Details

Time bar (total: 9.4s)

analyze1.7s (17.6%)

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)

sample184.0ms (2%)

Algorithm
intervals
Results
47.0ms256×body128valid
14.0ms256×pre128true
1.0ms26×pre128false
Compiler

Compiled 95 to 69 computations (27.4% saved)

simplify196.0ms (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
1.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
8.3b
(/.f32 (fma.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) n0_i (*.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))
1.3b
(+.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)

localize61.0ms (0.7%)

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)
0.2b
(*.f32 (-.f32 1 u) normAngle)
0.5b
(*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
1.8b
(*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))

series113.0ms (1.2%)

Counts
4 → 96
Calls

4 calls:

59.0ms
(*.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)))
6.0ms
(*.f32 (-.f32 1 u) normAngle)

rewrite35.0ms (0.4%)

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:

9.0ms
(*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i)
8.0ms
(*.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)))
5.0ms
(*.f32 (-.f32 1 u) normAngle)

simplify119.0ms (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

prune368.0ms (3.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New22710237
Fresh011
Picked101
Done000
Total22811239
Error
0.1b
Counts
239 → 11
Alt Table
StatusErrorProgram
1.3b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (*.f32 (sqrt.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle))) (sqrt.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
1.2b
(+.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))
8.3b
(/.f32 (fma.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) n0_i (*.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))
1.3b
(+.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))
1.0b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 u n1_i))
1.4b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (*.f32 (*.f32 (cbrt.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle))) (cbrt.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) (cbrt.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
1.2b
(+.f32 (*.f32 (-.f32 1 (fma.f32 1/2 (*.f32 u (*.f32 u (*.f32 normAngle normAngle))) (/.f32 (*.f32 (*.f32 u normAngle) (cos.f32 normAngle)) (sin.f32 normAngle)))) n0_i) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
1.3b
(+.f32 (-.f32 n0_i (*.f32 u n0_i)) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
1.3b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (/.f32 (*.f32 u normAngle) (sin.f32 normAngle)) n1_i))
1.6b
(+.f32 (*.f32 (*.f32 (*.f32 (sin.f32 (-.f32 normAngle (*.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)))) n0_i) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
1.4b
(+.f32 (*.f32 (log.f32 (exp.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))
Compiler

Compiled 9476 to 4975 computations (47.5% saved)

localize44.0ms (0.5%)

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 u n1_i))
0.1b
(*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i)
0.2b
(*.f32 (-.f32 1 u) normAngle)
0.5b
(*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))

series63.0ms (0.7%)

Counts
1 → 48
Calls

1 calls:

63.0ms
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 u n1_i))

rewrite10.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-log-exp_binary32
+-commutative_binary32
flip-+_binary32
*-un-lft-identity_binary32
flip3-+_binary32
Counts
1 → 14
Calls

1 calls:

9.0ms
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 u n1_i))

simplify99.0ms (1.1%)

Algorithm
egg-herbie
Rules
484×cancel-sign-sub-inv_binary32
324×fma-neg_binary32
315×associate-*r*_binary32
267×fma-def_binary32
246×distribute-rgt-out_binary32
Counts
62 → 43
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01942000
16501890
226051818
345811818
449951818
549811818

prune350.0ms (3.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2073210
Fresh6410
Picked101
Done000
Total2147221
Error
0b
Counts
221 → 7
Alt Table
StatusErrorProgram
2.5b
(-.f32 (fma.f32 n1_i u n0_i) (/.f32 (*.f32 (cos.f32 normAngle) (*.f32 u (*.f32 n0_i normAngle))) (sin.f32 normAngle)))
1.3b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (*.f32 (sqrt.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle))) (sqrt.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
1.4b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (*.f32 (*.f32 (cbrt.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle))) (cbrt.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) (cbrt.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
1.3b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (/.f32 (*.f32 u normAngle) (sin.f32 normAngle)) n1_i))
1.6b
(+.f32 (*.f32 (*.f32 (*.f32 (sin.f32 (-.f32 normAngle (*.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)))) n0_i) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
0.9b
(+.f32 n0_i (*.f32 u (-.f32 n1_i n0_i)))
17.0b
(*.f32 (sqrt.f32 (+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 u n1_i))) (sqrt.f32 (+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 u n1_i))))
Compiler

Compiled 7179 to 3846 computations (46.4% saved)

localize17.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.1b
(+.f32 n0_i (*.f32 u (-.f32 n1_i n0_i)))
0.1b
(*.f32 u (-.f32 n1_i n0_i))

series15.0ms (0.2%)

Counts
2 → 72
Calls

2 calls:

8.0ms
(+.f32 n0_i (*.f32 u (-.f32 n1_i n0_i)))
7.0ms
(*.f32 u (-.f32 n1_i n0_i))

rewrite18.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt_binary32
36×prod-diff_binary32
35×*-un-lft-identity_binary32
33×add-cube-cbrt_binary32
26×associate-+r+_binary32
Counts
2 → 92
Calls

2 calls:

6.0ms
(*.f32 u (-.f32 n1_i n0_i))
4.0ms
(+.f32 n0_i (*.f32 u (-.f32 n1_i n0_i)))

simplify99.0ms (1.1%)

Algorithm
egg-herbie
Rules
969×fma-neg_binary32
665×fma-def_binary32
409×distribute-rgt-in_binary32
379×distribute-lft-in_binary32
287×*-commutative_binary32
Counts
164 → 141
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01701649
12881433
210301375
333711321
442301321
550501321

prune145.0ms (1.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1392141
Fresh246
Picked101
Done000
Total1426148
Error
0b
Counts
148 → 6
Alt Table
StatusErrorProgram
1.3b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (/.f32 (*.f32 u normAngle) (sin.f32 normAngle)) n1_i))
17.3b
(+.f32 n0_i (*.f32 (sqrt.f32 (*.f32 u (-.f32 n1_i n0_i))) (sqrt.f32 (*.f32 u (-.f32 n1_i n0_i)))))
1.1b
(+.f32 n0_i (*.f32 (sqrt.f32 u) (*.f32 (sqrt.f32 u) (-.f32 n1_i n0_i))))
2.5b
(-.f32 (fma.f32 n1_i u n0_i) (/.f32 (*.f32 (cos.f32 normAngle) (*.f32 u (*.f32 n0_i normAngle))) (sin.f32 normAngle)))
1.4b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (*.f32 (*.f32 (cbrt.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle))) (cbrt.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) (cbrt.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
1.6b
(+.f32 (*.f32 (*.f32 (*.f32 (sin.f32 (-.f32 normAngle (*.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)))) n0_i) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
Compiler

Compiled 2760 to 767 computations (72.2% saved)

localize25.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(+.f32 n0_i (*.f32 (sqrt.f32 u) (*.f32 (sqrt.f32 u) (-.f32 n1_i n0_i))))
0.3b
(*.f32 (sqrt.f32 u) (-.f32 n1_i n0_i))
0.3b
(*.f32 (sqrt.f32 u) (*.f32 (sqrt.f32 u) (-.f32 n1_i n0_i)))

series46.0ms (0.5%)

Counts
3 → 88
Calls

3 calls:

19.0ms
(*.f32 (sqrt.f32 u) (-.f32 n1_i n0_i))
16.0ms
(+.f32 n0_i (*.f32 (sqrt.f32 u) (*.f32 (sqrt.f32 u) (-.f32 n1_i n0_i))))
11.0ms
(*.f32 (sqrt.f32 u) (*.f32 (sqrt.f32 u) (-.f32 n1_i n0_i)))

rewrite49.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
117×distribute-lft-in_binary32
117×distribute-rgt-in_binary32
90×prod-diff_binary32
85×add-sqr-sqrt_binary32
81×*-un-lft-identity_binary32
Counts
3 → 199
Calls

3 calls:

9.0ms
(+.f32 n0_i (*.f32 (sqrt.f32 u) (*.f32 (sqrt.f32 u) (-.f32 n1_i n0_i))))
9.0ms
(*.f32 (sqrt.f32 u) (*.f32 (sqrt.f32 u) (-.f32 n1_i n0_i)))
7.0ms
(*.f32 (sqrt.f32 u) (-.f32 n1_i n0_i))

simplify94.0ms (1%)

Algorithm
egg-herbie
Rules
840×fma-def_binary32
659×distribute-rgt-in_binary32
623×distribute-lft-in_binary32
259×associate-*l*_binary32
232×associate-*r*_binary32
Counts
287 → 281
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02843244
13732887
214112725
354322725

prune268.0ms (2.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2801281
Fresh145
Picked011
Done000
Total2816287
Error
0b
Counts
287 → 6
Alt Table
StatusErrorProgram
1.1b
(+.f32 n0_i (*.f32 (sqrt.f32 u) (*.f32 (sqrt.f32 u) (-.f32 n1_i n0_i))))
2.5b
(-.f32 (fma.f32 n1_i u n0_i) (/.f32 (*.f32 (cos.f32 normAngle) (*.f32 u (*.f32 n0_i normAngle))) (sin.f32 normAngle)))
1.1b
(+.f32 n0_i (*.f32 (sqrt.f32 (sqrt.f32 u)) (*.f32 (sqrt.f32 (sqrt.f32 u)) (*.f32 (sqrt.f32 u) (-.f32 n1_i n0_i)))))
1.4b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (*.f32 (*.f32 (cbrt.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle))) (cbrt.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) (cbrt.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
1.3b
(+.f32 (*.f32 (*.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (*.f32 (/.f32 (*.f32 u normAngle) (sin.f32 normAngle)) n1_i))
1.6b
(+.f32 (*.f32 (*.f32 (*.f32 (sin.f32 (-.f32 normAngle (*.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)))) n0_i) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
Compiler

Compiled 6869 to 1454 computations (78.8% saved)

regimes2.3s (24.1%)

Accuracy

Total 0.4b remaining (92.4%)

Threshold costs 0.4b (92.4%)

Counts
361 → 1
Compiler

Compiled 44433 to 28367 computations (36.2% 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 (32.4%)

Algorithm
intervals
Results
1.6s8000×body128valid
518.0ms8000×pre128true
55.0ms982×pre128false
Compiler

Compiled 273 to 171 computations (37.4% saved)

Profiling

Loading profile data...