1/4 binary64)))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1/2 binary64)) #s(literal 1 binary64)) (log.f64 x))
(pow.f64 (pow.f64 (exp.f64 #s(literal -1/2 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (log.f64 x)))
(pow.f64 (exp.f64 #s(literal -1/4 binary64)) (*.f64 #s(literal 2 binary64) (log.f64 x)))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (/.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64)))))
(*.f64 (pow.f64 x #s(literal -1/8 binary64)) (pow.f64 x #s(literal -3/8 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64)))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64)))) (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 (pow.f64 x #s(literal -3/8 binary64)) (pow.f64 x #s(literal -1/8 binary64)))
(*.f64 (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 #s(literal -1 binary64))) (pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 (-.f64 #s(literal 0 binary64) x))))
x
(exp.f64 (log.f64 x))
(exp.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 x)) #s(literal -2 binary64)))
(exp.f64 (*.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1/2 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x))
(sqrt.f64 (*.f64 x x))
(neg.f64 (-.f64 #s(literal 0 binary64) x))
(/.f64 x #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64))
(/.f64 (sqrt.f64 x) (pow.f64 x #s(literal -1/2 binary64)))
(/.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))))
(/.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal -3/4 binary64)))
(/.f64 (*.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal -3/4 binary64)))
(/.f64 (*.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64)) (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64)))))
(/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 1/4 binary64))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/4 binary64))))
(/.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (neg.f64 (pow.f64 x #s(literal -3/4 binary64))))
(/.f64 (*.f64 (sqrt.f64 x) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))))
(/.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal -1/4 binary64)))
(/.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) (exp.f64 (log.f64 (/.f64 #s(literal -1 binary64) x))))
(/.f64 (exp.f64 (log.f64 (-.f64 #s(literal 0 binary64) x))) (exp.f64 (log.f64 #s(literal -1 binary64))))
(/.f64 (neg.f64 (*.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64))) (neg.f64 (pow.f64 x #s(literal -3/4 binary64))))
(/.f64 (neg.f64 (*.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -1 binary64))) (neg.f64 (*.f64 (pow.f64 x #s(literal -1/4 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 1/4 binary64)))) (neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/4 binary64)))))
(/.f64 (neg.f64 (*.f64 (sqrt.f64 x) #s(literal -1 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (pow.f64 x #s(literal 3/4 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/4 binary64))))
(pow.f64 x #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal -2 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) #s(literal -2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal -4 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (*.f64 x x) (*.f64 x x)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (*.f64 (log.f64 x) #s(literal -2 binary64)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 x))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (log.f64 x)))
(*.f64 x #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) x)
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x))
(*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64))
(*.f64 (sqrt.f64 x) (sqrt.f64 x))
(*.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) (exp.f64 (log.f64 (-.f64 #s(literal 0 binary64) x))))
y
(exp.f64 (log.f64 y))
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 y)) #s(literal -1 binary64)))
(exp.f64 (+.f64 (*.f64 (log.f64 y) #s(literal 1/4 binary64)) (*.f64 (log.f64 y) #s(literal 3/4 binary64))))
(exp.f64 (+.f64 (*.f64 (log.f64 y) #s(literal 1/2 binary64)) (*.f64 (log.f64 y) #s(literal 1/2 binary64))))
(exp.f64 (+.f64 (*.f64 (log.f64 y) #s(literal 3/4 binary64)) (*.f64 (log.f64 y) #s(literal 1/4 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) y))
(sqrt.f64 (*.f64 y y))
(neg.f64 (-.f64 #s(literal 0 binary64) y))
(/.f64 y #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) y))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) y))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) y)))
(/.f64 (-.f64 #s(literal 0 binary64) y) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) y) (exp.f64 (log.f64 #s(literal -1 binary64))))
(pow.f64 y #s(literal 1 binary64))
(pow.f64 (sqrt.f64 y) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 y #s(literal -1/2 binary64)) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal -1 binary64))
(pow.f64 (pow.f64 y #s(literal 1/4 binary64)) #s(literal 4 binary64))
(pow.f64 (*.f64 (*.f64 y y) (*.f64 y y)) #s(literal 1/4 binary64))
(*.f64 y #s(literal 1 binary64))
(*.f64 (sqrt.f64 y) (sqrt.f64 y))
(*.f64 #s(literal 1 binary64) y)
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) y))
(*.f64 (-.f64 #s(literal 0 binary64) y) #s(literal -1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 y)) (-.f64 #s(literal 0 binary64) (sqrt.f64 y)))
(*.f64 (pow.f64 y #s(literal 3/4 binary64)) (pow.f64 y #s(literal 1/4 binary64)))
(*.f64 (pow.f64 y #s(literal 1/4 binary64)) (pow.f64 y #s(literal 3/4 binary64)))
#s(literal 1 binary64)

simplify279.0ms (4.3%)

Algorithm
1×egg-herbie
Rules
2368×accelerator-lowering-fma.f32
2368×accelerator-lowering-fma.f64
2096×*-lowering-*.f32
2096×*-lowering-*.f64
1446×div-sub
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0341256
1761188
21951176
34841176
420201176
541021176
649831176
756031176
858971176
959701176
1060061176
1169921176
1274641176
1378261176
1478561176
1578621176
1678991176
1779491176
1879971176
1979971176
2079971176
080251176
Stop Event
1×iter limit
1×node limit
Counts
276 → 276
Calls
Call 1
Inputs
(* x (sqrt (pow y 3)))
(* x (sqrt (pow y 3)))
(* x (sqrt (pow y 3)))
(* x (sqrt (pow y 3)))
(* x (sqrt (pow y 3)))
(* x (sqrt (pow y 3)))
(* x (sqrt (pow y 3)))
(* x (sqrt (pow y 3)))
(* x (sqrt (pow y 3)))
(* x (sqrt (pow y 3)))
(* x (sqrt (pow y 3)))
(* x (sqrt (pow y 3)))
(* x (sqrt (pow y 3)))
(* x (sqrt (pow y 3)))
(* x (sqrt (pow y 3)))
(* x (sqrt (pow y 3)))
(* x (sqrt (pow y 3)))
(* x (sqrt (pow y 3)))
(* x (sqrt (pow y 3)))
(* x (sqrt (pow y 3)))
(* (* x (pow (sqrt -1) 2)) (sqrt (pow y 3)))
(* (* x (pow (sqrt -1) 2)) (sqrt (pow y 3)))
(* (* x (pow (sqrt -1) 2)) (sqrt (pow y 3)))
(* (* x (pow (sqrt -1) 2)) (sqrt (pow y 3)))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (* (pow y 2) (pow (sqrt -1) 2)))
(* x (* (pow y 2) (pow (sqrt -1) 2)))
(* x (* (pow y 2) (pow (sqrt -1) 2)))
(* x (* (pow y 2) (pow (sqrt -1) 2)))
(sqrt (pow y 3))
(sqrt (pow y 3))
(sqrt (pow y 3))
(sqrt (pow y 3))
(sqrt (pow y 3))
(sqrt (pow y 3))
(sqrt (pow y 3))
(sqrt (pow y 3))
(* (sqrt (pow y 3)) (pow (sqrt -1) 2))
(* (sqrt (pow y 3)) (pow (sqrt -1) 2))
(* (sqrt (pow y 3)) (pow (sqrt -1) 2))
(* (sqrt (pow y 3)) (pow (sqrt -1) 2))
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(sqrt y)
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
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x
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Outputs
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(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
x
x
x
x
x
x
x
x
x
x
x
x
y
y
y
y
y
y
y
y
y
y
y
y

eval598.0ms (9.2%)

Compiler

Compiled 30773 to 3223 computations (89.5% saved)

prune339.0ms (5.2%)

Pruning

8 alts after pruning (3 fresh and 5 done)

PrunedKeptTotal
New226132264
Fresh000
Picked404
Done156
Total226682274
Accuracy
100.0%
Counts
2274 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
34.5%
(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) y)) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) y) (-.f64 #s(literal 0 binary64) y))) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) y) (/.f64 (/.f64 #s(literal 1 binary64) x) y)))
53.9%
(/.f64 y (/.f64 (/.f64 #s(literal 1 binary64) y) x))
53.8%
(/.f64 y (/.f64 (/.f64 #s(literal 1 binary64) x) y))
✓95.1%
(+.f64 (*.f64 x (*.f64 y y)) x)
✓53.9%
(*.f64 (*.f64 x y) y)
✓95.1%
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
✓49.1%
(*.f64 x (*.f64 y y))
✓50.2%
x
Compiler

Compiled 245 to 96 computations (60.8% saved)

regimes34.0ms (0.5%)

Counts
18 → 1
Calls
Call 1
Inputs
x
(*.f64 x (*.f64 y y))
(*.f64 (*.f64 x y) y)
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(+.f64 (*.f64 x (*.f64 y y)) x)
(/.f64 y (/.f64 #s(literal 1 binary64) (*.f64 x y)))
(/.f64 y (/.f64 (/.f64 #s(literal 1 binary64) x) y))
(/.f64 y (/.f64 (/.f64 #s(literal 1 binary64) y) x))
(/.f64 (*.f64 y y) (/.f64 #s(literal 1 binary64) x))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 y y))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 y y))) x))
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))))
(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) y)) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) y) (-.f64 #s(literal 0 binary64) y))) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) y) (/.f64 (/.f64 #s(literal 1 binary64) x) y)))
(fma.f64 (*.f64 x y) y x)
(pow.f64 (/.f64 y (pow.f64 x #s(literal -1/2 binary64))) #s(literal 2 binary64))
(*.f64 (*.f64 x (pow.f64 y #s(literal 3/2 binary64))) (sqrt.f64 y))
(*.f64 (pow.f64 y #s(literal 3/2 binary64)) (/.f64 (sqrt.f64 y) (/.f64 #s(literal 1 binary64) x)))
(fma.f64 (*.f64 x y) (pow.f64 (sqrt.f64 y) #s(literal 2 binary64)) x)
Outputs
(fma.f64 (*.f64 x y) y x)
Calls

5 calls:

9.0ms
(+.f64 #s(literal 1 binary64) (*.f64 y y))
7.0ms
x
5.0ms
y
5.0ms
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
5.0ms
(*.f64 y y)
Results
AccuracySegmentsBranch
99.9%1x
99.9%1y
99.9%1(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
99.9%1(+.f64 #s(literal 1 binary64) (*.f64 y y))
99.9%1(*.f64 y y)
Compiler

Compiled 27 to 18 computations (33.3% saved)

regimes22.0ms (0.3%)

Counts
13 → 2
Calls
Call 1
Inputs
x
(*.f64 x (*.f64 y y))
(*.f64 (*.f64 x y) y)
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(+.f64 (*.f64 x (*.f64 y y)) x)
(/.f64 y (/.f64 #s(literal 1 binary64) (*.f64 x y)))
(/.f64 y (/.f64 (/.f64 #s(literal 1 binary64) x) y))
(/.f64 y (/.f64 (/.f64 #s(literal 1 binary64) y) x))
(/.f64 (*.f64 y y) (/.f64 #s(literal 1 binary64) x))
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 y y))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 y y))) x))
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 y y))) (-.f64 #s(literal 1 binary64) (*.f64 y (*.f64 y (*.f64 y y)))))
(/.f64 (-.f64 (*.f64 #s(literal 0 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) y)) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) y) (-.f64 #s(literal 0 binary64) y))) (*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) y) (/.f64 (/.f64 #s(literal 1 binary64) x) y)))
Outputs
(/.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 y y))))
(*.f64 (*.f64 x y) y)
Calls

5 calls:

6.0ms
y
4.0ms
x
4.0ms
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
4.0ms
(*.f64 y y)
3.0ms
(+.f64 #s(literal 1 binary64) (*.f64 y y))
Results
AccuracySegmentsBranch
95.2%1x
99.9%2y
99.9%2(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
99.9%2(+.f64 #s(literal 1 binary64) (*.f64 y y))
99.9%2(*.f64 y y)
Compiler

Compiled 27 to 18 computations (33.3% saved)

regimes9.0ms (0.1%)

Counts
9 → 2
Calls
Call 1
Inputs
x
(*.f64 x (*.f64 y y))
(*.f64 (*.f64 x y) y)
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(+.f64 (*.f64 x (*.f64 y y)) x)
(/.f64 y (/.f64 #s(literal 1 binary64) (*.f64 x y)))
(/.f64 y (/.f64 (/.f64 #s(literal 1 binary64) x) y))
(/.f64 y (/.f64 (/.f64 #s(literal 1 binary64) y) x))
(/.f64 (*.f64 y y) (/.f64 #s(literal 1 binary64) x))
Outputs
(+.f64 (*.f64 x (*.f64 y y)) x)
(*.f64 (*.f64 x y) y)
Calls

3 calls:

3.0ms
y
3.0ms
(*.f64 y y)
3.0ms
(+.f64 #s(literal 1 binary64) (*.f64 y y))
Results
AccuracySegmentsBranch
99.9%2y
99.9%2(+.f64 #s(literal 1 binary64) (*.f64 y y))
99.9%2(*.f64 y y)
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes8.0ms (0.1%)

Counts
4 → 2
Calls
Call 1
Inputs
x
(*.f64 x (*.f64 y y))
(*.f64 (*.f64 x y) y)
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
Outputs
(*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y)))
(*.f64 (*.f64 x y) y)
Calls

3 calls:

4.0ms
(*.f64 y y)
2.0ms
y
2.0ms
(+.f64 #s(literal 1 binary64) (*.f64 y y))
Results
AccuracySegmentsBranch
99.9%2y
99.9%2(+.f64 #s(literal 1 binary64) (*.f64 y y))
99.9%2(*.f64 y y)
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0.1%)

Counts
3 → 2
Calls
Call 1
Inputs
x
(*.f64 x (*.f64 y y))
(*.f64 (*.f64 x y) y)
Outputs
x
(*.f64 (*.f64 x y) y)
Calls

2 calls:

2.0ms
y
2.0ms
(*.f64 y y)
Results
AccuracySegmentsBranch
99.5%2y
99.5%2(*.f64 y y)
Compiler

Compiled 8 to 5 computations (37.5% saved)

regimes5.0ms (0.1%)

Counts
2 → 2
Calls
Call 1
Inputs
x
(*.f64 x (*.f64 y y))
Outputs
x
(*.f64 x (*.f64 y y))
Calls

3 calls:

2.0ms
y
2.0ms
x
1.0ms
(*.f64 y y)
Results
AccuracySegmentsBranch
60.4%5x
94.7%2y
94.7%2(*.f64 y y)
Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes14.0ms (0.2%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
x
Outputs
x
Calls

2 calls:

12.0ms
x
1.0ms
y
Results
AccuracySegmentsBranch
50.2%1x
50.2%1y
Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
3.7473612581296687e+111
5.07075317972129e+114
Compiler

Compiled 14 to 10 computations (28.6% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
3.7473612581296687e+111
5.07075317972129e+114
Compiler

Compiled 14 to 10 computations (28.6% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
3.7473612581296687e+111
5.07075317972129e+114
Compiler

Compiled 14 to 10 computations (28.6% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
2.9139260914535742e-16
22103.52515548268
Compiler

Compiled 14 to 10 computations (28.6% saved)

bsearch14.0ms (0.2%)

Algorithm
1×binary-search
Stop Event
1×narrow-enough
Steps
TimeLeftRight
12.0ms
2.9139260914535742e-16
22103.52515548268
Results
7.0ms176×0valid
Compiler

Compiled 124 to 87 computations (29.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-add: 1.0ms (37.8% of total)
ival-mult: 1.0ms (37.8% of total)
const: 0.0ms (0% of total)
backward-pass: 0.0ms (0% of total)

soundness1.0ms (0%)

Stop Event
1×fuel
Compiler

Compiled 89 to 23 computations (74.2% saved)

preprocess55.0ms (0.8%)

Remove

(negabs x)

(abs y)

Compiler

Compiled 478 to 212 computations (55.6% saved)

end0.0ms (0%)

Profiling

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