Details

analyze1.9s (11.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	3%	97%	0
0%	3%	97%	1
0%	3%	97%	2
0%	3%	97%	3
0%	3%	97%	4
0%	3%	97%	5
0%	1.5%	98.5%	6
0%	1.5%	98.5%	7
0%	1.5%	98.5%	8
0%	1.5%	98.5%	9
0%	1.5%	98.5%	10
0.6%	0.9%	98.5%	11
0.6%	0.9%	98.5%	12
0.6%	0.9%	98.5%	13
0.6%	0.9%	98.5%	14

Compiler

Compiled 69 to 51 computations (26.1% saved)

sample129.0ms (0.8%)

Algorithm

1×

intervals

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

31.0ms	256×	body	128	valid
13.0ms	260×	pre	128	true
0.0ms	4×	body	128	nan

Compiler

Compiled 104 to 78 computations (25% saved)

simplify47.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

788×	`fma-neg_binary32`
718×	`fma-def_binary32`
560×	`exp-diff_binary32`
512×	`exp-sum_binary32`
448×	`sub-neg_binary32`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	35
1	53	33
2	145	31
3	532	29
4	2119	29
5	4431	29
6	4975	29

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
▶	0.2b	(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))

Status

Error

Program

0.2b

(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))

▶

0.2b

(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))

Compiler

Compiled 160 to 112 computations (30% saved)

localize50.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
✓	0.1b	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
✓	0.1b	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
✓	0.1b	(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))

series221.0ms (1.4%)

Counts

4 → 180

Calls

4 calls:

120.0ms	(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
48.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
41.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
11.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary32`
39×	`*-un-lft-identity_binary32`
35×	`add-cube-cbrt_binary32`
28×	`exp-sum_binary32`
27×	`prod-diff_binary32`

Counts

4 → 123

Calls

4 calls:

11.0ms	(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
4.0ms	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
3.0ms	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
0.0ms	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)

simplify175.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

392×	`times-frac_binary32`
288×	`associate-/l*_binary32`
278×	`associate-r_binary32`
275×	`associate-+r+_binary32`
243×	`fma-def_binary32`

Counts

303 → 223

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	441	11185
1	1198	10395
2	5156	10395

prune469.0ms (2.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	217	6	223
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	219	6	225

Error

0.0b

Counts

225 → 6

Alt Table

Status	Error	Program
	0.2b	(*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
▶	0.1b	(.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
	12.0b	(.f32 (.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v)) (exp.f32 (fma.f32 (neg.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (*.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))))
	2.7b	(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (+.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (-.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
	0.2b	(.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))
	0.2b	(.f32 (.f32 (cbrt.f32 (/.f32 1/2 v)) (cbrt.f32 (/.f32 1/2 v))) (*.f32 (cbrt.f32 (/.f32 1/2 v)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))

Compiler

Compiled 11015 to 6394 computations (42% saved)

localize75.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
	0.1b	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
	0.1b	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
✓	0.3b	(/.f32 (sqrt.f32 1/2) (sqrt.f32 v))

series18.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

18.0ms

(/.f32 (sqrt.f32 1/2) (sqrt.f32 v))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`sqrt-prod_binary32`
36×	`times-frac_binary32`
31×	`add-sqr-sqrt_binary32`
29×	`*-un-lft-identity_binary32`
29×	`add-cube-cbrt_binary32`

Counts

1 → 64

Calls

1 calls:

5.0ms

(/.f32 (sqrt.f32 1/2) (sqrt.f32 v))

simplify135.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

850×	`fma-neg_binary32`
761×	`times-frac_binary32`
622×	`div-sub_binary32`
577×	`associate-/l/_binary32`
510×	`fma-def_binary32`

Counts

64 → 62

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	80	1071
1	122	1037
2	218	1037
3	339	1037
4	488	1037
5	626	1037
6	1177	1037
7	3142	1037
8	4430	1037
9	4328	1037
10	4940	1037
11	4751	1037

prune625.0ms (3.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	244	3	247
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	247	6	253

Error

0.0b

Counts

253 → 6

Alt Table

Status	Error	Program
	0.1b	(.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (pow.f32 (exp.f32 (*.f32 (cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))
	12.0b	(.f32 (.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v)) (exp.f32 (fma.f32 (neg.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (*.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))))
	2.6b	(.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (pow.f32 (exp.f32 (+.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)))) (-.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))
	0.2b	(*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
	0.2b	(.f32 (.f32 (cbrt.f32 (/.f32 1/2 v)) (cbrt.f32 (/.f32 1/2 v))) (*.f32 (cbrt.f32 (/.f32 1/2 v)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
▶	0.1b	(.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))) (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))) (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))

Compiler

Compiled 11801 to 6806 computations (42.3% saved)

localize76.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))
	0.3b	(/.f32 (sqrt.f32 1/2) (sqrt.f32 v))
✓	0.3b	(.f32 (.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))) (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))) (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))))
✓	0.5b	(*.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))) (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))))

series412.0ms (2.5%)

Counts

3 → 16

Calls

3 calls:

227.0ms

(*.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))) (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))))

166.0ms

(cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))

20.0ms

(*.f32 (*.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))) (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))) (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))))

rewrite122.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

368×	`add-sqr-sqrt_binary32`
361×	`cbrt-prod_binary32`
324×	`sqrt-prod_binary32`
324×	`times-frac_binary32`
174×	`*-un-lft-identity_binary32`

Counts

3 → 353

Calls

3 calls:

34.0ms

(*.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))) (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))))

22.0ms

(*.f32 (*.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))) (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))) (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))))

3.0ms

(cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))

simplify354.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

692×	`unswap-sqr_binary32`
320×	`log-prod_binary32`
297×	`*-commutative_binary32`
272×	`associate-/l*_binary32`
253×	`associate-l_binary32`

Counts

369 → 346

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	254	12108
1	400	11556
2	1249	10960
3	2874	10660
4	4473	10660
5	4978	10660

prune2.5s (15.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	702	2	704
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	703	7	710

Error

0.0b

Counts

710 → 7

Alt Table

Status	Error	Program
	0.1b	(.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (.f32 (.f32 (.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))) 5) (cbrt.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))))) (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
	0.1b	(.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (pow.f32 (exp.f32 (*.f32 (cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))
	12.0b	(.f32 (.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v)) (exp.f32 (fma.f32 (neg.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (*.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))))
	2.6b	(.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (pow.f32 (exp.f32 (+.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)))) (-.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))
	0.2b	(*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
✓	0.1b	(.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))) (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))) (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
▶	0.1b	(.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (.f32 (*.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))) 8) (cbrt.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))))) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))

Compiler

Compiled 37101 to 23017 computations (38% saved)

localize89.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))
	0.3b	(/.f32 (sqrt.f32 1/2) (sqrt.f32 v))
✓	0.3b	(*.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))) 8) (cbrt.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))))
✓	1.4b	(pow.f32 (cbrt.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))) 8)

series245.0ms (1.5%)

Counts

2 → 8

Calls

2 calls:

227.0ms

(pow.f32 (cbrt.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))) 8)

18.0ms

(*.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))) 8) (cbrt.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))))

rewrite100.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

425×	`cbrt-prod_binary32`
268×	`add-sqr-sqrt_binary32`
172×	`sqrt-prod_binary32`
172×	`times-frac_binary32`
141×	`unpow-prod-down_binary32`

Counts

2 → 239

Calls

2 calls:

42.0ms

(*.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))) 8) (cbrt.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))))

8.0ms

(pow.f32 (cbrt.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))) 8)

simplify414.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

430×	`*-commutative_binary32`
402×	`sqr-pow_binary32`
232×	`unswap-sqr_binary32`
230×	`fma-def_binary32`
221×	`associate-/l*_binary32`

Counts

247 → 250

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	286	8860
1	502	8740
2	1343	8582
3	1921	8523
4	2623	8509
5	4789	8509
6	4994	8509
7	4956	8509
8	4844	8509

prune2.0s (12%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	542	4	546
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	546	7	553

Error

0.0b

Counts

553 → 7

Alt Table

Status	Error	Program
	0.1b	(.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (.f32 (*.f32 (pow.f32 (sqrt.f32 (cbrt.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))))) 8) (pow.f32 (cbrt.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))) 5)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
	0.1b	(.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (pow.f32 (exp.f32 (*.f32 (cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (cbrt.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))
	0.1b	(.f32 (expm1.f32 (log1p.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))) (.f32 (*.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))) 8) (cbrt.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))))) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
	0.1b	(.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (.f32 (*.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (sqrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))))) 9) (pow.f32 (cbrt.f32 (cbrt.f32 (sqrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))))) 9)) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
	2.6b	(.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (pow.f32 (exp.f32 (+.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)))) (-.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))
✓	0.1b	(.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (.f32 (.f32 (.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))) (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))) (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)))) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
	0.1b	(.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v)) (.f32 (.f32 (exp.f32 (.f32 (log.f32 (cbrt.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))))) 8)) (cbrt.f32 (cbrt.f32 (/.f32 (sqrt.f32 1/2) (sqrt.f32 v))))) (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))

Compiler

Compiled 27734 to 17990 computations (35.1% saved)

regimes3.4s (21.2%)

Accuracy

Total 0.0b remaining (31.8%)

Threshold costs 0.0b (31.8%)

Counts

268 → 1

Compiler

Compiled 96695 to 69127 computations (28.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary32`
2×	`+-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	34	80
1	42	80
2	46	80
3	48	80
4	49	80
5	48	80

end29.0ms (0.2%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 270 to 210 computations (22.2% saved)

sample2.7s (16.8%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
586.0ms	8114×	pre	128	true
13.0ms	114×	body	128	nan

Compiler

Compiled 488 to 349 computations (28.5% saved)

Details

analyze1.9s (11.4%)

sample129.0ms (0.8%)

simplify47.0ms (0.3%)

prune5.0ms (0%)

localize50.0ms (0.3%)

series221.0ms (1.4%)

rewrite30.0ms (0.2%)

simplify175.0ms (1.1%)

prune469.0ms (2.9%)

localize75.0ms (0.5%)

series18.0ms (0.1%)

rewrite9.0ms (0.1%)

simplify135.0ms (0.8%)

prune625.0ms (3.8%)

localize76.0ms (0.5%)

series412.0ms (2.5%)

rewrite122.0ms (0.7%)

simplify354.0ms (2.2%)

prune2.5s (15.1%)

localize89.0ms (0.5%)

series245.0ms (1.5%)

rewrite100.0ms (0.6%)

simplify414.0ms (2.5%)

prune2.0s (12%)

regimes3.4s (21.2%)

simplify4.0ms (0%)

end29.0ms (0.2%)

sample2.7s (16.8%)

Profiling