Details

Time bar (total: 9.1s)

analyze1.6s (17.4%)

Algorithm
search
Search
TrueOtherFalseIter
0%0.8%99.2%0
0%0.8%99.2%1
0%0.8%99.2%2
0%0.8%99.2%3
0%0.8%99.2%4
0%0.8%99.2%5
0.2%0.4%99.4%6
0.2%0.4%99.4%7
0.2%0.4%99.4%8
0.2%0.4%99.4%9
0.3%0.2%99.5%10
0.3%0.2%99.5%11
0.3%0.2%99.5%12
0.3%0.2%99.5%13
0.3%0.1%99.6%14
Compiler

Compiled 62 to 45 computations (27.4% saved)

sample196.0ms (2.2%)

Algorithm
intervals
Results
47.0ms256×body128valid
15.0ms256×pre128true
2.0ms38×pre128false
Compiler

Compiled 95 to 69 computations (27.4% saved)

simplify194.0ms (2.1%)

Algorithm
egg-herbie
Rules
2213×fma-def_binary32
1110×div-sub_binary32
1069×fma-neg_binary32
619×times-frac_binary32
350×sub-neg_binary32
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01837
13831
27831
313726
420326
523226
627426
737226
843226
952326
1066626
11112126
12205126
13203426
14209226
15241726
16272226
17289726
18216926
19243926
20229926
21229926
22229926
23229926
24229926
25229926
26211426

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.6b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.7b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
9.0b
(/.f32 (fma.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) n0_i (*.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))
Compiler

Compiled 146 to 95 computations (34.9% saved)

localize56.0ms (0.6%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f32 (-.f32 1 u) normAngle)
0.2b
(*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i)
0.4b
(*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
1.2b
(*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))

series111.0ms (1.2%)

Counts
4 → 96
Calls

4 calls:

58.0ms
(*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i)
27.0ms
(*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
22.0ms
(*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))
4.0ms
(*.f32 (-.f32 1 u) normAngle)

rewrite42.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt_binary32
39×add-exp-log_binary32
32×associate-*r*_binary32
28×*-un-lft-identity_binary32
25×add-cbrt-cube_binary32
Counts
4 → 127
Calls

4 calls:

10.0ms
(*.f32 (-.f32 1 u) normAngle)
9.0ms
(*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))
7.0ms
(*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
7.0ms
(*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i)

simplify115.0ms (1.3%)

Algorithm
egg-herbie
Rules
518×associate-*r*_binary32
451×associate-*l*_binary32
394×fma-def_binary32
309×*-commutative_binary32
269×associate-+r+_binary32
Counts
223 → 237
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04104670
111994259
244154255
350524255

prune353.0ms (3.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New22710237
Fresh011
Picked101
Done000
Total22811239
Error
0.0b
Counts
239 → 11
Alt Table
StatusErrorProgram
9.0b
(/.f32 (fma.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) n0_i (*.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))
18.3b
(+.f32 (exp.f32 (log.f32 (*.f32 (/.f32 (sin.f32 (-.f32 normAngle (*.f32 u normAngle))) (sin.f32 normAngle)) n0_i))) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
1.0b
(+.f32 (*.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (*.f32 (cbrt.f32 (/.f32 1 (sin.f32 normAngle))) (cbrt.f32 (/.f32 1 (sin.f32 normAngle))))) (cbrt.f32 (/.f32 1 (sin.f32 normAngle)))) n0_i) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
0.6b
(+.f32 (-.f32 n0_i (*.f32 u n0_i)) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
5.9b
(+.f32 n0_i (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
0.7b
(+.f32 (*.f32 (/.f32 (sin.f32 (-.f32 normAngle (*.f32 u normAngle))) (sin.f32 normAngle)) n0_i) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
0.7b
(+.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 n0_i (sin.f32 normAngle))) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
0.8b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 u n1_i))
5.7b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
1.0b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (exp.f32 (log.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
0.6b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
Compiler

Compiled 9390 to 4961 computations (47.2% saved)

localize81.0ms (0.9%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f32 (-.f32 1 u) normAngle)
0.2b
(*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i)
0.4b
(*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
1.1b
(/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle))

series24.0ms (0.3%)

Counts
1 → 8
Calls

1 calls:

23.0ms
(/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle))

rewrite5.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary32
times-frac_binary32
add-sqr-sqrt_binary32
add-cube-cbrt_binary32
associate-/r*_binary32
Counts
1 → 29
Calls

1 calls:

3.0ms
(/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle))

simplify66.0ms (0.7%)

Algorithm
egg-herbie
Rules
579×associate-*r*_binary32
577×associate-*l*_binary32
538×times-frac_binary32
489×fma-def_binary32
252×associate-+l+_binary32
Counts
37 → 46
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0127931
1329877
21052840
34802831
45721831

prune322.0ms (3.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2094213
Fresh4610
Picked101
Done000
Total21410224
Error
0.0b
Counts
224 → 10
Alt Table
StatusErrorProgram
0.7b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (log1p.f32 (expm1.f32 (/.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sqrt.f32 (sin.f32 normAngle))) (sqrt.f32 (sin.f32 normAngle))))) n1_i))
0.8b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 u n1_i))
9.0b
(/.f32 (fma.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) n0_i (*.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))
18.3b
(+.f32 (exp.f32 (log.f32 (*.f32 (/.f32 (sin.f32 (-.f32 normAngle (*.f32 u normAngle))) (sin.f32 normAngle)) n0_i))) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
1.0b
(+.f32 (*.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (*.f32 (cbrt.f32 (/.f32 1 (sin.f32 normAngle))) (cbrt.f32 (/.f32 1 (sin.f32 normAngle))))) (cbrt.f32 (/.f32 1 (sin.f32 normAngle)))) n0_i) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
5.9b
(+.f32 n0_i (*.f32 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
0.6b
(+.f32 (-.f32 n0_i (*.f32 u n0_i)) (*.f32 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
0.7b
(+.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 n0_i (sin.f32 normAngle))) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
0.6b
(+.f32 (*.f32 (/.f32 (sin.f32 (-.f32 normAngle (*.f32 u normAngle))) (sin.f32 normAngle)) n0_i) (*.f32 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
5.7b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
Compiler

Compiled 8606 to 3862 computations (55.1% saved)

localize50.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(log1p.f32 (expm1.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle))))
0.0b
(-.f32 n0_i (*.f32 u n0_i))
0.1b
(+.f32 (-.f32 n0_i (*.f32 u n0_i)) (*.f32 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
1.1b
(/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle))

series75.0ms (0.8%)

Counts
3 → 87
Calls

3 calls:

49.0ms
(+.f32 (-.f32 n0_i (*.f32 u n0_i)) (*.f32 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
21.0ms
(log1p.f32 (expm1.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle))))
4.0ms
(-.f32 n0_i (*.f32 u n0_i))

rewrite10.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
10×add-log-exp_binary32
*-un-lft-identity_binary32
add-sqr-sqrt_binary32
add-cube-cbrt_binary32
prod-diff_binary32
Counts
3 → 56
Calls

3 calls:

5.0ms
(+.f32 (-.f32 n0_i (*.f32 u n0_i)) (*.f32 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
2.0ms
(-.f32 n0_i (*.f32 u n0_i))
0.0ms
(log1p.f32 (expm1.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle))))

simplify98.0ms (1.1%)

Algorithm
egg-herbie
Rules
524×fma-neg_binary32
521×cancel-sign-sub-inv_binary32
240×fma-def_binary32
219×associate-*r*_binary32
206×distribute-rgt-in_binary32
Counts
143 → 121
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02282866
16952676
224232599
345862597
449452597

prune205.0ms (2.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1616167
Fresh819
Picked101
Done000
Total1707177
Error
0b
Counts
177 → 7
Alt Table
StatusErrorProgram
1.0b
(fma.f32 (*.f32 (cbrt.f32 (-.f32 n0_i (*.f32 u n0_i))) (cbrt.f32 (-.f32 n0_i (*.f32 u n0_i)))) (cbrt.f32 (-.f32 n0_i (*.f32 u n0_i))) (*.f32 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
0.6b
(+.f32 (*.f32 (/.f32 (sin.f32 (-.f32 normAngle (*.f32 u normAngle))) (sin.f32 normAngle)) n0_i) (*.f32 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
5.6b
(+.f32 (-.f32 n0_i (*.f32 u n0_i)) (*.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
0.4b
(+.f32 (-.f32 n0_i (*.f32 u n0_i)) (*.f32 (+.f32 u (*.f32 (*.f32 (*.f32 normAngle normAngle) 1/6) (-.f32 u (pow.f32 u 3)))) n1_i))
0.4b
(-.f32 (+.f32 (fma.f32 n1_i u n0_i) (*.f32 n1_i (*.f32 (*.f32 (*.f32 normAngle normAngle) 1/6) (-.f32 u (pow.f32 u 3))))) (*.f32 u n0_i))
0.7b
(+.f32 n0_i (*.f32 u (-.f32 n1_i n0_i)))
0.6b
(fma.f32 n0_i (-.f32 1 u) (*.f32 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
Compiler

Compiled 4972 to 1695 computations (65.9% saved)

localize52.0ms (0.6%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f32 n1_i (*.f32 (*.f32 (*.f32 normAngle normAngle) 1/6) (-.f32 u (pow.f32 u 3))))
0.1b
(-.f32 (+.f32 (fma.f32 n1_i u n0_i) (*.f32 n1_i (*.f32 (*.f32 (*.f32 normAngle normAngle) 1/6) (-.f32 u (pow.f32 u 3))))) (*.f32 u n0_i))
0.1b
(*.f32 (*.f32 (*.f32 normAngle normAngle) 1/6) (-.f32 u (pow.f32 u 3)))
0.2b
(*.f32 (*.f32 normAngle normAngle) 1/6)

series181.0ms (2%)

Counts
4 → 120
Calls

4 calls:

90.0ms
(-.f32 (+.f32 (fma.f32 n1_i u n0_i) (*.f32 n1_i (*.f32 (*.f32 (*.f32 normAngle normAngle) 1/6) (-.f32 u (pow.f32 u 3))))) (*.f32 u n0_i))
54.0ms
(*.f32 n1_i (*.f32 (*.f32 (*.f32 normAngle normAngle) 1/6) (-.f32 u (pow.f32 u 3))))
32.0ms
(*.f32 (*.f32 (*.f32 normAngle normAngle) 1/6) (-.f32 u (pow.f32 u 3)))
4.0ms
(*.f32 (*.f32 normAngle normAngle) 1/6)

rewrite103.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
245×distribute-lft-in_binary32
245×distribute-rgt-in_binary32
219×prod-diff_binary32
161×add-sqr-sqrt_binary32
156×*-un-lft-identity_binary32
Counts
4 → 396
Calls

4 calls:

21.0ms
(*.f32 n1_i (*.f32 (*.f32 (*.f32 normAngle normAngle) 1/6) (-.f32 u (pow.f32 u 3))))
15.0ms
(*.f32 (*.f32 (*.f32 normAngle normAngle) 1/6) (-.f32 u (pow.f32 u 3)))
5.0ms
(-.f32 (+.f32 (fma.f32 n1_i u n0_i) (*.f32 n1_i (*.f32 (*.f32 (*.f32 normAngle normAngle) 1/6) (-.f32 u (pow.f32 u 3))))) (*.f32 u n0_i))
4.0ms
(*.f32 (*.f32 normAngle normAngle) 1/6)

simplify293.0ms (3.2%)

Algorithm
egg-herbie
Rules
841×fma-def_binary32
519×distribute-rgt-in_binary32
460×distribute-lft-in_binary32
411×*-commutative_binary32
183×cancel-sign-sub-inv_binary32
Counts
516 → 413
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
054417455
186014391
2182912375
3492212375

prune627.0ms (6.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New4121413
Fresh156
Picked011
Done000
Total4137420
Error
0b
Counts
420 → 7
Alt Table
StatusErrorProgram
1.0b
(fma.f32 (*.f32 (cbrt.f32 (-.f32 n0_i (*.f32 u n0_i))) (cbrt.f32 (-.f32 n0_i (*.f32 u n0_i)))) (cbrt.f32 (-.f32 n0_i (*.f32 u n0_i))) (*.f32 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
0.5b
(+.f32 (fma.f32 1/6 (*.f32 (*.f32 normAngle normAngle) (*.f32 u n1_i)) n0_i) (*.f32 u (-.f32 n1_i n0_i)))
0.6b
(+.f32 (*.f32 (/.f32 (sin.f32 (-.f32 normAngle (*.f32 u normAngle))) (sin.f32 normAngle)) n0_i) (*.f32 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
5.6b
(+.f32 (-.f32 n0_i (*.f32 u n0_i)) (*.f32 (log.f32 (exp.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
0.4b
(+.f32 (-.f32 n0_i (*.f32 u n0_i)) (*.f32 (+.f32 u (*.f32 (*.f32 (*.f32 normAngle normAngle) 1/6) (-.f32 u (pow.f32 u 3)))) n1_i))
0.4b
(-.f32 (+.f32 (fma.f32 n1_i u n0_i) (*.f32 n1_i (*.f32 (*.f32 (*.f32 normAngle normAngle) 1/6) (-.f32 u (pow.f32 u 3))))) (*.f32 u n0_i))
0.6b
(fma.f32 n0_i (-.f32 1 u) (*.f32 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
Compiler

Compiled 17393 to 8447 computations (51.4% saved)

regimes1.2s (13.3%)

Accuracy

Total 0.4b remaining (94.3%)

Threshold costs 0.4b (94.3%)

Counts
190 → 1
Compiler

Compiled 27358 to 18137 computations (33.7% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary32
+-commutative_binary32
sub-neg_binary32
neg-sub0_binary32
neg-mul-1_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02452
13552
23952
34152
44252
54152

end1.0ms (0%)

Compiler

Compiled 38 to 25 computations (34.2% saved)

sample3.0s (33.4%)

Algorithm
intervals
Results
1.6s8000×body128valid
492.0ms8000×pre128true
59.0ms1023×pre128false
Compiler

Compiled 278 to 178 computations (36% saved)

Profiling

Loading profile data...