Details

Time bar (total: 16.7s)

analyze3.0s (18.2%)

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)

sample6.4s (38.5%)

Results
5.5s8256×body128valid
750.0ms1042×body128invalid
Compiler

Compiled 153 to 110 computations (28.1% saved)

simplify213.0ms (1.3%)

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

prune8.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.9b
(+.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))
8.7b
(/.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)

localize175.0ms (1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(+.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))
0.1b
(*.f32 (-.f32 1 u) normAngle)
0.4b
(*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
1.6b
(*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))

series323.0ms (1.9%)

Counts
4 → 108
Calls

4 calls:

199.0ms
(+.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))
65.0ms
(*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))
50.0ms
(*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
8.0ms
(*.f32 (-.f32 1 u) normAngle)

rewrite139.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
342×log1p-udef_binary32
194×add-sqr-sqrt_binary32
180×log1p-expm1-u_binary32
180×expm1-log1p-u_binary32
177×add-cbrt-cube_binary32
Counts
4 → 113
Calls

4 calls:

133.0ms
(+.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))
133.0ms
(*.f32 (-.f32 1 u) normAngle)
133.0ms
(*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
133.0ms
(*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01863
138463
2490463
3543963
000
100

simplify154.0ms (0.9%)

Algorithm
egg-herbie
Rules
495×fma-def_binary32
451×associate-*r*_binary32
384×associate-+r+_binary32
284×associate-*l*_binary32
269×+-commutative_binary32
Counts
221 → 168
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03143470
110813419
242913415
350033415

prune531.0ms (3.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1644168
Fresh011
Picked101
Done000
Total1655170
Error
0b
Counts
170 → 5
Alt Table
StatusErrorProgram
0.7b
(fma.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)) n1_i (*.f32 (/.f32 (sin.f32 (*.f32 normAngle (-.f32 1 u))) (sin.f32 normAngle)) n0_i))
0.3b
(-.f32 (fma.f32 1/2 (*.f32 u (*.f32 (*.f32 normAngle normAngle) n0_i)) (fma.f32 u n1_i (fma.f32 1/6 (*.f32 (*.f32 normAngle normAngle) (*.f32 u n1_i)) (fma.f32 1/6 (*.f32 (pow.f32 u 3) (*.f32 (*.f32 normAngle normAngle) n0_i)) n0_i)))) (fma.f32 1/6 (*.f32 u (*.f32 (*.f32 normAngle normAngle) n0_i)) (fma.f32 1/6 (*.f32 (*.f32 (pow.f32 u 3) (*.f32 normAngle normAngle)) n1_i) (fma.f32 u n0_i (*.f32 1/2 (*.f32 (*.f32 u u) (*.f32 (*.f32 normAngle normAngle) n0_i)))))))
1.0b
(+.f32 (*.f32 (/.f32 (sqrt.f32 (sin.f32 (*.f32 normAngle (-.f32 1 u)))) (/.f32 (sin.f32 normAngle) (sqrt.f32 (sin.f32 (*.f32 normAngle (-.f32 1 u)))))) n0_i) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
0.9b
(+.f32 (*.f32 (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (*.f32 normAngle (-.f32 1 u))) (sin.f32 normAngle))) 3) n0_i) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
8.7b
(/.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 6904 to 3684 computations (46.6% saved)

localize225.0ms (1.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f32 (pow.f32 u 3) (*.f32 (*.f32 normAngle normAngle) n0_i))
0.1b
(*.f32 (*.f32 normAngle normAngle) n0_i)
0.1b
(-.f32 (fma.f32 1/2 (*.f32 u (*.f32 (*.f32 normAngle normAngle) n0_i)) (fma.f32 u n1_i (fma.f32 1/6 (*.f32 (*.f32 normAngle normAngle) (*.f32 u n1_i)) (fma.f32 1/6 (*.f32 (pow.f32 u 3) (*.f32 (*.f32 normAngle normAngle) n0_i)) n0_i)))) (fma.f32 1/6 (*.f32 u (*.f32 (*.f32 normAngle normAngle) n0_i)) (fma.f32 1/6 (*.f32 (*.f32 (pow.f32 u 3) (*.f32 normAngle normAngle)) n1_i) (fma.f32 u n0_i (*.f32 1/2 (*.f32 (*.f32 u u) (*.f32 (*.f32 normAngle normAngle) n0_i)))))))
0.1b
(*.f32 (pow.f32 u 3) (*.f32 normAngle normAngle))

series551.0ms (3.3%)

Counts
4 → 132
Calls

4 calls:

437.0ms
(-.f32 (fma.f32 1/2 (*.f32 u (*.f32 (*.f32 normAngle normAngle) n0_i)) (fma.f32 u n1_i (fma.f32 1/6 (*.f32 (*.f32 normAngle normAngle) (*.f32 u n1_i)) (fma.f32 1/6 (*.f32 (pow.f32 u 3) (*.f32 (*.f32 normAngle normAngle) n0_i)) n0_i)))) (fma.f32 1/6 (*.f32 u (*.f32 (*.f32 normAngle normAngle) n0_i)) (fma.f32 1/6 (*.f32 (*.f32 (pow.f32 u 3) (*.f32 normAngle normAngle)) n1_i) (fma.f32 u n0_i (*.f32 1/2 (*.f32 (*.f32 u u) (*.f32 (*.f32 normAngle normAngle) n0_i)))))))
69.0ms
(*.f32 (pow.f32 u 3) (*.f32 (*.f32 normAngle normAngle) n0_i))
26.0ms
(*.f32 (pow.f32 u 3) (*.f32 normAngle normAngle))
18.0ms
(*.f32 (*.f32 normAngle normAngle) n0_i)

rewrite99.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
275×log1p-expm1-u_binary32
275×expm1-log1p-u_binary32
272×add-cbrt-cube_binary32
271×add-log-exp_binary32
270×add-cube-cbrt_binary32
Counts
4 → 63
Calls

4 calls:

93.0ms
(*.f32 (pow.f32 u 3) (*.f32 (*.f32 normAngle normAngle) n0_i))
93.0ms
(*.f32 (*.f32 normAngle normAngle) n0_i)
93.0ms
(-.f32 (fma.f32 1/2 (*.f32 u (*.f32 (*.f32 normAngle normAngle) n0_i)) (fma.f32 u n1_i (fma.f32 1/6 (*.f32 (*.f32 normAngle normAngle) (*.f32 u n1_i)) (fma.f32 1/6 (*.f32 (pow.f32 u 3) (*.f32 (*.f32 normAngle normAngle) n0_i)) n0_i)))) (fma.f32 1/6 (*.f32 u (*.f32 (*.f32 normAngle normAngle) n0_i)) (fma.f32 1/6 (*.f32 (*.f32 (pow.f32 u 3) (*.f32 normAngle normAngle)) n1_i) (fma.f32 u n0_i (*.f32 1/2 (*.f32 (*.f32 u u) (*.f32 (*.f32 normAngle normAngle) n0_i)))))))
93.0ms
(*.f32 (pow.f32 u 3) (*.f32 normAngle normAngle))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
028128
1596125
24955125
000
100

simplify256.0ms (1.5%)

Algorithm
egg-herbie
Rules
735×cancel-sign-sub-inv_binary32
654×associate-*l*_binary32
538×associate-*r*_binary32
328×fma-neg_binary32
288×sub-neg_binary32
Counts
195 → 107
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01444194
14493910
215933486
344473486
450283486

prune602.0ms (3.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1481149
Fresh134
Picked011
Done000
Total1495154
Error
0b
Counts
154 → 5
Alt Table
StatusErrorProgram
0.4b
(+.f32 (*.f32 u (*.f32 (*.f32 normAngle normAngle) (+.f32 (*.f32 1/6 n1_i) (*.f32 n0_i 1/3)))) (+.f32 n0_i (*.f32 u (-.f32 n1_i n0_i))))
0.7b
(fma.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)) n1_i (*.f32 (/.f32 (sin.f32 (*.f32 normAngle (-.f32 1 u))) (sin.f32 normAngle)) n0_i))
0.3b
(-.f32 (fma.f32 1/2 (*.f32 u (*.f32 (*.f32 normAngle normAngle) n0_i)) (fma.f32 u n1_i (fma.f32 1/6 (*.f32 (*.f32 normAngle normAngle) (*.f32 u n1_i)) (fma.f32 1/6 (*.f32 (pow.f32 u 3) (*.f32 (*.f32 normAngle normAngle) n0_i)) n0_i)))) (fma.f32 1/6 (*.f32 u (*.f32 (*.f32 normAngle normAngle) n0_i)) (fma.f32 1/6 (*.f32 (*.f32 (pow.f32 u 3) (*.f32 normAngle normAngle)) n1_i) (fma.f32 u n0_i (*.f32 1/2 (*.f32 (*.f32 u u) (*.f32 (*.f32 normAngle normAngle) n0_i)))))))
0.9b
(+.f32 (*.f32 (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (*.f32 normAngle (-.f32 1 u))) (sin.f32 normAngle))) 3) n0_i) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
8.7b
(/.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 10950 to 4554 computations (58.4% saved)

localize110.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(+.f32 n0_i (*.f32 u (-.f32 n1_i n0_i)))
0.1b
(*.f32 (*.f32 normAngle normAngle) (+.f32 (*.f32 1/6 n1_i) (*.f32 n0_i 1/3)))
0.3b
(*.f32 1/6 n1_i)
0.3b
(*.f32 n0_i 1/3)

series56.0ms (0.3%)

Counts
4 → 84
Calls

4 calls:

35.0ms
(*.f32 (*.f32 normAngle normAngle) (+.f32 (*.f32 1/6 n1_i) (*.f32 n0_i 1/3)))
15.0ms
(+.f32 n0_i (*.f32 u (-.f32 n1_i n0_i)))
3.0ms
(*.f32 n0_i 1/3)
3.0ms
(*.f32 1/6 n1_i)

rewrite106.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
305×expm1-udef_binary32
305×log1p-udef_binary32
172×add-sqr-sqrt_binary32
166×log1p-expm1-u_binary32
166×expm1-log1p-u_binary32
Counts
4 → 89
Calls

4 calls:

102.0ms
(+.f32 n0_i (*.f32 u (-.f32 n1_i n0_i)))
102.0ms
(*.f32 (*.f32 normAngle normAngle) (+.f32 (*.f32 1/6 n1_i) (*.f32 n0_i 1/3)))
102.0ms
(*.f32 1/6 n1_i)
102.0ms
(*.f32 n0_i 1/3)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01532
133830
2442630
3524630
000
100

simplify327.0ms (2%)

Algorithm
egg-herbie
Rules
753×fabs-mul_binary32
751×fma-neg_binary32
745×distribute-rgt-neg-in_binary32
679×cube-prod_binary32
594×distribute-lft-neg-in_binary32
Counts
173 → 108
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
037873
187846
2182846
3330792
4806792
51479792
62161792
73474792
84006792
94069792
104164792
114250792
124373792
133319792
143979792
154408792
164992792
174881792

prune415.0ms (2.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1071108
Fresh123
Picked101
Done011
Total1094113
Error
0b
Counts
113 → 4
Alt Table
StatusErrorProgram
0.3b
(+.f32 (*.f32 u (*.f32 (*.f32 normAngle normAngle) (+.f32 (*.f32 1/6 n1_i) (*.f32 n0_i 1/3)))) (fma.f32 u (-.f32 n1_i n0_i) n0_i))
0.3b
(-.f32 (fma.f32 1/2 (*.f32 u (*.f32 (*.f32 normAngle normAngle) n0_i)) (fma.f32 u n1_i (fma.f32 1/6 (*.f32 (*.f32 normAngle normAngle) (*.f32 u n1_i)) (fma.f32 1/6 (*.f32 (pow.f32 u 3) (*.f32 (*.f32 normAngle normAngle) n0_i)) n0_i)))) (fma.f32 1/6 (*.f32 u (*.f32 (*.f32 normAngle normAngle) n0_i)) (fma.f32 1/6 (*.f32 (*.f32 (pow.f32 u 3) (*.f32 normAngle normAngle)) n1_i) (fma.f32 u n0_i (*.f32 1/2 (*.f32 (*.f32 u u) (*.f32 (*.f32 normAngle normAngle) n0_i)))))))
0.9b
(+.f32 (*.f32 (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (*.f32 normAngle (-.f32 1 u))) (sin.f32 normAngle))) 3) n0_i) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
8.7b
(/.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 3033 to 1369 computations (54.9% saved)

localize190.0ms (1.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(+.f32 (*.f32 1/6 n1_i) (*.f32 n0_i 1/3))
0.1b
(*.f32 (*.f32 normAngle normAngle) (+.f32 (*.f32 1/6 n1_i) (*.f32 n0_i 1/3)))
0.3b
(*.f32 1/6 n1_i)
0.3b
(*.f32 n0_i 1/3)

series7.0ms (0%)

Counts
1 → 24
Calls

1 calls:

7.0ms
(+.f32 (*.f32 1/6 n1_i) (*.f32 n0_i 1/3))

rewrite61.0ms (0.4%)

Algorithm
batch-egg-rewrite
Rules
806×log1p-expm1-u_binary32
806×expm1-log1p-u_binary32
152×log1p-udef_binary32
85×add-sqr-sqrt_binary32
80×add-log-exp_binary32
Counts
1 → 39
Calls

1 calls:

59.0ms
(+.f32 (*.f32 1/6 n1_i) (*.f32 n0_i 1/3))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
088
11728
220488
350828
000
100

simplify18.0ms (0.1%)

Algorithm
egg-herbie
Rules
fma-def_binary32
*-commutative_binary32
+-commutative_binary32
Counts
63 → 42
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08168
112168
215168
315168

prune256.0ms (1.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1020102
Fresh022
Picked011
Done011
Total1024106
Error
0b
Counts
106 → 4
Alt Table
StatusErrorProgram
0.3b
(+.f32 (*.f32 u (*.f32 (*.f32 normAngle normAngle) (+.f32 (*.f32 1/6 n1_i) (*.f32 n0_i 1/3)))) (fma.f32 u (-.f32 n1_i n0_i) n0_i))
0.3b
(-.f32 (fma.f32 1/2 (*.f32 u (*.f32 (*.f32 normAngle normAngle) n0_i)) (fma.f32 u n1_i (fma.f32 1/6 (*.f32 (*.f32 normAngle normAngle) (*.f32 u n1_i)) (fma.f32 1/6 (*.f32 (pow.f32 u 3) (*.f32 (*.f32 normAngle normAngle) n0_i)) n0_i)))) (fma.f32 1/6 (*.f32 u (*.f32 (*.f32 normAngle normAngle) n0_i)) (fma.f32 1/6 (*.f32 (*.f32 (pow.f32 u 3) (*.f32 normAngle normAngle)) n1_i) (fma.f32 u n0_i (*.f32 1/2 (*.f32 (*.f32 u u) (*.f32 (*.f32 normAngle normAngle) n0_i)))))))
0.9b
(+.f32 (*.f32 (pow.f32 (cbrt.f32 (/.f32 (sin.f32 (*.f32 normAngle (-.f32 1 u))) (sin.f32 normAngle))) 3) n0_i) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
8.7b
(/.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 2740 to 1300 computations (52.6% saved)

regimes2.3s (13.4%)

Accuracy

Total 0.3b remaining (95%)

Threshold costs 0.3b (95%)

Counts
196 → 1
Compiler

Compiled 29463 to 18907 computations (35.8% saved)

simplify5.0ms (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
01629
12429
22929
33129
43229
53229

end180.0ms (1.1%)

Compiler

Compiled 195 to 113 computations (42.1% saved)

Profiling

Loading profile data...