Details

analyze4.6s (20%)

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
0.8%	99%	0.2%	11
1.2%	98.6%	0.2%	12
1.8%	98%	0.2%	13
2%	97.7%	0.2%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample294.0ms (1.3%)

Algorithm

1×

intervals

Results

210.0ms	174×	body	1024	valid
26.0ms	41×	body	512	valid
19.0ms	7×	body	2048	valid
7.0ms	18×	body	256	valid
3.0ms	16×	body	128	valid

Compiler

Compiled 54 to 40 computations (25.9% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

47×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`*-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	29
1	28	29
2	43	29
3	53	29
4	60	29
5	78	29
6	104	29
7	125	29
8	142	29
9	152	29
10	156	29
11	158	29
12	144	29

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

14.7b

Counts

2 → 2

Alt Table

Status	Error	Program
	14.7b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
▶	14.7b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)

Status

Error

Program

14.7b

(*.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)

▶

14.7b

(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)

Compiler

Compiled 117 to 82 computations (29.9% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
1.1b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
3.0b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite216.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

2.5b

Rules

34×	`add-cube-cbrt_binary64`
30×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
16×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`

Counts

4 → 149

Calls

4 calls:

14.0ms	(cos.f64 (-.f64 lambda1 lambda2))
14.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
14.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
11.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 4392 to 637 computations (85.5% saved)

series116.0ms (0.5%)

Error

14.3b

Counts

4 → 47

Calls

4 calls:

41.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
25.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
20.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
16.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 2552 to 1673 computations (34.4% saved)

simplify174.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

652×	`prod-exp_binary64`
521×	`fma-def_binary64`
434×	`fma-neg_binary64`
266×	`cancel-sign-sub-inv_binary64`
198×	`unswap-sqr_binary64`

Counts

196 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	239	4562
1	600	3753
2	1724	3588
3	3887	3430
4	4474	3430
5	5398	3430

prune97.0ms (0.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	88	17	105
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	90	17	107

Error

2.5b

Counts

107 → 17

Alt Table

Status	Error	Program
	14.8b	(.f64 (/.f64 (-.f64 (/.f64 (.f64 PI.f64 PI.f64) 4) (.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (+.f64 (/.f64 PI.f64 2) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
	2.9b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) 3) (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (fma.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (sin.f64 lambda2) (-.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))) R)
	15.0b	(.f64 (.f64 (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 2)) (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
▶	2.8b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
	15.4b	(.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (*.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	14.9b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3)) R)
	15.4b	(.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (.f64 R (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))))
	14.7b	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
	37.5b	(.f64 (cbrt.f64 (pow.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R) 2)) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)))
	14.9b	(.f64 (-.f64 (exp.f64 (log1p.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))) 1) R)
	2.8b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (/.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)
	14.8b	(.f64 (/.f64 (-.f64 (pow.f64 (/.f64 PI.f64 2) 3) (pow.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3)) (fma.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (+.f64 (/.f64 PI.f64 2) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (/.f64 (.f64 PI.f64 PI.f64) 4))) R)
	14.8b	(.f64 (.f64 (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
	14.7b	(.f64 (acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
	38.9b	(.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)) (sqrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)))
	15.4b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R))) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)))
	46.7b	(cbrt.f64 (pow.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R) 3))

Compiler

Compiled 3378 to 1147 computations (66% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
1.1b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite246.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

2.4b

Rules

37×	`pow1_binary64`
28×	`add-sqr-sqrt_binary64`
20×	`add-exp-log_binary64`
20×	`add-cube-cbrt_binary64`
18×	`add-cbrt-cube_binary64`

Counts

4 → 150

Calls

4 calls:

16.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
16.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
15.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
11.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)

Compiler

Compiled 4502 to 670 computations (85.1% saved)

series162.0ms (0.7%)

Error

2.5b

Counts

4 → 46

Calls

4 calls:

66.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
35.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
22.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
19.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 3515 to 2179 computations (38% saved)

simplify178.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

522×	`*-commutative_binary64`
462×	`prod-exp_binary64`
436×	`fma-def_binary64`
396×	`fma-neg_binary64`
282×	`unswap-sqr_binary64`

Counts

196 → 110

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	235	5096
1	536	4309
2	1539	4270
3	3473	4252
4	4953	4252
5	4963	4252

prune127.0ms (0.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	96	14	110
Fresh	14	2	16
Picked	1	0	1
Done	0	0	0
Total	111	16	127

Error

2.4b

Counts

127 → 16

Alt Table

Status	Error	Program
	2.9b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) 3) (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (fma.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (sin.f64 lambda2) (-.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))) R)
	2.8b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 2)) (cbrt.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
	3.0b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3)) R)
	33.4b	(.f64 (.f64 (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (sqrt.f64 R)) (.f64 (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) (sqrt.f64 R)))
	3.1b	(.f64 (-.f64 (exp.f64 (log1p.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) 1) R)
	46.7b	(cbrt.f64 (pow.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R) 3))
	3.0b	(.f64 (/.f64 (-.f64 (pow.f64 (/.f64 PI.f64 2) 3) (pow.f64 (asin.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3)) (fma.f64 (asin.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (+.f64 (/.f64 PI.f64 2) (asin.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (/.f64 (*.f64 PI.f64 PI.f64) 4))) R)
	3.0b	(.f64 (.f64 (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
	3.2b	(.f64 (.f64 (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 2)) (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
▶	2.8b	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
	3.8b	(.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	3.7b	(.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) (.f64 R (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))
	32.1b	(.f64 (cbrt.f64 (pow.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R) 2)) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)))
	3.7b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R))) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)))
	3.0b	(.f64 (/.f64 (-.f64 (/.f64 (.f64 PI.f64 PI.f64) 4) (.f64 (asin.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (asin.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (+.f64 (/.f64 PI.f64 2) (asin.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
	2.8b	(.f64 (acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)

Compiler

Compiled 4116 to 1258 computations (69.4% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
0.4b	(exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
0.9b	(log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))))
1.1b	(acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))

rewrite212.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

2.4b

Rules

28×	`pow1_binary64`
24×	`add-cube-cbrt_binary64`
20×	`add-sqr-sqrt_binary64`
14×	`add-cbrt-cube_binary64`
14×	`acos-asin_binary64`

Counts

4 → 142

Calls

4 calls:

12.0ms	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
11.0ms	(exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
11.0ms	(acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))
10.0ms	(log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))))

Compiler

Compiled 5240 to 517 computations (90.1% saved)

series270.0ms (1.2%)

Error

2.4b

Counts

4 → 51

Calls

4 calls:

120.0ms	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
84.0ms	(log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))))
34.0ms	(exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
29.0ms	(acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))

Compiler

Compiled 3219 to 2272 computations (29.4% saved)

simplify246.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

656×	`fma-def_binary64`
488×	`fma-neg_binary64`
434×	`associate-l_binary64`
312×	`associate-r_binary64`
297×	`prod-exp_binary64`

Counts

193 → 120

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	154	8223
1	261	7287
2	634	6991
3	2128	6815
4	4134	6815
5	4991	6815

prune130.0ms (0.6%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	112	8	120
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	118	18	136

Error

2.4b

Counts

136 → 18

Alt Table

Status	Error	Program
	2.9b	(.f64 (log.f64 (/.f64 1 (exp.f64 (-.f64 (asin.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (/.f64 PI.f64 2))))) R)
	3.8b	(.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	3.4b	(.f64 (log.f64 (.f64 (pow.f64 (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) 2) (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) R)
	33.4b	(.f64 (.f64 (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (sqrt.f64 R)) (.f64 (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) (sqrt.f64 R)))
	3.1b	(.f64 (-.f64 (exp.f64 (log1p.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) 1) R)
	2.9b	(.f64 (log.f64 (/.f64 (sqrt.f64 (exp.f64 PI.f64)) (exp.f64 (asin.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))) R)
	3.7b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R))) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)))
	2.8b	(.f64 (acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
	4.4b	(.f64 (/.f64 (.f64 9 (pow.f64 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))) 3)) (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))))) R)
	3.0b	(.f64 (.f64 (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
	3.2b	(.f64 (.f64 (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 2)) (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
▶	2.8b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 2)) (cbrt.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
	3.7b	(.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) (.f64 R (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))
	32.1b	(.f64 (cbrt.f64 (pow.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R) 2)) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)))
	3.0b	(.f64 (log.f64 (-.f64 (exp.f64 (log1p.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))) 1)) R)
	3.0b	(.f64 (log.f64 (exp.f64 (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3)))) R)
	2.9b	(.f64 (log.f64 (expm1.f64 (log1p.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) R)
	3.7b	(.f64 (.f64 (cbrt.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))) (.f64 (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))) R)

Compiler

Compiled 4575 to 1254 computations (72.6% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 2)) (cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
1.1b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 2)) (cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
7.2b	(cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
26.4b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 2))

rewrite274.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

2.4b

Rules

22×	`pow1/3_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
12×	`add-exp-log_binary64`
12×	`log1p-expm1-u_binary64`

Counts

4 → 141

Calls

4 calls:

16.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 2)) (cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
13.0ms	(cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
12.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 2)) (cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
12.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 2))

Compiler

Compiled 5068 to 1519 computations (70% saved)

series144.0ms (0.6%)

Error

2.4b

Counts

4 → 33

Calls

4 calls:

42.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 2))
35.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 2)) (cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
31.0ms	(cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
20.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 2)) (cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

Compiler

Compiled 3009 to 1888 computations (37.3% saved)

simplify176.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

500×	`unswap-sqr_binary64`
455×	`log-prod_binary64`
355×	`fma-def_binary64`
342×	`*-commutative_binary64`
342×	`distribute-rgt-in_binary64`

Counts

174 → 107

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	194	4016
1	456	3576
2	1156	3043
3	2382	3013
4	4425	3013
5	4939	3013
6	4942	3013

prune145.0ms (0.6%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	16	17
Picked	0	1	1
Done	0	0	0
Total	107	18	125

Error

2.4b

Counts

125 → 18

Alt Table

Status	Error	Program
	3.4b	(.f64 (log.f64 (.f64 (pow.f64 (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) 2) (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) R)
	33.4b	(.f64 (.f64 (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (sqrt.f64 R)) (.f64 (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) (sqrt.f64 R)))
	3.1b	(.f64 (-.f64 (exp.f64 (log1p.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) 1) R)
	2.9b	(.f64 (log.f64 (/.f64 (sqrt.f64 (exp.f64 PI.f64)) (exp.f64 (asin.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))) R)
	3.7b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R))) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)))
	2.9b	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) R)
	3.0b	(.f64 (log.f64 (exp.f64 (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3)))) R)
	2.8b	(.f64 (acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
	4.4b	(.f64 (/.f64 (.f64 9 (pow.f64 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))) 3)) (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))))) R)
	3.0b	(.f64 (.f64 (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
	3.2b	(.f64 (.f64 (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 2)) (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
	2.8b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 2)) (cbrt.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
	3.8b	(.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	3.7b	(.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) (.f64 R (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))
	32.1b	(.f64 (cbrt.f64 (pow.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R) 2)) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)))
	3.0b	(.f64 (log.f64 (-.f64 (exp.f64 (log1p.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))) 1)) R)
	2.9b	(.f64 (log.f64 (expm1.f64 (log1p.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) R)
	3.7b	(.f64 (.f64 (cbrt.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))) (.f64 (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))) R)

Compiler

Compiled 3680 to 1132 computations (69.2% saved)

regimes5.6s (24%)

Accuracy

Total 0.3b remaining (9.6%)

Threshold costs 0.3b (9.6%)

Compiler

Compiled 152044 to 89783 computations (40.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	43
1	27	43
2	27	43

end32.0ms (0.1%)

Remove: (sort lambda1 lambda2)
Compiler: Compiled 217 to 154 computations (29% saved)

sample9.6s (41.4%)

Algorithm

1×

intervals

Results

6.7s	5576×	body	1024	valid
881.0ms	1339×	body	512	valid
683.0ms	252×	body	2048	valid
218.0ms	508×	body	256	valid
68.0ms	325×	body	128	valid
6.0ms	5×	body	1024	invalid

Compiler

Compiled 989 to 501 computations (49.3% saved)

Iter	Nodes	Cost
0	18	29
1	28	29
2	43	29
3	53	29
4	60	29
5	78	29
6	104	29
7	125	29
8	142	29
9	152	29
10	156	29
11	158	29
12	144	29

Iter	Nodes	Cost
0	18	29
1	28	29
2	43	29
3	53	29
4	60	29
5	78	29
6	104	29
7	125	29
8	142	29
9	152	29
10	156	29
11	158	29
12	144	29

Details

analyze4.6s (20%)

sample294.0ms (1.3%)

simplify15.0ms (0.1%)

prune4.0ms (0%)

localize21.0ms (0.1%)

rewrite216.0ms (0.9%)

series116.0ms (0.5%)

simplify174.0ms (0.8%)

prune97.0ms (0.4%)

localize35.0ms (0.1%)

rewrite246.0ms (1.1%)

series162.0ms (0.7%)

simplify178.0ms (0.8%)

prune127.0ms (0.5%)

localize29.0ms (0.1%)

rewrite212.0ms (0.9%)

series270.0ms (1.2%)

simplify246.0ms (1.1%)

prune130.0ms (0.6%)

localize33.0ms (0.1%)

rewrite274.0ms (1.2%)

series144.0ms (0.6%)

simplify176.0ms (0.8%)

prune145.0ms (0.6%)

regimes5.6s (24%)

simplify3.0ms (0%)

end32.0ms (0.1%)

sample9.6s (41.4%)

Profiling

Iter	Nodes	Cost
0	18	29
1	28	29
2	43	29
3	53	29
4	60	29
5	78	29
6	104	29
7	125	29
8	142	29
9	152	29
10	156	29
11	158	29
12	144	29