Details

Time bar (total: 12.4s)

analyze1.9s (15.2%)

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)

sample3.9s (31.2%)

Results
3.3s8256×body128valid
446.0ms1006×body128invalid
Compiler

Compiled 153 to 110 computations (28.1% saved)

simplify197.0ms (1.6%)

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

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.7b
Counts
3 → 2
Alt Table
StatusErrorProgram
7.0b
(/.f32 (fma.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) n0_i (*.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))
0.8b
(+.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))
Compiler

Compiled 146 to 95 computations (34.9% saved)

localize67.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i)
0.1b
(*.f32 (-.f32 1 u) normAngle)
0.4b
(*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
1.4b
(*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))

series122.0ms (1%)

Counts
4 → 96
Calls

4 calls:

63.0ms
(*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i)
30.0ms
(*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
23.0ms
(*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))
5.0ms
(*.f32 (-.f32 1 u) normAngle)

rewrite89.0ms (0.7%)

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:

61.0ms
(*.f32 (-.f32 1 u) normAngle)
7.0ms
(*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i)
7.0ms
(*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
6.0ms
(*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))

simplify117.0ms (0.9%)

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

prune373.0ms (3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2325237
Fresh011
Picked101
Done000
Total2336239
Error
0.0b
Counts
239 → 6
Alt Table
StatusErrorProgram
1.0b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (*.f32 (cbrt.f32 (/.f32 1 (sin.f32 normAngle))) (cbrt.f32 (/.f32 1 (sin.f32 normAngle))))) (cbrt.f32 (/.f32 1 (sin.f32 normAngle)))) n1_i))
7.0b
(/.f32 (fma.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) n0_i (*.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))
0.3b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (-.f32 (+.f32 (*.f32 1/120 (*.f32 (pow.f32 u 5) (pow.f32 normAngle 4))) (+.f32 (*.f32 31/15120 (*.f32 u (pow.f32 normAngle 6))) (+.f32 (*.f32 1/720 (*.f32 (pow.f32 u 5) (pow.f32 normAngle 6))) (+.f32 u (+.f32 (*.f32 7/360 (*.f32 u (pow.f32 normAngle 4))) (*.f32 1/6 (*.f32 u (pow.f32 normAngle 2)))))))) (+.f32 (*.f32 1/6 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 2))) (+.f32 (*.f32 1/5040 (*.f32 (pow.f32 u 7) (pow.f32 normAngle 6))) (+.f32 (*.f32 1/36 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 4))) (*.f32 7/2160 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 6))))))) n1_i))
1.0b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (*.f32 (*.f32 (cbrt.f32 (sin.f32 (*.f32 u normAngle))) (cbrt.f32 (sin.f32 (*.f32 u normAngle)))) (/.f32 (cbrt.f32 (sin.f32 (*.f32 u normAngle))) (sin.f32 normAngle))) n1_i))
0.7b
(+.f32 (-.f32 n0_i (*.f32 u n0_i)) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
0.4b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (fma.f32 (/.f32 u (sin.f32 normAngle)) normAngle (*.f32 (/.f32 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 3)) (sin.f32 normAngle)) -1/6)) n1_i))
Compiler

Compiled 9340 to 4937 computations (47.1% saved)

localize220.0ms (1.8%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f32 1/6 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 2)))
0.1b
(*.f32 (-.f32 1 u) normAngle)
0.2b
(*.f32 1/6 (*.f32 u (pow.f32 normAngle 2)))
0.4b
(*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))

series42.0ms (0.3%)

Counts
2 → 0
Calls

2 calls:

21.0ms
(*.f32 1/6 (*.f32 u (pow.f32 normAngle 2)))
21.0ms
(*.f32 1/6 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 2)))

rewrite12.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
35×add-exp-log_binary32
26×prod-exp_binary32
12×add-cbrt-cube_binary32
pow-exp_binary32
pow-to-exp_binary32
Counts
2 → 48
Calls

2 calls:

5.0ms
(*.f32 1/6 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 2)))
4.0ms
(*.f32 1/6 (*.f32 u (pow.f32 normAngle 2)))

simplify65.0ms (0.5%)

Algorithm
egg-herbie
Rules
995×fma-def_binary32
445×associate-+l+_binary32
392×unswap-sqr_binary32
384×*-commutative_binary32
310×associate-+r+_binary32
Counts
48 → 60
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
081715
1176643
2642643
31223634
42144634
53987634
64994634

prune675.0ms (5.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1751176
Fresh055
Picked101
Done000
Total1766182
Error
0.0b
Counts
182 → 6
Alt Table
StatusErrorProgram
1.0b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (*.f32 (cbrt.f32 (/.f32 1 (sin.f32 normAngle))) (cbrt.f32 (/.f32 1 (sin.f32 normAngle))))) (cbrt.f32 (/.f32 1 (sin.f32 normAngle)))) n1_i))
7.0b
(/.f32 (fma.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) n0_i (*.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))
0.2b
(+.f32 (*.f32 (-.f32 1 u) n0_i) (*.f32 (-.f32 (+.f32 (*.f32 1/120 (*.f32 (pow.f32 u 5) (pow.f32 normAngle 4))) (+.f32 (*.f32 31/15120 (*.f32 u (pow.f32 normAngle 6))) (+.f32 (*.f32 1/720 (*.f32 (pow.f32 u 5) (pow.f32 normAngle 6))) (+.f32 u (+.f32 (*.f32 7/360 (*.f32 u (pow.f32 normAngle 4))) (*.f32 1/6 (*.f32 u (pow.f32 normAngle 2)))))))) (+.f32 (*.f32 1/6 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 2))) (+.f32 (*.f32 1/5040 (*.f32 (pow.f32 u 7) (pow.f32 normAngle 6))) (+.f32 (*.f32 1/36 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 4))) (*.f32 7/2160 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 6))))))) n1_i))
1.0b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (*.f32 (*.f32 (cbrt.f32 (sin.f32 (*.f32 u normAngle))) (cbrt.f32 (sin.f32 (*.f32 u normAngle)))) (/.f32 (cbrt.f32 (sin.f32 (*.f32 u normAngle))) (sin.f32 normAngle))) n1_i))
0.7b
(+.f32 (-.f32 n0_i (*.f32 u n0_i)) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
0.4b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (fma.f32 (/.f32 u (sin.f32 normAngle)) normAngle (*.f32 (/.f32 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 3)) (sin.f32 normAngle)) -1/6)) n1_i))
Compiler

Compiled 19747 to 14518 computations (26.5% saved)

localize249.0ms (2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f32 (pow.f32 u 3) (pow.f32 normAngle 2))
0.1b
(*.f32 1/6 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 2)))
0.1b
(*.f32 (-.f32 1 u) n0_i)
0.2b
(*.f32 1/6 (*.f32 u (pow.f32 normAngle 2)))

series21.0ms (0.2%)

Counts
2 → 12
Calls

2 calls:

17.0ms
(*.f32 (pow.f32 u 3) (pow.f32 normAngle 2))
4.0ms
(*.f32 (-.f32 1 u) n0_i)

rewrite20.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt_binary32
18×associate-*l*_binary32
17×unswap-sqr_binary32
16×add-exp-log_binary32
14×unpow-prod-down_binary32
Counts
2 → 81
Calls

2 calls:

7.0ms
(*.f32 (pow.f32 u 3) (pow.f32 normAngle 2))
5.0ms
(*.f32 (-.f32 1 u) n0_i)

simplify80.0ms (0.6%)

Algorithm
egg-herbie
Rules
653×fma-def_binary32
524×distribute-rgt-in_binary32
494×distribute-lft-in_binary32
360×*-commutative_binary32
304×log-prod_binary32
Counts
93 → 109
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01241199
12441131
28991024
31914942
44910942
55075942

prune688.0ms (5.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1690169
Fresh055
Picked011
Done000
Total1696175
Error
0.0b
Counts
175 → 6
Alt Table
StatusErrorProgram
1.0b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (*.f32 (cbrt.f32 (/.f32 1 (sin.f32 normAngle))) (cbrt.f32 (/.f32 1 (sin.f32 normAngle))))) (cbrt.f32 (/.f32 1 (sin.f32 normAngle)))) n1_i))
7.0b
(/.f32 (fma.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) n0_i (*.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))
0.2b
(+.f32 (*.f32 (-.f32 1 u) n0_i) (*.f32 (-.f32 (+.f32 (*.f32 1/120 (*.f32 (pow.f32 u 5) (pow.f32 normAngle 4))) (+.f32 (*.f32 31/15120 (*.f32 u (pow.f32 normAngle 6))) (+.f32 (*.f32 1/720 (*.f32 (pow.f32 u 5) (pow.f32 normAngle 6))) (+.f32 u (+.f32 (*.f32 7/360 (*.f32 u (pow.f32 normAngle 4))) (*.f32 1/6 (*.f32 u (pow.f32 normAngle 2)))))))) (+.f32 (*.f32 1/6 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 2))) (+.f32 (*.f32 1/5040 (*.f32 (pow.f32 u 7) (pow.f32 normAngle 6))) (+.f32 (*.f32 1/36 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 4))) (*.f32 7/2160 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 6))))))) n1_i))
1.0b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (*.f32 (*.f32 (cbrt.f32 (sin.f32 (*.f32 u normAngle))) (cbrt.f32 (sin.f32 (*.f32 u normAngle)))) (/.f32 (cbrt.f32 (sin.f32 (*.f32 u normAngle))) (sin.f32 normAngle))) n1_i))
0.7b
(+.f32 (-.f32 n0_i (*.f32 u n0_i)) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
0.4b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (fma.f32 (/.f32 u (sin.f32 normAngle)) normAngle (*.f32 (/.f32 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 3)) (sin.f32 normAngle)) -1/6)) n1_i))
Compiler

Compiled 17158 to 12919 computations (24.7% saved)

localize92.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f32 (/.f32 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 3)) (sin.f32 normAngle)) -1/6)
0.1b
(*.f32 (-.f32 1 u) normAngle)
0.4b
(*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
2.9b
(/.f32 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 3)) (sin.f32 normAngle))

series86.0ms (0.7%)

Counts
2 → 28
Calls

2 calls:

45.0ms
(*.f32 (/.f32 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 3)) (sin.f32 normAngle)) -1/6)
40.0ms
(/.f32 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 3)) (sin.f32 normAngle))

rewrite19.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
60×add-exp-log_binary32
29×prod-exp_binary32
20×div-exp_binary32
16×add-cbrt-cube_binary32
12×pow-exp_binary32
Counts
2 → 68
Calls

2 calls:

7.0ms
(*.f32 (/.f32 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 3)) (sin.f32 normAngle)) -1/6)
5.0ms
(/.f32 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 3)) (sin.f32 normAngle))

simplify82.0ms (0.7%)

Algorithm
egg-herbie
Rules
625×fma-neg_binary32
449×*-commutative_binary32
425×associate-/r*_binary32
347×associate-/l/_binary32
319×fma-def_binary32
Counts
96 → 94
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01402109
13321880
214641848
345691846
451061846

prune459.0ms (3.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New2100210
Fresh044
Picked011
Done011
Total2106216
Error
0.0b
Counts
216 → 6
Alt Table
StatusErrorProgram
1.0b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (*.f32 (cbrt.f32 (/.f32 1 (sin.f32 normAngle))) (cbrt.f32 (/.f32 1 (sin.f32 normAngle))))) (cbrt.f32 (/.f32 1 (sin.f32 normAngle)))) n1_i))
7.0b
(/.f32 (fma.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) n0_i (*.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))
0.2b
(+.f32 (*.f32 (-.f32 1 u) n0_i) (*.f32 (-.f32 (+.f32 (*.f32 1/120 (*.f32 (pow.f32 u 5) (pow.f32 normAngle 4))) (+.f32 (*.f32 31/15120 (*.f32 u (pow.f32 normAngle 6))) (+.f32 (*.f32 1/720 (*.f32 (pow.f32 u 5) (pow.f32 normAngle 6))) (+.f32 u (+.f32 (*.f32 7/360 (*.f32 u (pow.f32 normAngle 4))) (*.f32 1/6 (*.f32 u (pow.f32 normAngle 2)))))))) (+.f32 (*.f32 1/6 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 2))) (+.f32 (*.f32 1/5040 (*.f32 (pow.f32 u 7) (pow.f32 normAngle 6))) (+.f32 (*.f32 1/36 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 4))) (*.f32 7/2160 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 6))))))) n1_i))
1.0b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (*.f32 (*.f32 (cbrt.f32 (sin.f32 (*.f32 u normAngle))) (cbrt.f32 (sin.f32 (*.f32 u normAngle)))) (/.f32 (cbrt.f32 (sin.f32 (*.f32 u normAngle))) (sin.f32 normAngle))) n1_i))
0.7b
(+.f32 (-.f32 n0_i (*.f32 u n0_i)) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
0.4b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (fma.f32 (/.f32 u (sin.f32 normAngle)) normAngle (*.f32 (/.f32 (*.f32 (pow.f32 u 3) (pow.f32 normAngle 3)) (sin.f32 normAngle)) -1/6)) n1_i))
Compiler

Compiled 9228 to 5225 computations (43.4% saved)

regimes2.6s (20.9%)

Accuracy

Total 0.3b remaining (85.3%)

Threshold costs 0.3b (85.3%)

Counts
223 → 1
Compiler

Compiled 45038 to 30122 computations (33.1% saved)

simplify9.0ms (0.1%)

Algorithm
egg-herbie
Rules
37×*-commutative_binary32
28×+-commutative_binary32
19×sub-neg_binary32
17×neg-sub0_binary32
17×neg-mul-1_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057139
192139
2103139
3124139
4155139
5195139
6225139
7240139
8246139
9247139
10242139

end261.0ms (2.1%)

Compiler

Compiled 453 to 328 computations (27.6% saved)

Profiling

Loading profile data...