Details

analyze7.4s (27.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0%	99.8%	0.2%	13
0%	99.8%	0.2%	14

Compiler

Compiled 39 to 24 computations (38.5% saved)

sample11.4s (42.3%)

Results

8.2s	4033×	body	1024	valid
1.6s	1353×	body	512	valid
883.0ms	2285×	body	128	valid
466.0ms	570×	body	256	valid
72.0ms	15×	body	2048	valid

Compiler

Compiled 77 to 47 computations (39% saved)

simplify50.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

571×	`fma-def_binary64`
244×	`fma-neg_binary64`
103×	`unsub-neg_binary64`
90×	`associate-l_binary64`
88×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	53
1	40	53
2	66	53
3	85	53
4	99	53
5	133	53
6	173	53
7	217	53
8	281	53
9	305	53
10	362	53
11	407	53
12	468	53
13	604	53
14	728	53
15	836	53
16	943	53
17	891	53
18	893	53
19	899	53
20	904	53
21	841	53

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))

Status

Error

Program

▶

0.2b

(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))

Compiler

Compiled 144 to 76 computations (47.2% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sin.f64 theta) (sin.f64 delta))
✓	0.3b	(asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))
✓	0.3b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))
✓	0.6b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))

series133.0ms (0.5%)

Counts

4 → 132

Calls

4 calls:

63.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))
53.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))
10.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
7.0ms	(asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`

Counts

4 → 72

Calls

4 calls:

4.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))
4.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
3.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))
0.0ms	(asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))

simplify195.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

447×	`fma-neg_binary64`
376×	`distribute-rgt-neg-in_binary64`
325×	`distribute-lft-neg-in_binary64`
257×	`associate-r_binary64`
241×	`neg-mul-1_binary64`

Counts

204 → 185

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	262	6113
1	696	5704
2	2227	5493
3	4796	5493
4	4989	5493
5	4924	5493

prune749.0ms (2.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	177	8	185
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	178	8	186

Error

0.0b

Counts

186 → 8

Alt Table

Status	Error	Program
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (cbrt.f64 (.f64 (.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))))
	12.7b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (.f64 (*.f64 (sin.f64 phi1) delta) (cos.f64 theta))))))
	30.6b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sqrt.f64 (sin.f64 theta)) (.f64 (sqrt.f64 (sin.f64 theta)) (sin.f64 delta))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (fma.f64 (.f64 (cbrt.f64 (cos.f64 delta)) (cbrt.f64 (cos.f64 delta))) (cbrt.f64 (cos.f64 delta)) (neg.f64 (.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (sin.f64 phi1)))) (fma.f64 (neg.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))) (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (sin.f64 phi1))))))
▶	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log.f64 (/.f64 (exp.f64 (cos.f64 delta)) (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))))
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 theta) (sin.f64 delta))) (cbrt.f64 (.f64 (sin.f64 theta) (sin.f64 delta)))) (cbrt.f64 (.f64 (sin.f64 theta) (sin.f64 delta)))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
	3.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 delta) (sin.f64 theta)) 3)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))

Compiler

Compiled 8588 to 1874 computations (78.2% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta)))
✓	0.3b	(.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))))
✓	0.3b	(pow.f64 (sin.f64 phi1) 2)
✓	0.6b	(-.f64 (cos.f64 delta) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))))))

series162.0ms (0.6%)

Counts

4 → 36

Calls

4 calls:

72.0ms	(.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))))
69.0ms	(-.f64 (cos.f64 delta) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))))))
16.0ms	(.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta)))
4.0ms	(pow.f64 (sin.f64 phi1) 2)

rewrite29.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64`
19×	`pow1_binary64`
18×	`add-cbrt-cube_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`

Counts

4 → 97

Calls

4 calls:

8.0ms	(-.f64 (cos.f64 delta) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))))))
6.0ms	(.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))))
5.0ms	(.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta)))
2.0ms	(pow.f64 (sin.f64 phi1) 2)

simplify108.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

547×	`fma-neg_binary64`
445×	`associate-r_binary64`
404×	`distribute-rgt-neg-in_binary64`
367×	`distribute-lft-neg-in_binary64`
362×	`associate-l_binary64`

Counts

133 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	308	4632
1	865	3768
2	3035	3479
3	5127	3479

prune441.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	178	3	181
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	182	7	189

Error

0.0b

Counts

189 → 7

Alt Table

Status	Error	Program
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log.f64 (/.f64 (exp.f64 (cos.f64 delta)) (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))))
▶	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (cbrt.f64 (pow.f64 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta)))) 3))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log1p.f64 (expm1.f64 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta))))))))
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 theta) (sin.f64 delta))) (cbrt.f64 (.f64 (sin.f64 theta) (sin.f64 delta)))) (cbrt.f64 (.f64 (sin.f64 theta) (sin.f64 delta)))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
	3.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 delta) (sin.f64 theta)) 3)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))
	30.6b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sqrt.f64 (sin.f64 theta)) (.f64 (sqrt.f64 (sin.f64 theta)) (sin.f64 delta))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))

Compiler

Compiled 9385 to 2839 computations (69.7% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta)))
✓	0.3b	(*.f64 (cos.f64 phi1) (cos.f64 phi1))
✓	0.5b	(cbrt.f64 (pow.f64 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta)))) 3))
✓	0.5b	(pow.f64 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta)))) 3)

series308.0ms (1.1%)

Counts

4 → 120

Calls

4 calls:

188.0ms	(pow.f64 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta)))) 3)
71.0ms	(cbrt.f64 (pow.f64 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta)))) 3))
46.0ms	(.f64 (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta)))
3.0ms	(*.f64 (cos.f64 phi1) (cos.f64 phi1))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`pow1_binary64`
19×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

4 → 109

Calls

4 calls:

7.0ms	(.f64 (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta)))
4.0ms	(*.f64 (cos.f64 phi1) (cos.f64 phi1))
2.0ms	(pow.f64 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta)))) 3)
2.0ms	(cbrt.f64 (pow.f64 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta)))) 3))

simplify235.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

582×	`unswap-sqr_binary64`
449×	`*-commutative_binary64`
429×	`fma-neg_binary64`
311×	`fma-def_binary64`
257×	`sub-neg_binary64`

Counts

229 → 226

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	447	7928
1	1302	7381
2	3186	7356
3	4988	7354
4	5089	7354

prune500.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	222	4	226
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	226	7	233

Error

0.0b

Counts

233 → 7

Alt Table

Status	Error	Program
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 theta) (sin.f64 delta))) (cbrt.f64 (.f64 (sin.f64 theta) (sin.f64 delta)))) (cbrt.f64 (.f64 (sin.f64 theta) (sin.f64 delta)))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
	15.9b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (cbrt.f64 (.f64 (pow.f64 (-.f64 (.f64 (cos.f64 delta) (pow.f64 (cos.f64 phi1) 2)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 theta) (cos.f64 phi1))))) 3/2) (pow.f64 (-.f64 (.f64 (cos.f64 delta) (pow.f64 (cos.f64 phi1) 2)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (*.f64 (cos.f64 theta) (cos.f64 phi1))))) 3/2)))))
▶	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log1p.f64 (expm1.f64 (cbrt.f64 (pow.f64 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta)))) 3))))))
	3.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 delta) (sin.f64 theta)) 3)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (cbrt.f64 (.f64 (pow.f64 (-.f64 (.f64 (cos.f64 delta) (pow.f64 (cos.f64 phi1) 2)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 theta) (cos.f64 phi1))))) 2) (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (.f64 (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 (cos.f64 delta) (pow.f64 (cos.f64 phi1) 2)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 theta) (cos.f64 phi1))))) 2)) (cbrt.f64 (-.f64 (.f64 (cos.f64 delta) (pow.f64 (cos.f64 phi1) 2)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (*.f64 (cos.f64 theta) (cos.f64 phi1)))))))))
	30.6b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sqrt.f64 (sin.f64 theta)) (.f64 (sqrt.f64 (sin.f64 theta)) (sin.f64 delta))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))

Compiler

Compiled 11626 to 3638 computations (68.7% saved)

localize62.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (cos.f64 phi1) (cos.f64 phi1))
✓	0.4b	(expm1.f64 (cbrt.f64 (pow.f64 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta)))) 3)))
	0.5b	(cbrt.f64 (pow.f64 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta)))) 3))
	0.5b	(pow.f64 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta)))) 3)

series112.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

112.0ms

(expm1.f64 (cbrt.f64 (pow.f64 (fma.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (*.f64 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta)))) 3)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`log1p-expm1-u_binary64`
1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

(expm1.f64 (cbrt.f64 (pow.f64 (fma.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (*.f64 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta)))) 3)))

simplify115.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

455×	`associate-r_binary64`
450×	`cancel-sign-sub-inv_binary64`
309×	`associate-l_binary64`
284×	`fma-neg_binary64`
213×	`*-commutative_binary64`

Counts

47 → 44

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	198	2547
1	608	2464
2	2481	2254
3	4791	2249
4	4984	2249
5	4974	2249

prune663.0ms (2.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	199	6	205

Error

0.0b

Counts

205 → 6

Alt Table

Status	Error	Program
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 theta) (sin.f64 delta))) (cbrt.f64 (.f64 (sin.f64 theta) (sin.f64 delta)))) (cbrt.f64 (.f64 (sin.f64 theta) (sin.f64 delta)))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
	15.9b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (cbrt.f64 (.f64 (pow.f64 (-.f64 (.f64 (cos.f64 delta) (pow.f64 (cos.f64 phi1) 2)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 theta) (cos.f64 phi1))))) 3/2) (pow.f64 (-.f64 (.f64 (cos.f64 delta) (pow.f64 (cos.f64 phi1) 2)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (*.f64 (cos.f64 theta) (cos.f64 phi1))))) 3/2)))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log1p.f64 (expm1.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 (cos.f64 delta) (pow.f64 (cos.f64 phi1) 2)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 theta) (cos.f64 phi1))))) 3))))))
	3.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 delta) (sin.f64 theta)) 3)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 (cos.f64 delta) (pow.f64 (cos.f64 phi1) 2)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 theta) (cos.f64 phi1))))) 2)) (cbrt.f64 (-.f64 (.f64 (cos.f64 delta) (pow.f64 (cos.f64 phi1) 2)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (*.f64 (cos.f64 theta) (cos.f64 phi1)))))))))
	30.6b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sqrt.f64 (sin.f64 theta)) (.f64 (sqrt.f64 (sin.f64 theta)) (sin.f64 delta))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))

Compiler

Compiled 11062 to 3809 computations (65.6% saved)

regimes3.9s (14.4%)

Accuracy

Total 0.1b remaining (61%)

Threshold costs 0.1b (61%)

Counts

339 → 1

Compiler

Compiled 97214 to 59066 computations (39.2% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64`
8×	`+-commutative_binary64`
7×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	58
1	39	58
2	46	58
3	58	58
4	71	58
5	80	58
6	86	58
7	88	58
8	88	58

end206.0ms (0.8%)

Compiler: Compiled 373 to 218 computations (41.6% saved)

Iter	Nodes	Cost
0	23	53
1	40	53
2	66	53
3	85	53
4	99	53
5	133	53
6	173	53
7	217	53
8	281	53
9	305	53
10	362	53
11	407	53
12	468	53
13	604	53
14	728	53
15	836	53
16	943	53
17	891	53
18	893	53
19	899	53
20	904	53
21	841	53

Iter	Nodes	Cost
0	23	53
1	40	53
2	66	53
3	85	53
4	99	53
5	133	53
6	173	53
7	217	53
8	281	53
9	305	53
10	362	53
11	407	53
12	468	53
13	604	53
14	728	53
15	836	53
16	943	53
17	891	53
18	893	53
19	899	53
20	904	53
21	841	53

Details

analyze7.4s (27.6%)

sample11.4s (42.3%)

simplify50.0ms (0.2%)

prune5.0ms (0%)

localize26.0ms (0.1%)

series133.0ms (0.5%)

rewrite14.0ms (0.1%)

simplify195.0ms (0.7%)

prune749.0ms (2.8%)

localize26.0ms (0.1%)

series162.0ms (0.6%)

rewrite29.0ms (0.1%)

simplify108.0ms (0.4%)

prune441.0ms (1.6%)

localize29.0ms (0.1%)

series308.0ms (1.1%)

rewrite21.0ms (0.1%)

simplify235.0ms (0.9%)

prune500.0ms (1.9%)

localize62.0ms (0.2%)

series112.0ms (0.4%)

rewrite1.0ms (0%)

simplify115.0ms (0.4%)

prune663.0ms (2.5%)

regimes3.9s (14.4%)

simplify5.0ms (0%)

end206.0ms (0.8%)

Profiling

Iter	Nodes	Cost
0	23	53
1	40	53
2	66	53
3	85	53
4	99	53
5	133	53
6	173	53
7	217	53
8	281	53
9	305	53
10	362	53
11	407	53
12	468	53
13	604	53
14	728	53
15	836	53
16	943	53
17	891	53
18	893	53
19	899	53
20	904	53
21	841	53