Details

analyze1.9s (22.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.3%	93.7%	0
0%	6.3%	93.7%	1
0%	6.3%	93.7%	2
0%	6.3%	93.7%	3
0%	6.3%	93.7%	4
0%	6.3%	93.7%	5
0.8%	5.5%	93.7%	6
0.8%	5.5%	93.7%	7
1%	4.9%	94.1%	8
1.4%	4.4%	94.2%	9
1.4%	3.9%	94.8%	10
1.5%	3%	95.5%	11
1.7%	2.7%	95.6%	12
1.7%	2.2%	96.1%	13
1.8%	1.6%	96.6%	14

Compiler

Compiled 44 to 30 computations (31.8% saved)

sample2.8s (34.3%)

Results

1.9s	8256×	body	128	valid
947.0ms	4462×	body	128	invalid

Compiler

Compiled 88 to 60 computations (31.8% saved)

preprocess58.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

479×	`fma-neg_binary32`
238×	`unsub-neg_binary32`
234×	`fma-def_binary32`
203×	`sub-neg_binary32`
194×	`div-sub_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	112
1	67	112
2	108	112
3	225	112
4	405	112
5	625	112
6	989	112
7	2006	112
8	3687	112
9	4699	112
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 21 to 13 computations (38.1% saved)

simplify43.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

664×	`div-sub_binary32`
600×	`fma-neg_binary32`
543×	`fma-def_binary32`
191×	`distribute-neg-in_binary32`
181×	`unsub-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	28
1	26	28
2	40	28
3	78	28
4	139	28
5	204	28
6	319	28
7	595	28
8	1065	28
9	1967	28
10	3608	28
11	4882	28

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

3.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.0b	(asin.f32 (/.f32 h (sqrt.f32 (-.f32 (.f32 eta eta) (/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O))))))))

Compiler

Compiled 81 to 48 computations (40.7% saved)

localize40.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f32 (.f32 eta eta) (/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O)))))
✓	0.0b	(/.f32 h (sqrt.f32 (-.f32 (.f32 eta eta) (/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O)))))))
✓	0.1b	(asin.f32 (/.f32 h (sqrt.f32 (-.f32 (.f32 eta eta) (/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O))))))))
✓	2.6b	(sqrt.f32 (-.f32 (.f32 eta eta) (/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O))))))

series264.0ms (3.2%)

Counts

4 → 104

Calls

30 calls:

41.0ms	(/.f32 h (sqrt.f32 (-.f32 (.f32 eta eta) (/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O)))))))	h	0
38.0ms	(/.f32 h (sqrt.f32 (-.f32 (.f32 eta eta) (/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O)))))))	h	-inf
37.0ms	(/.f32 h (sqrt.f32 (-.f32 (.f32 eta eta) (/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O)))))))	h	inf
33.0ms	(/.f32 h (sqrt.f32 (-.f32 (.f32 eta eta) (/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O)))))))	eta	0
13.0ms	(/.f32 h (sqrt.f32 (-.f32 (.f32 eta eta) (/.f32 (.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O)))))))	sinTheta_O	inf

rewrite155.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

898×	`prod-diff_binary32`
288×	`egg-rr`
153×	`add-sqr-sqrt_binary32`
147×	`add-cbrt-cube_binary32`
147×	`log1p-expm1-u_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	98
1	311	98
2	4262	98

Stop Event

1×	node limit

Counts

4 → 288

simplify103.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

321×	`cancel-sign-sub-inv_binary32`
240×	`fma-def_binary32`
196×	`times-frac_binary32`
189×	`associate-/r*_binary32`
172×	`associate-/l*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	260	4664
1	891	4519
2	3800	4517

Stop Event

1×	node limit

Counts

392 → 379

prune528.0ms (6.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	370	9	379
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	371	9	380

Error

0.3b

Counts

380 → 9

Alt Table

Status	Error	Program
	3.2b	(asin.f32 (.f32 h (pow.f32 (-.f32 (.f32 eta eta) (.f32 (/.f32 sinTheta_O (sqrt.f32 (-.f32 1 (.f32 sinTheta_O sinTheta_O)))) sinTheta_O)) -1/2)))
	3.8b	(asin.f32 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (pow.f32 eta 2) (.f32 (pow.f32 sinTheta_O 2) (sqrt.f32 (/.f32 1 (-.f32 1 (pow.f32 sinTheta_O 2)))))))) h))
	3.0b	(asin.f32 (/.f32 h (sqrt.f32 (fma.f32 eta eta (/.f32 (.f32 sinTheta_O (neg.f32 sinTheta_O)) (sqrt.f32 (-.f32 1 (.f32 sinTheta_O sinTheta_O))))))))
▶	0.9b	(asin.f32 (/.f32 h (-.f32 eta (*.f32 1/2 (/.f32 (pow.f32 sinTheta_O 2) eta)))))
	3.6b	(asin.f32 (/.f32 h (pow.f32 (cbrt.f32 (sqrt.f32 (-.f32 (.f32 eta eta) (.f32 (/.f32 sinTheta_O (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O)))) sinTheta_O)))) 3)))
	10.0b	(asin.f32 (/.f32 h (sqrt.f32 (/.f32 (-.f32 (pow.f32 eta 4) (/.f32 (pow.f32 sinTheta_O 4) (-.f32 1 (.f32 sinTheta_O sinTheta_O)))) (fma.f32 eta eta (.f32 (/.f32 sinTheta_O (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O)))) sinTheta_O))))))
	18.9b	(pow.f32 (sqrt.f32 (asin.f32 (/.f32 h (sqrt.f32 (-.f32 (.f32 eta eta) (.f32 (/.f32 sinTheta_O (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O)))) sinTheta_O)))))) 2)
	3.6b	(pow.f32 (cbrt.f32 (asin.f32 (/.f32 h (sqrt.f32 (-.f32 (.f32 eta eta) (.f32 (/.f32 sinTheta_O (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O)))) sinTheta_O)))))) 3)
	3.2b	(asin.f32 (pow.f32 (/.f32 (sqrt.f32 (-.f32 (.f32 eta eta) (.f32 (/.f32 sinTheta_O (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O)))) sinTheta_O))) h) -1))

Compiler

Compiled 18602 to 11202 computations (39.8% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f32 1/2 (/.f32 (pow.f32 sinTheta_O 2) eta))
✓	0.0b	(/.f32 h (-.f32 eta (*.f32 1/2 (/.f32 (pow.f32 sinTheta_O 2) eta))))
✓	0.1b	(asin.f32 (/.f32 h (-.f32 eta (*.f32 1/2 (/.f32 (pow.f32 sinTheta_O 2) eta)))))
✓	4.2b	(/.f32 (pow.f32 sinTheta_O 2) eta)

series96.0ms (1.2%)

Counts

4 → 24

Calls

30 calls:

17.0ms	(/.f32 h (-.f32 eta (*.f32 1/2 (/.f32 (pow.f32 sinTheta_O 2) eta))))	h	-inf
16.0ms	(/.f32 h (-.f32 eta (*.f32 1/2 (/.f32 (pow.f32 sinTheta_O 2) eta))))	h	inf
14.0ms	(/.f32 h (-.f32 eta (*.f32 1/2 (/.f32 (pow.f32 sinTheta_O 2) eta))))	h	0
4.0ms	(/.f32 h (-.f32 eta (*.f32 1/2 (/.f32 (pow.f32 sinTheta_O 2) eta))))	eta	0
3.0ms	(*.f32 1/2 (/.f32 (pow.f32 sinTheta_O 2) eta))	eta	0

rewrite70.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

705×	`prod-diff_binary32`
138×	`add-sqr-sqrt_binary32`
133×	`log1p-expm1-u_binary32`
133×	`expm1-log1p-u_binary32`
131×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	51
1	274	51
2	3717	51

Stop Event

1×	node limit

Counts

4 → 124

simplify37.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

531×	`cancel-sign-sub-inv_binary32`
363×	`fma-neg_binary32`
334×	`times-frac_binary32`
296×	`distribute-lft-neg-in_binary32`
295×	`distribute-rgt-neg-in_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	804
1	178	798
2	612	786
3	3006	780

Stop Event

1×	node limit

Counts

148 → 139

prune165.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	134	5	139
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	139	9	148

Error

0.1b

Counts

148 → 9

Alt Table

Status	Error	Program
	3.8b	(asin.f32 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (pow.f32 eta 2) (.f32 (pow.f32 sinTheta_O 2) (sqrt.f32 (/.f32 1 (-.f32 1 (pow.f32 sinTheta_O 2)))))))) h))
	1.1b	(asin.f32 (pow.f32 (/.f32 (+.f32 eta (.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) eta) -1/2)) h) -1))
	3.6b	(asin.f32 (/.f32 h (pow.f32 (cbrt.f32 (sqrt.f32 (-.f32 (.f32 eta eta) (.f32 (/.f32 sinTheta_O (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O)))) sinTheta_O)))) 3)))
	1.5b	(asin.f32 (.f32 (pow.f32 (cbrt.f32 h) 2) (.f32 (cbrt.f32 h) (/.f32 1 (+.f32 eta (.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) eta) -1/2))))))
	10.0b	(asin.f32 (/.f32 h (sqrt.f32 (/.f32 (-.f32 (pow.f32 eta 4) (/.f32 (pow.f32 sinTheta_O 4) (-.f32 1 (.f32 sinTheta_O sinTheta_O)))) (fma.f32 eta eta (.f32 (/.f32 sinTheta_O (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O)))) sinTheta_O))))))
	1.1b	(asin.f32 (.f32 h (/.f32 1 (+.f32 eta (.f32 (/.f32 (*.f32 sinTheta_O sinTheta_O) eta) -1/2)))))
	3.6b	(pow.f32 (cbrt.f32 (asin.f32 (/.f32 h (sqrt.f32 (-.f32 (.f32 eta eta) (.f32 (/.f32 sinTheta_O (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O)))) sinTheta_O)))))) 3)
	17.8b	(pow.f32 (sqrt.f32 (asin.f32 (/.f32 h (+.f32 eta (.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) eta) -1/2))))) 2)
▶	0.8b	(asin.f32 (/.f32 h (-.f32 eta (*.f32 1/2 (pow.f32 (/.f32 sinTheta_O (sqrt.f32 eta)) 2)))))

Compiler

Compiled 3776 to 2114 computations (44% saved)

localize33.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f32 h (-.f32 eta (*.f32 1/2 (pow.f32 (/.f32 sinTheta_O (sqrt.f32 eta)) 2))))
✓	0.1b	(asin.f32 (/.f32 h (-.f32 eta (*.f32 1/2 (pow.f32 (/.f32 sinTheta_O (sqrt.f32 eta)) 2)))))
✓	0.2b	(pow.f32 (/.f32 sinTheta_O (sqrt.f32 eta)) 2)
✓	0.3b	(/.f32 sinTheta_O (sqrt.f32 eta))

series113.0ms (1.4%)

Counts

4 → 93

Calls

30 calls:

17.0ms	(/.f32 h (-.f32 eta (*.f32 1/2 (pow.f32 (/.f32 sinTheta_O (sqrt.f32 eta)) 2))))	h	-inf
15.0ms	(/.f32 h (-.f32 eta (*.f32 1/2 (pow.f32 (/.f32 sinTheta_O (sqrt.f32 eta)) 2))))	h	0
14.0ms	(/.f32 h (-.f32 eta (*.f32 1/2 (pow.f32 (/.f32 sinTheta_O (sqrt.f32 eta)) 2))))	h	inf
7.0ms	(/.f32 sinTheta_O (sqrt.f32 eta))	eta	-inf
7.0ms	(pow.f32 (/.f32 sinTheta_O (sqrt.f32 eta)) 2)	eta	-inf

rewrite75.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

768×	`prod-diff_binary32`
144×	`add-sqr-sqrt_binary32`
141×	`egg-rr`
139×	`log1p-expm1-u_binary32`
139×	`expm1-log1p-u_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	53
1	291	47
2	3834	47

Stop Event

1×	node limit

Counts

4 → 141

simplify54.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

538×	`cancel-sign-sub-inv_binary32`
366×	`fma-neg_binary32`
334×	`times-frac_binary32`
314×	`distribute-rgt-neg-in_binary32`
235×	`associate-/l*_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	74	1734
1	208	1730
2	666	1630
3	3107	1624

Stop Event

1×	node limit

Counts

234 → 165

prune172.0ms (2.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	163	11	174

Error

0.1b

Counts

174 → 11

Alt Table

Status	Error	Program
	3.8b	(asin.f32 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (pow.f32 eta 2) (.f32 (pow.f32 sinTheta_O 2) (sqrt.f32 (/.f32 1 (-.f32 1 (pow.f32 sinTheta_O 2)))))))) h))
	1.1b	(asin.f32 (pow.f32 (/.f32 (+.f32 eta (.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) eta) -1/2)) h) -1))
	3.6b	(asin.f32 (/.f32 h (pow.f32 (cbrt.f32 (sqrt.f32 (-.f32 (.f32 eta eta) (.f32 (/.f32 sinTheta_O (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O)))) sinTheta_O)))) 3)))
	1.5b	(asin.f32 (.f32 (pow.f32 (cbrt.f32 h) 2) (.f32 (cbrt.f32 h) (/.f32 1 (+.f32 eta (.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) eta) -1/2))))))
	10.0b	(asin.f32 (/.f32 h (sqrt.f32 (/.f32 (-.f32 (pow.f32 eta 4) (/.f32 (pow.f32 sinTheta_O 4) (-.f32 1 (.f32 sinTheta_O sinTheta_O)))) (fma.f32 eta eta (.f32 (/.f32 sinTheta_O (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O)))) sinTheta_O))))))
	1.1b	(asin.f32 (.f32 h (/.f32 1 (+.f32 eta (.f32 (/.f32 (*.f32 sinTheta_O sinTheta_O) eta) -1/2)))))
▶	0.8b	(asin.f32 (/.f32 h (-.f32 eta (.f32 1/2 (/.f32 (.f32 sinTheta_O (/.f32 sinTheta_O (sqrt.f32 eta))) (sqrt.f32 eta))))))
	0.8b	(asin.f32 (/.f32 h (-.f32 eta (*.f32 1/2 (pow.f32 (cbrt.f32 (pow.f32 (/.f32 sinTheta_O (sqrt.f32 eta)) 3)) 2)))))
	3.6b	(pow.f32 (cbrt.f32 (asin.f32 (/.f32 h (sqrt.f32 (-.f32 (.f32 eta eta) (.f32 (/.f32 sinTheta_O (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O)))) sinTheta_O)))))) 3)
	17.8b	(pow.f32 (sqrt.f32 (asin.f32 (/.f32 h (+.f32 eta (.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) eta) -1/2))))) 2)
✓	0.8b	(asin.f32 (/.f32 h (-.f32 eta (*.f32 1/2 (pow.f32 (/.f32 sinTheta_O (sqrt.f32 eta)) 2)))))

Compiler

Compiled 4338 to 2406 computations (44.5% saved)

localize37.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(asin.f32 (/.f32 h (-.f32 eta (.f32 1/2 (/.f32 (.f32 sinTheta_O (/.f32 sinTheta_O (sqrt.f32 eta))) (sqrt.f32 eta))))))
✓	0.1b	(*.f32 sinTheta_O (/.f32 sinTheta_O (sqrt.f32 eta)))
	0.3b	(/.f32 sinTheta_O (sqrt.f32 eta))
✓	2.3b	(/.f32 (*.f32 sinTheta_O (/.f32 sinTheta_O (sqrt.f32 eta))) (sqrt.f32 eta))

series45.0ms (0.5%)

Counts

3 → 68

Calls

21 calls:

8.0ms	(/.f32 (*.f32 sinTheta_O (/.f32 sinTheta_O (sqrt.f32 eta))) (sqrt.f32 eta))	eta	-inf
8.0ms	(*.f32 sinTheta_O (/.f32 sinTheta_O (sqrt.f32 eta)))	eta	-inf
4.0ms	(*.f32 sinTheta_O (/.f32 sinTheta_O (sqrt.f32 eta)))	sinTheta_O	-inf
2.0ms	(*.f32 sinTheta_O (/.f32 sinTheta_O (sqrt.f32 eta)))	eta	inf
2.0ms	(*.f32 sinTheta_O (/.f32 sinTheta_O (sqrt.f32 eta)))	sinTheta_O	inf

rewrite90.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

849×	`prod-diff_binary32`
152×	`add-sqr-sqrt_binary32`
144×	`log1p-expm1-u_binary32`
144×	`expm1-log1p-u_binary32`
143×	`add-cbrt-cube_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	48
1	298	34
2	4364	34

Stop Event

1×	node limit

Counts

3 → 105

simplify41.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

473×	`associate-/r/_binary32`
408×	`times-frac_binary32`
393×	`associate-/l/_binary32`
286×	`cancel-sign-sub-inv_binary32`
237×	`fma-def_binary32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	21	940
1	44	940
2	82	876
3	169	876
4	474	876
5	1998	872

Stop Event

1×	node limit

Counts

173 → 113

prune190.0ms (2.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	150	11	161

Error

0.1b

Counts

161 → 11

Alt Table

Status	Error	Program
	3.8b	(asin.f32 (.f32 (sqrt.f32 (/.f32 1 (-.f32 (pow.f32 eta 2) (.f32 (pow.f32 sinTheta_O 2) (sqrt.f32 (/.f32 1 (-.f32 1 (pow.f32 sinTheta_O 2)))))))) h))
	1.1b	(asin.f32 (pow.f32 (/.f32 (+.f32 eta (.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) eta) -1/2)) h) -1))
	3.6b	(asin.f32 (/.f32 h (pow.f32 (cbrt.f32 (sqrt.f32 (-.f32 (.f32 eta eta) (.f32 (/.f32 sinTheta_O (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O)))) sinTheta_O)))) 3)))
	1.5b	(asin.f32 (.f32 (pow.f32 (cbrt.f32 h) 2) (.f32 (cbrt.f32 h) (/.f32 1 (+.f32 eta (.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) eta) -1/2))))))
	10.0b	(asin.f32 (/.f32 h (sqrt.f32 (/.f32 (-.f32 (pow.f32 eta 4) (/.f32 (pow.f32 sinTheta_O 4) (-.f32 1 (.f32 sinTheta_O sinTheta_O)))) (fma.f32 eta eta (.f32 (/.f32 sinTheta_O (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O)))) sinTheta_O))))))
	1.1b	(asin.f32 (.f32 h (/.f32 1 (+.f32 eta (.f32 (/.f32 (*.f32 sinTheta_O sinTheta_O) eta) -1/2)))))
✓	0.8b	(asin.f32 (/.f32 h (-.f32 eta (.f32 1/2 (/.f32 (.f32 sinTheta_O (/.f32 sinTheta_O (sqrt.f32 eta))) (sqrt.f32 eta))))))
	0.8b	(asin.f32 (/.f32 h (-.f32 eta (*.f32 1/2 (pow.f32 (cbrt.f32 (pow.f32 (/.f32 sinTheta_O (sqrt.f32 eta)) 3)) 2)))))
	3.6b	(pow.f32 (cbrt.f32 (asin.f32 (/.f32 h (sqrt.f32 (-.f32 (.f32 eta eta) (.f32 (/.f32 sinTheta_O (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O)))) sinTheta_O)))))) 3)
	17.8b	(pow.f32 (sqrt.f32 (asin.f32 (/.f32 h (+.f32 eta (.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) eta) -1/2))))) 2)
✓	0.8b	(asin.f32 (/.f32 h (-.f32 eta (*.f32 1/2 (pow.f32 (/.f32 sinTheta_O (sqrt.f32 eta)) 2)))))

Compiler

Compiled 3907 to 2027 computations (48.1% saved)

regimes968.0ms (11.7%)

Accuracy

Total 0.2b remaining (63.8%)

Threshold costs 0.2b (63.8%)

Counts

92 → 2

Compiler

Compiled 24198 to 16686 computations (31% saved)

bsearch0.0ms (0%)

Algorithm

1×	binary-search

Calls

1 calls:

0.0ms

(/.f32 (*.f32 sinTheta_O sinTheta_O) (sqrt.f32 (-.f32 1 (*.f32 sinTheta_O sinTheta_O))))

Steps

Iters	Point		Range
1.401298464324817e-44	∈ [	0.0	,	2.942726775082116e-44	]

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	54
1	29	54
2	40	54
3	46	54
4	49	54

Stop Event

1×

saturated

end156.0ms (1.9%)

Stop Event

1×

fuel

Compiler

Compiled 312 to 213 computations (31.7% saved)

Details

analyze1.9s (22.5%)

sample2.8s (34.3%)

preprocess58.0ms (0.7%)

simplify43.0ms (0.5%)

prune3.0ms (0%)

localize40.0ms (0.5%)

series264.0ms (3.2%)

rewrite155.0ms (1.9%)

simplify103.0ms (1.3%)

prune528.0ms (6.4%)

localize29.0ms (0.4%)

series96.0ms (1.2%)

rewrite70.0ms (0.8%)

simplify37.0ms (0.4%)

prune165.0ms (2%)

localize33.0ms (0.4%)

series113.0ms (1.4%)

rewrite75.0ms (0.9%)

simplify54.0ms (0.6%)

prune172.0ms (2.1%)

localize37.0ms (0.5%)

series45.0ms (0.5%)

rewrite90.0ms (1.1%)

simplify41.0ms (0.5%)

prune190.0ms (2.3%)

regimes968.0ms (11.7%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end156.0ms (1.9%)

Profiling