Details

analyze1.8s (11.9%)

Algorithm

1×

Search

True	Other	False	Iter
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)

sample3.6s (24.2%)

Results

3.1s	8256×	body	128	valid
423.0ms	1114×	body	128	invalid

Compiler

Compiled 153 to 110 computations (28.1% saved)

simplify202.0ms (1.3%)

Algorithm

1×	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)

Iter	Nodes	Cost
0	18	37
1	38	31
2	78	31
3	137	26
4	203	26
5	232	26
6	274	26
7	372	26
8	432	26
9	523	26
10	666	26
11	1121	26
12	2051	26
13	2034	26
14	2092	26
15	2417	26
16	2722	26
17	2897	26
18	2169	26
19	2439	26
20	2299	26
21	2299	26
22	2299	26
23	2299	26
24	2299	26
25	2299	26
26	2114	26

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

1.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	9.5b	(/.f32 (fma.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) n0_i (.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))
▶	1.2b	(+.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))

Status

Error

Program

9.5b

(/.f32 (fma.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) n0_i (*.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (sin.f32 normAngle))

▶

1.2b

(+.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)

localize62.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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)
✓	0.8b	(.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
✓	2.5b	(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))

series109.0ms (0.7%)

Counts

4 → 96

Calls

4 calls:

58.0ms	(.f32 (.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i)
26.0ms	(.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
21.0ms	(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))
4.0ms	(*.f32 (-.f32 1 u) normAngle)

rewrite33.0ms (0.2%)

Algorithm

1×	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:

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)))
5.0ms	(*.f32 (-.f32 1 u) normAngle)

simplify111.0ms (0.7%)

Algorithm

1×	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)

Iter	Nodes	Cost
0	410	4670
1	1199	4259
2	4415	4255
3	5052	4255

prune385.0ms (2.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	229	8	237
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	230	9	239

Error

0.4b

Counts

239 → 9

Alt Table

Status	Error	Program
	9.5b	(/.f32 (fma.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) n0_i (.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (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 (sin.f32 (.f32 u normAngle)) (/.f32 1 (.f32 (cbrt.f32 (sin.f32 normAngle)) (cbrt.f32 (sin.f32 normAngle))))) (/.f32 1 (cbrt.f32 (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 (sqrt.f32 (sin.f32 (.f32 u normAngle))) (.f32 (sqrt.f32 (sin.f32 (.f32 u normAngle))) (/.f32 1 (sin.f32 normAngle)))) n1_i))
	9.4b	(+.f32 (cbrt.f32 (pow.f32 (.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle)) n0_i) 3)) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	1.4b	(+.f32 (.f32 (.f32 (sqrt.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle))) (/.f32 (sqrt.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))
	1.3b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (+.f32 1 (sqrt.f32 u)) (.f32 (-.f32 1 (sqrt.f32 u)) normAngle))) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	3.0b	(+.f32 (-.f32 (fma.f32 1/6 (/.f32 (.f32 (cos.f32 normAngle) (.f32 (pow.f32 u 3) (.f32 (pow.f32 normAngle 3) n0_i))) (sin.f32 normAngle)) n0_i) (fma.f32 1/2 (.f32 (.f32 u u) (.f32 normAngle (.f32 normAngle n0_i))) (/.f32 (.f32 (cos.f32 normAngle) (.f32 u (.f32 normAngle n0_i))) (sin.f32 normAngle)))) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	1.2b	(+.f32 (-.f32 n0_i (.f32 u n0_i)) (.f32 (.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
▶	0.7b	(+.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))

Compiler

Compiled 9568 to 5079 computations (46.9% saved)

localize216.0ms (1.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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)))
	0.8b	(.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))

series31.0ms (0.2%)

Counts

2 → 0

Calls

2 calls:

19.0ms	(.f32 1/6 (.f32 (pow.f32 u 3) (pow.f32 normAngle 2)))
11.0ms	(.f32 1/6 (.f32 u (pow.f32 normAngle 2)))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-exp-log_binary32`
26×	`prod-exp_binary32`
12×	`add-cbrt-cube_binary32`
7×	`pow-exp_binary32`
7×	`pow-to-exp_binary32`

Counts

2 → 48

Calls

2 calls:

6.0ms	(.f32 1/6 (.f32 (pow.f32 u 3) (pow.f32 normAngle 2)))
5.0ms	(.f32 1/6 (.f32 u (pow.f32 normAngle 2)))

simplify63.0ms (0.4%)

Algorithm

1×	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)

Iter	Nodes	Cost
0	81	715
1	176	643
2	642	643
3	1223	634
4	2144	634
5	3987	634
6	4994	634

prune717.0ms (4.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	172	4	176
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	175	10	185

Error

0.0b

Counts

185 → 10

Alt Table

Status	Error	Program
	9.5b	(/.f32 (fma.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) n0_i (.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (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 (sin.f32 (.f32 u normAngle)) (/.f32 1 (.f32 (cbrt.f32 (sin.f32 normAngle)) (cbrt.f32 (sin.f32 normAngle))))) (/.f32 1 (cbrt.f32 (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 (sqrt.f32 (sin.f32 (.f32 u normAngle))) (.f32 (sqrt.f32 (sin.f32 (.f32 u normAngle))) (/.f32 1 (sin.f32 normAngle)))) n1_i))
	0.8b	(+.f32 (.f32 (.f32 (sin.f32 (/.f32 (.f32 normAngle (-.f32 1 (.f32 u u))) (+.f32 1 u))) (/.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))
	1.2b	(+.f32 (-.f32 n0_i (.f32 u n0_i)) (.f32 (.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	9.4b	(+.f32 (cbrt.f32 (pow.f32 (.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle)) n0_i) 3)) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	3.0b	(+.f32 (-.f32 (fma.f32 1/6 (/.f32 (.f32 (cos.f32 normAngle) (.f32 (pow.f32 u 3) (.f32 (pow.f32 normAngle 3) n0_i))) (sin.f32 normAngle)) n0_i) (fma.f32 1/2 (.f32 (.f32 u u) (.f32 normAngle (.f32 normAngle n0_i))) (/.f32 (.f32 (cos.f32 normAngle) (.f32 u (.f32 normAngle n0_i))) (sin.f32 normAngle)))) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
▶	0.2b	(+.f32 (.f32 (+.f32 (+.f32 (.f32 (.f32 normAngle normAngle) (+.f32 (.f32 1/6 (pow.f32 u 3)) (.f32 u 1/3))) (.f32 (pow.f32 normAngle 4) (+.f32 (.f32 u 1/45) (.f32 1/24 (pow.f32 u 4))))) (-.f32 1 (fma.f32 1/120 (.f32 (pow.f32 u 5) (pow.f32 normAngle 4)) (+.f32 u (fma.f32 (.f32 (pow.f32 u 3) (pow.f32 normAngle 4)) 1/18 (.f32 1/2 (.f32 u (.f32 u (.f32 normAngle 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))
	0.8b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (+.f32 1 (sqrt.f32 u)) (.f32 normAngle (-.f32 1 (sqrt.f32 u))))) (/.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))
	0.5b	(+.f32 (.f32 (.f32 (.f32 (sqrt.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle))) (/.f32 1 (sqrt.f32 (sin.f32 normAngle)))) (.f32 (sqrt.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle))) (/.f32 1 (sqrt.f32 (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))

Compiler

Compiled 20631 to 15170 computations (26.5% saved)

localize307.0ms (2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f32 u 1/45)
✓	0.3b	(*.f32 u 1/3)
✓	0.4b	(*.f32 1/6 (pow.f32 u 3))
✓	0.4b	(*.f32 1/24 (pow.f32 u 4))

series11.0ms (0.1%)

Counts

4 → 24

Calls

4 calls:

5.0ms	(*.f32 1/6 (pow.f32 u 3))
3.0ms	(*.f32 1/24 (pow.f32 u 4))
2.0ms	(*.f32 u 1/3)
2.0ms	(*.f32 u 1/45)

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary32`
25×	`associate-r_binary32`
18×	`add-exp-log_binary32`
15×	`*-un-lft-identity_binary32`
15×	`add-cube-cbrt_binary32`

Counts

4 → 100

Calls

4 calls:

5.0ms	(*.f32 1/6 (pow.f32 u 3))
4.0ms	(*.f32 1/24 (pow.f32 u 4))
3.0ms	(*.f32 u 1/3)
3.0ms	(*.f32 u 1/45)

simplify93.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

656×	`fma-def_binary32`
378×	`*-commutative_binary32`
316×	`times-frac_binary32`
289×	`associate-/l*_binary32`
282×	`associate-/l/_binary32`

Counts

124 → 126

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	1024
1	290	929
2	726	917
3	1192	883
4	2193	883
5	4258	883
6	4758	883
7	4822	883

prune839.0ms (5.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	126	10	136

Error

0.0b

Counts

136 → 10

Alt Table

Status	Error	Program
	9.5b	(/.f32 (fma.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) n0_i (.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (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 (sin.f32 (.f32 u normAngle)) (/.f32 1 (.f32 (cbrt.f32 (sin.f32 normAngle)) (cbrt.f32 (sin.f32 normAngle))))) (/.f32 1 (cbrt.f32 (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 (sqrt.f32 (sin.f32 (.f32 u normAngle))) (.f32 (sqrt.f32 (sin.f32 (.f32 u normAngle))) (/.f32 1 (sin.f32 normAngle)))) n1_i))
	0.8b	(+.f32 (.f32 (.f32 (sin.f32 (/.f32 (.f32 normAngle (-.f32 1 (.f32 u u))) (+.f32 1 u))) (/.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))
	1.2b	(+.f32 (-.f32 n0_i (.f32 u n0_i)) (.f32 (.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	9.4b	(+.f32 (cbrt.f32 (pow.f32 (.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle)) n0_i) 3)) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	3.0b	(+.f32 (-.f32 (fma.f32 1/6 (/.f32 (.f32 (cos.f32 normAngle) (.f32 (pow.f32 u 3) (.f32 (pow.f32 normAngle 3) n0_i))) (sin.f32 normAngle)) n0_i) (fma.f32 1/2 (.f32 (.f32 u u) (.f32 normAngle (.f32 normAngle n0_i))) (/.f32 (.f32 (cos.f32 normAngle) (.f32 u (.f32 normAngle n0_i))) (sin.f32 normAngle)))) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
✓	0.2b	(+.f32 (.f32 (+.f32 (+.f32 (.f32 (.f32 normAngle normAngle) (+.f32 (.f32 1/6 (pow.f32 u 3)) (.f32 u 1/3))) (.f32 (pow.f32 normAngle 4) (+.f32 (.f32 u 1/45) (.f32 1/24 (pow.f32 u 4))))) (-.f32 1 (fma.f32 1/120 (.f32 (pow.f32 u 5) (pow.f32 normAngle 4)) (+.f32 u (fma.f32 (.f32 (pow.f32 u 3) (pow.f32 normAngle 4)) 1/18 (.f32 1/2 (.f32 u (.f32 u (.f32 normAngle 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))
	0.8b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (+.f32 1 (sqrt.f32 u)) (.f32 normAngle (-.f32 1 (sqrt.f32 u))))) (/.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))
▶	0.5b	(+.f32 (.f32 (.f32 (.f32 (sqrt.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle))) (/.f32 1 (sqrt.f32 (sin.f32 normAngle)))) (.f32 (sqrt.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle))) (/.f32 1 (sqrt.f32 (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))

Compiler

Compiled 20661 to 14987 computations (27.5% saved)

localize261.0ms (1.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f32 1/6 (.f32 u (pow.f32 normAngle 2)))
✓	0.2b	(/.f32 1 (sqrt.f32 (sin.f32 normAngle)))
✓	0.3b	(.f32 (.f32 (sqrt.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle))) (/.f32 1 (sqrt.f32 (sin.f32 normAngle)))) (.f32 (sqrt.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle))) (/.f32 1 (sqrt.f32 (sin.f32 normAngle)))))
✓	0.4b	(.f32 (sqrt.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle))) (/.f32 1 (sqrt.f32 (sin.f32 normAngle))))

series101.0ms (0.7%)

Counts

3 → 56

Calls

3 calls:

65.0ms

(*.f32 (sqrt.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle))) (/.f32 1 (sqrt.f32 (sin.f32 normAngle))))

26.0ms

(*.f32 (*.f32 (sqrt.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle))) (/.f32 1 (sqrt.f32 (sin.f32 normAngle)))) (*.f32 (sqrt.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle))) (/.f32 1 (sqrt.f32 (sin.f32 normAngle)))))

9.0ms

(/.f32 1 (sqrt.f32 (sin.f32 normAngle)))

rewrite52.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`add-exp-log_binary32`
69×	`prod-exp_binary32`
57×	`add-sqr-sqrt_binary32`
46×	`add-cbrt-cube_binary32`
46×	`pow1_binary32`

Counts

3 → 174

Calls

3 calls:

17.0ms

(*.f32 (*.f32 (sqrt.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle))) (/.f32 1 (sqrt.f32 (sin.f32 normAngle)))) (*.f32 (sqrt.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle))) (/.f32 1 (sqrt.f32 (sin.f32 normAngle)))))

10.0ms

(*.f32 (sqrt.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle))) (/.f32 1 (sqrt.f32 (sin.f32 normAngle))))

3.0ms

(/.f32 1 (sqrt.f32 (sin.f32 normAngle)))

simplify169.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

468×	`associate-r_binary32`
425×	`associate-l_binary32`
375×	`fma-def_binary32`
302×	`associate-+r+_binary32`
288×	`*-commutative_binary32`

Counts

230 → 230

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	395	6382
1	1111	4985
2	4204	4985
3	4977	4985
4	4965	4985

prune2.2s (14.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	404	0	404
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	404	10	414

Error

0.0b

Counts

414 → 10

Alt Table

Status	Error	Program
	9.5b	(/.f32 (fma.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) n0_i (.f32 (sin.f32 (*.f32 u normAngle)) n1_i)) (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 (sin.f32 (.f32 u normAngle)) (/.f32 1 (.f32 (cbrt.f32 (sin.f32 normAngle)) (cbrt.f32 (sin.f32 normAngle))))) (/.f32 1 (cbrt.f32 (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 (sqrt.f32 (sin.f32 (.f32 u normAngle))) (.f32 (sqrt.f32 (sin.f32 (.f32 u normAngle))) (/.f32 1 (sin.f32 normAngle)))) n1_i))
	0.8b	(+.f32 (.f32 (.f32 (sin.f32 (/.f32 (.f32 normAngle (-.f32 1 (.f32 u u))) (+.f32 1 u))) (/.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))
	1.2b	(+.f32 (-.f32 n0_i (.f32 u n0_i)) (.f32 (.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	9.4b	(+.f32 (cbrt.f32 (pow.f32 (.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle)) n0_i) 3)) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	3.0b	(+.f32 (-.f32 (fma.f32 1/6 (/.f32 (.f32 (cos.f32 normAngle) (.f32 (pow.f32 u 3) (.f32 (pow.f32 normAngle 3) n0_i))) (sin.f32 normAngle)) n0_i) (fma.f32 1/2 (.f32 (.f32 u u) (.f32 normAngle (.f32 normAngle n0_i))) (/.f32 (.f32 (cos.f32 normAngle) (.f32 u (.f32 normAngle n0_i))) (sin.f32 normAngle)))) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
✓	0.2b	(+.f32 (.f32 (+.f32 (+.f32 (.f32 (.f32 normAngle normAngle) (+.f32 (.f32 1/6 (pow.f32 u 3)) (.f32 u 1/3))) (.f32 (pow.f32 normAngle 4) (+.f32 (.f32 u 1/45) (.f32 1/24 (pow.f32 u 4))))) (-.f32 1 (fma.f32 1/120 (.f32 (pow.f32 u 5) (pow.f32 normAngle 4)) (+.f32 u (fma.f32 (.f32 (pow.f32 u 3) (pow.f32 normAngle 4)) 1/18 (.f32 1/2 (.f32 u (.f32 u (.f32 normAngle 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))
	0.8b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (+.f32 1 (sqrt.f32 u)) (.f32 normAngle (-.f32 1 (sqrt.f32 u))))) (/.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))
✓	0.5b	(+.f32 (.f32 (.f32 (.f32 (sqrt.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle))) (/.f32 1 (sqrt.f32 (sin.f32 normAngle)))) (.f32 (sqrt.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle))) (/.f32 1 (sqrt.f32 (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))

Compiler

Compiled 54084 to 39573 computations (26.8% saved)

regimes3.2s (21%)

Accuracy

Total 0.2b remaining (84%)

Threshold costs 0.2b (84%)

Counts

271 → 1

Compiler

Compiled 90303 to 66282 computations (26.6% saved)

simplify17.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

53×	`*-commutative_binary32`
39×	`+-commutative_binary32`
21×	`sub-neg_binary32`
19×	`neg-sub0_binary32`
19×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	94	280
1	152	280
2	167	280
3	194	280
4	229	280
5	271	280
6	301	280
7	316	280
8	322	280
9	323	280
10	318	280

end504.0ms (3.3%)

Compiler: Compiled 1085 to 796 computations (26.6% saved)

Iter	Nodes	Cost
0	94	280
1	152	280
2	167	280
3	194	280
4	229	280
5	271	280
6	301	280
7	316	280
8	322	280
9	323	280
10	318	280

Iter	Nodes	Cost
0	94	280
1	152	280
2	167	280
3	194	280
4	229	280
5	271	280
6	301	280
7	316	280
8	322	280
9	323	280
10	318	280

Details

analyze1.8s (11.9%)

sample3.6s (24.2%)

simplify202.0ms (1.3%)

prune4.0ms (0%)

localize62.0ms (0.4%)

series109.0ms (0.7%)

rewrite33.0ms (0.2%)

simplify111.0ms (0.7%)

prune385.0ms (2.5%)

localize216.0ms (1.4%)

series31.0ms (0.2%)

rewrite13.0ms (0.1%)

simplify63.0ms (0.4%)

prune717.0ms (4.8%)

localize307.0ms (2%)

series11.0ms (0.1%)

rewrite18.0ms (0.1%)

simplify93.0ms (0.6%)

prune839.0ms (5.6%)

localize261.0ms (1.7%)

series101.0ms (0.7%)

rewrite52.0ms (0.3%)

simplify169.0ms (1.1%)

prune2.2s (14.3%)

regimes3.2s (21%)

simplify17.0ms (0.1%)

end504.0ms (3.3%)

Profiling

Iter	Nodes	Cost
0	94	280
1	152	280
2	167	280
3	194	280
4	229	280
5	271	280
6	301	280
7	316	280
8	322	280
9	323	280
10	318	280