Details

analyze4.9s (33.6%)

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%	0.6%	99.4%	6
0%	0.6%	99.4%	7
0%	0.6%	99.4%	8
0%	0.6%	99.4%	9
0%	0.5%	99.5%	10
0%	0.5%	99.5%	11
0%	0.5%	99.5%	12
0%	0.5%	99.5%	13
0%	0.4%	99.6%	14

Compiler

Compiled 62 to 45 computations (27.4% saved)

sample3.8s (26.1%)

Results

3.3s	8256×	body	128	valid
416.0ms	1026×	body	128	invalid

Compiler

Compiled 153 to 110 computations (28.1% saved)

simplify201.0ms (1.4%)

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

prune5.0ms (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

0.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	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))
▶	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))

Status

Error

Program

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))

▶

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)

localize60.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f32 (-.f32 1 u) normAngle)
✓	0.2b	(.f32 (.f32 (sin.f32 (*.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i)
✓	0.3b	(.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle)))
✓	1.7b	(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))

series122.0ms (0.8%)

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)))
24.0ms	(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))
4.0ms	(*.f32 (-.f32 1 u) normAngle)

rewrite39.0ms (0.3%)

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:

12.0ms	(.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)
7.0ms	(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))
5.0ms	(*.f32 (-.f32 1 u) normAngle)

simplify135.0ms (0.9%)

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

prune432.0ms (3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	226	11	237
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	228	11	239

Error

0.0b

Counts

239 → 11

Alt Table

Status	Error	Program
	0.9b	(+.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))
▶	0.6b	(+.f32 (.f32 (-.f32 (+.f32 1 (.f32 (.f32 normAngle normAngle) (+.f32 (.f32 1/6 (pow.f32 u 3)) (.f32 u 1/3)))) (fma.f32 1/2 (.f32 u (.f32 u (.f32 normAngle normAngle))) u)) n0_i) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	0.9b	(+.f32 (.f32 (.f32 (.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sqrt.f32 (/.f32 1 (sin.f32 normAngle)))) (sqrt.f32 (/.f32 1 (sin.f32 normAngle)))) 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 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (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 (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (sqrt.f32 (/.f32 1 (sin.f32 normAngle)))) (sqrt.f32 (/.f32 1 (sin.f32 normAngle)))) n1_i))
	5.5b	(+.f32 n0_i (.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 (.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))
	1.1b	(+.f32 (.f32 (.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (.f32 (cbrt.f32 (sin.f32 normAngle)) (cbrt.f32 (sin.f32 normAngle)))) (/.f32 1 (cbrt.f32 (sin.f32 normAngle)))) n0_i) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	0.9b	(+.f32 (.f32 (.f32 (sin.f32 (.f32 (-.f32 1 u) normAngle)) (/.f32 1 (sin.f32 normAngle))) n0_i) (.f32 u n1_i))
	0.8b	(+.f32 (.f32 (.f32 (sqrt.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle))) (sqrt.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 n0_i (.f32 u n0_i)) (.f32 (.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))

Compiler

Compiled 9522 to 5005 computations (47.4% saved)

localize99.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (-.f32 (+.f32 1 (.f32 (.f32 normAngle normAngle) (+.f32 (.f32 1/6 (pow.f32 u 3)) (.f32 u 1/3)))) (fma.f32 1/2 (.f32 u (.f32 u (.f32 normAngle normAngle))) u)) n0_i)
✓	0.3b	(*.f32 u 1/3)
✓	0.4b	(*.f32 1/6 (pow.f32 u 3))
	1.7b	(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))

series128.0ms (0.9%)

Counts

3 → 48

Calls

3 calls:

123.0ms

(*.f32 (-.f32 (+.f32 1 (*.f32 (*.f32 normAngle normAngle) (+.f32 (*.f32 1/6 (pow.f32 u 3)) (*.f32 u 1/3)))) (fma.f32 1/2 (*.f32 u (*.f32 u (*.f32 normAngle normAngle))) u)) n0_i)

3.0ms

(*.f32 1/6 (pow.f32 u 3))

2.0ms

(*.f32 u 1/3)

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary32`
18×	`associate-r_binary32`
13×	`*-un-lft-identity_binary32`
12×	`add-exp-log_binary32`
11×	`associate-l_binary32`

Counts

3 → 77

Calls

3 calls:

6.0ms

(*.f32 (-.f32 (+.f32 1 (*.f32 (*.f32 normAngle normAngle) (+.f32 (*.f32 1/6 (pow.f32 u 3)) (*.f32 u 1/3)))) (fma.f32 1/2 (*.f32 u (*.f32 u (*.f32 normAngle normAngle))) u)) n0_i)

5.0ms

(*.f32 1/6 (pow.f32 u 3))

3.0ms

(*.f32 u 1/3)

simplify131.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

914×	`fma-neg_binary32`
813×	`fma-def_binary32`
487×	`exp-prod_binary32`
467×	`*-commutative_binary32`
429×	`cancel-sign-sub-inv_binary32`

Counts

125 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	196	3277
1	461	2776
2	1503	2442
3	3663	2310
4	4893	2310
5	5220	2310

prune444.0ms (3.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	199	2	201
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	202	10	212

Error

0.0b

Counts

212 → 10

Alt Table

Status	Error	Program
	0.9b	(+.f32 (.f32 (.f32 (.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sqrt.f32 (/.f32 1 (sin.f32 normAngle)))) (sqrt.f32 (/.f32 1 (sin.f32 normAngle)))) 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 (log1p.f32 (expm1.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
	0.8b	(+.f32 (.f32 (.f32 (sqrt.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle))) (sqrt.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 (-.f32 (+.f32 1 (.f32 (.f32 normAngle normAngle) (+.f32 (.f32 1/6 (pow.f32 u 3)) (.f32 u 1/3)))) (fma.f32 1/2 (.f32 u (.f32 u (.f32 normAngle normAngle))) u)) n0_i) (*.f32 u n1_i))
	0.8b	(+.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)) (sqrt.f32 (/.f32 1 (sin.f32 normAngle)))) (sqrt.f32 (/.f32 1 (sin.f32 normAngle)))) n1_i))
	5.5b	(+.f32 n0_i (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
	0.9b	(+.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))
	0.8b	(+.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))
	1.1b	(+.f32 (.f32 (.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (.f32 (cbrt.f32 (sin.f32 normAngle)) (cbrt.f32 (sin.f32 normAngle)))) (/.f32 1 (cbrt.f32 (sin.f32 normAngle)))) n0_i) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
▶	0.7b	(+.f32 (-.f32 (+.f32 (.f32 1/3 (.f32 u (.f32 n0_i (pow.f32 normAngle 2)))) n0_i) (.f32 u n0_i)) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))

Compiler

Compiled 10486 to 5372 computations (48.8% saved)

localize74.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f32 (-.f32 (+.f32 (.f32 1/3 (.f32 u (.f32 n0_i (pow.f32 normAngle 2)))) n0_i) (.f32 u n0_i)) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))
✓	0.1b	(.f32 1/3 (.f32 u (*.f32 n0_i (pow.f32 normAngle 2))))
✓	0.1b	(-.f32 (+.f32 (.f32 1/3 (.f32 u (.f32 n0_i (pow.f32 normAngle 2)))) n0_i) (.f32 u n0_i))
	1.7b	(.f32 (sin.f32 (.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle)))

series147.0ms (1%)

Counts

3 → 90

Calls

3 calls:

87.0ms

(+.f32 (-.f32 (+.f32 (*.f32 1/3 (*.f32 u (*.f32 n0_i (pow.f32 normAngle 2)))) n0_i) (*.f32 u n0_i)) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))

32.0ms

(-.f32 (+.f32 (*.f32 1/3 (*.f32 u (*.f32 n0_i (pow.f32 normAngle 2)))) n0_i) (*.f32 u n0_i))

28.0ms

(*.f32 1/3 (*.f32 u (*.f32 n0_i (pow.f32 normAngle 2))))

rewrite34.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary32`
17×	`add-log-exp_binary32`
12×	`prod-exp_binary32`
12×	`add-cbrt-cube_binary32`
8×	`pow1_binary32`

Counts

3 → 75

Calls

3 calls:

14.0ms

(+.f32 (-.f32 (+.f32 (*.f32 1/3 (*.f32 u (*.f32 n0_i (pow.f32 normAngle 2)))) n0_i) (*.f32 u n0_i)) (*.f32 (*.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))

8.0ms

(-.f32 (+.f32 (*.f32 1/3 (*.f32 u (*.f32 n0_i (pow.f32 normAngle 2)))) n0_i) (*.f32 u n0_i))

6.0ms

(*.f32 1/3 (*.f32 u (*.f32 n0_i (pow.f32 normAngle 2))))

simplify149.0ms (1%)

Algorithm

1×	egg-herbie

Rules

520×	`fma-neg_binary32`
439×	`cancel-sign-sub-inv_binary32`
364×	`associate-r_binary32`
297×	`associate-l_binary32`
246×	`fma-def_binary32`

Counts

165 → 151

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	274	4827
1	760	4466
2	3007	4447
3	4567	4446
4	4950	4446

prune449.0ms (3.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	218	3	221
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	223	8	231

Error

Counts

231 → 8

Alt Table

Status	Error	Program
	0.7b	(+.f32 (-.f32 (+.f32 (.f32 1/3 (.f32 u (.f32 n0_i (pow.f32 normAngle 2)))) n0_i) (.f32 u n0_i)) (.f32 (.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sqrt.f32 (sin.f32 normAngle))) (/.f32 1 (sqrt.f32 (sin.f32 normAngle)))) n1_i))
▶	0.4b	(-.f32 (fma.f32 1/3 (.f32 n0_i (.f32 (.f32 normAngle normAngle) u)) (fma.f32 7/360 (.f32 n1_i (.f32 u (pow.f32 normAngle 4))) (fma.f32 u n1_i (fma.f32 1/6 (.f32 (.f32 normAngle normAngle) (.f32 u n1_i)) (fma.f32 1/120 (.f32 n1_i (.f32 (pow.f32 u 5) (pow.f32 normAngle 4))) n0_i))))) (fma.f32 1/6 (.f32 n1_i (.f32 (.f32 normAngle normAngle) (pow.f32 u 3))) (fma.f32 n0_i u (.f32 1/36 (.f32 n1_i (.f32 (pow.f32 u 3) (pow.f32 normAngle 4)))))))
	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 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
	0.6b	(-.f32 (+.f32 (.f32 1/3 (.f32 u (.f32 n0_i (pow.f32 normAngle 2)))) n0_i) (-.f32 (.f32 u n0_i) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i)))
	0.8b	(+.f32 (.f32 (.f32 (sqrt.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle))) (sqrt.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 (-.f32 (+.f32 1 (.f32 (.f32 normAngle normAngle) (+.f32 (.f32 1/6 (pow.f32 u 3)) (.f32 u 1/3)))) (fma.f32 1/2 (.f32 u (.f32 u (.f32 normAngle normAngle))) u)) n0_i) (*.f32 u n1_i))
	0.9b	(+.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))
	1.1b	(+.f32 (.f32 (.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (.f32 (cbrt.f32 (sin.f32 normAngle)) (cbrt.f32 (sin.f32 normAngle)))) (/.f32 1 (cbrt.f32 (sin.f32 normAngle)))) n0_i) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))

Compiler

Compiled 9276 to 4583 computations (50.6% saved)

localize148.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f32 n0_i (.f32 (*.f32 normAngle normAngle) u))
✓	0.1b	(.f32 (.f32 normAngle normAngle) (pow.f32 u 3))
✓	0.1b	(-.f32 (fma.f32 1/3 (.f32 n0_i (.f32 (.f32 normAngle normAngle) u)) (fma.f32 7/360 (.f32 n1_i (.f32 u (pow.f32 normAngle 4))) (fma.f32 u n1_i (fma.f32 1/6 (.f32 (.f32 normAngle normAngle) (.f32 u n1_i)) (fma.f32 1/120 (.f32 n1_i (.f32 (pow.f32 u 5) (pow.f32 normAngle 4))) n0_i))))) (fma.f32 1/6 (.f32 n1_i (.f32 (.f32 normAngle normAngle) (pow.f32 u 3))) (fma.f32 n0_i u (.f32 1/36 (.f32 n1_i (.f32 (pow.f32 u 3) (pow.f32 normAngle 4)))))))
✓	0.1b	(.f32 (.f32 normAngle normAngle) u)

series339.0ms (2.3%)

Counts

4 → 132

Calls

4 calls:

288.0ms	(-.f32 (fma.f32 1/3 (.f32 n0_i (.f32 (.f32 normAngle normAngle) u)) (fma.f32 7/360 (.f32 n1_i (.f32 u (pow.f32 normAngle 4))) (fma.f32 u n1_i (fma.f32 1/6 (.f32 (.f32 normAngle normAngle) (.f32 u n1_i)) (fma.f32 1/120 (.f32 n1_i (.f32 (pow.f32 u 5) (pow.f32 normAngle 4))) n0_i))))) (fma.f32 1/6 (.f32 n1_i (.f32 (.f32 normAngle normAngle) (pow.f32 u 3))) (fma.f32 n0_i u (.f32 1/36 (.f32 n1_i (.f32 (pow.f32 u 3) (pow.f32 normAngle 4)))))))
24.0ms	(.f32 n0_i (.f32 (*.f32 normAngle normAngle) u))
17.0ms	(.f32 (.f32 normAngle normAngle) (pow.f32 u 3))
10.0ms	(.f32 (.f32 normAngle normAngle) u)

rewrite35.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-exp-log_binary32`
23×	`add-sqr-sqrt_binary32`
23×	`add-cbrt-cube_binary32`
19×	`*-un-lft-identity_binary32`
18×	`prod-exp_binary32`

Counts

4 → 111

Calls

4 calls:

11.0ms	(.f32 (.f32 normAngle normAngle) (pow.f32 u 3))
6.0ms	(.f32 n0_i (.f32 (*.f32 normAngle normAngle) u))
4.0ms	(.f32 (.f32 normAngle normAngle) u)
3.0ms	(-.f32 (fma.f32 1/3 (.f32 n0_i (.f32 (.f32 normAngle normAngle) u)) (fma.f32 7/360 (.f32 n1_i (.f32 u (pow.f32 normAngle 4))) (fma.f32 u n1_i (fma.f32 1/6 (.f32 (.f32 normAngle normAngle) (.f32 u n1_i)) (fma.f32 1/120 (.f32 n1_i (.f32 (pow.f32 u 5) (pow.f32 normAngle 4))) n0_i))))) (fma.f32 1/6 (.f32 n1_i (.f32 (.f32 normAngle normAngle) (pow.f32 u 3))) (fma.f32 n0_i u (.f32 1/36 (.f32 n1_i (.f32 (pow.f32 u 3) (pow.f32 normAngle 4)))))))

simplify238.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

496×	`fma-neg_binary32`
385×	`associate-r_binary32`
338×	`associate-l_binary32`
272×	`unswap-sqr_binary32`
246×	`fma-def_binary32`

Counts

243 → 196

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	295	9718
1	750	8970
2	3081	8610
3	4767	8610
4	4979	8610

prune551.0ms (3.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	196	8	204

Error

Counts

204 → 8

Alt Table

Status	Error	Program
	0.7b	(+.f32 (-.f32 (+.f32 (.f32 1/3 (.f32 u (.f32 n0_i (pow.f32 normAngle 2)))) n0_i) (.f32 u n0_i)) (.f32 (.f32 (/.f32 (sin.f32 (*.f32 u normAngle)) (sqrt.f32 (sin.f32 normAngle))) (/.f32 1 (sqrt.f32 (sin.f32 normAngle)))) n1_i))
✓	0.4b	(-.f32 (fma.f32 1/3 (.f32 n0_i (.f32 (.f32 normAngle normAngle) u)) (fma.f32 7/360 (.f32 n1_i (.f32 u (pow.f32 normAngle 4))) (fma.f32 u n1_i (fma.f32 1/6 (.f32 (.f32 normAngle normAngle) (.f32 u n1_i)) (fma.f32 1/120 (.f32 n1_i (.f32 (pow.f32 u 5) (pow.f32 normAngle 4))) n0_i))))) (fma.f32 1/6 (.f32 n1_i (.f32 (.f32 normAngle normAngle) (pow.f32 u 3))) (fma.f32 n0_i u (.f32 1/36 (.f32 n1_i (.f32 (pow.f32 u 3) (pow.f32 normAngle 4)))))))
	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 (sin.f32 (*.f32 u normAngle)) (sin.f32 normAngle)))) n1_i))
	0.6b	(-.f32 (+.f32 (.f32 1/3 (.f32 u (.f32 n0_i (pow.f32 normAngle 2)))) n0_i) (-.f32 (.f32 u n0_i) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i)))
	0.8b	(+.f32 (.f32 (.f32 (sqrt.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (sin.f32 normAngle))) (sqrt.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 (-.f32 (+.f32 1 (.f32 (.f32 normAngle normAngle) (+.f32 (.f32 1/6 (pow.f32 u 3)) (.f32 u 1/3)))) (fma.f32 1/2 (.f32 u (.f32 u (.f32 normAngle normAngle))) u)) n0_i) (*.f32 u n1_i))
	0.9b	(+.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))
	1.1b	(+.f32 (.f32 (.f32 (/.f32 (sin.f32 (-.f32 normAngle (.f32 u normAngle))) (.f32 (cbrt.f32 (sin.f32 normAngle)) (cbrt.f32 (sin.f32 normAngle)))) (/.f32 1 (cbrt.f32 (sin.f32 normAngle)))) n0_i) (.f32 (.f32 (sin.f32 (*.f32 u normAngle)) (/.f32 1 (sin.f32 normAngle))) n1_i))

Compiler

Compiled 16670 to 9055 computations (45.7% saved)

regimes1.7s (11.4%)

Accuracy

Total 0.4b remaining (96.4%)

Threshold costs 0.4b (96.4%)

Counts

218 → 1

Compiler

Compiled 35488 to 23632 computations (33.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary32`
3×	`+-commutative_binary32`
2×	`sub-neg_binary32`
1×	`neg-sub0_binary32`
1×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	52
1	35	52
2	39	52
3	41	52
4	42	52
5	41	52

end206.0ms (1.4%)

Compiler: Compiled 397 to 241 computations (39.3% saved)

Details

analyze4.9s (33.6%)

sample3.8s (26.1%)

simplify201.0ms (1.4%)

prune5.0ms (0%)

localize60.0ms (0.4%)

series122.0ms (0.8%)

rewrite39.0ms (0.3%)

simplify135.0ms (0.9%)

prune432.0ms (3%)

localize99.0ms (0.7%)

series128.0ms (0.9%)

rewrite18.0ms (0.1%)

simplify131.0ms (0.9%)

prune444.0ms (3.1%)

localize74.0ms (0.5%)

series147.0ms (1%)

rewrite34.0ms (0.2%)

simplify149.0ms (1%)

prune449.0ms (3.1%)

localize148.0ms (1%)

series339.0ms (2.3%)

rewrite35.0ms (0.2%)

simplify238.0ms (1.6%)

prune551.0ms (3.8%)

regimes1.7s (11.4%)

simplify3.0ms (0%)

end206.0ms (1.4%)

Profiling