Details

analyze2.7s (15.4%)

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
7.8%	92%	0.2%	9
7.8%	92%	0.2%	10
10.1%	89.7%	0.2%	11
10.1%	89.7%	0.2%	12
13.9%	85.9%	0.2%	13
13.9%	85.9%	0.2%	14

Compiler

Compiled 29 to 18 computations (37.9% saved)

sample210.0ms (1.2%)

Algorithm

1×

intervals

Results

149.0ms	161×	body	1024	valid
24.0ms	42×	body	512	valid
10.0ms	6×	body	2048	valid
7.0ms	22×	body	256	valid
4.0ms	25×	body	128	valid

Compiler

Compiled 61 to 39 computations (36.1% saved)

simplify24.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

83×	`cancel-sign-sub-inv_binary64`
59×	`distribute-rgt-neg-in_binary64`
56×	`sub-neg_binary64`
47×	`distribute-rgt-in_binary64`
42×	`unsub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	39
1	31	39
2	59	39
3	105	39
4	129	39
5	196	39
6	248	39
7	309	39
8	420	39
9	430	39
10	436	39
11	385	39

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

13.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	13.7b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 84 to 51 computations (39.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.2b	(sin.f64 (-.f64 lambda1 lambda2))
3.2b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite157.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

5.9b

Rules

11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
11×	`pow1_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`

Counts

4 → 64

Calls

4 calls:

12.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
8.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 1966 to 330 computations (83.2% saved)

series244.0ms (1.4%)

Error

9.7b

Counts

4 → 58

Calls

4 calls:

81.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
48.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
24.0ms	(sin.f64 (-.f64 lambda1 lambda2))
22.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 4276 to 2089 computations (51.1% saved)

simplify130.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

609×	`distribute-rgt-neg-in_binary64`
528×	`distribute-lft-neg-in_binary64`
500×	`cancel-sign-sub-inv_binary64`
500×	`sub-neg_binary64`
364×	`neg-mul-1_binary64`

Counts

122 → 72

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	247	2344
1	644	2092
2	1901	1988
3	3379	1988
4	4620	1982
5	5029	1982

prune119.0ms (0.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	58	14	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	14	73

Error

5.9b

Counts

73 → 14

Alt Table

Status	Error	Program
	39.5b	(atan2.f64 (.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	13.9b	(atan2.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi2) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	13.8b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))))
	17.3b	(atan2.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	27.8b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda1) (-.f64 (.f64 1/6 (pow.f64 lambda2 3)) lambda2)) (-.f64 (.f64 1/2 (.f64 lambda2 (.f64 lambda2 (sin.f64 lambda1)))) (sin.f64 lambda1))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	25.5b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) lambda1) (sin.f64 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	24.7b	(atan2.f64 (log.f64 (pow.f64 (exp.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cos.f64 phi2))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	19.8b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda2))))
	13.8b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (sin.f64 phi1))))) (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (sin.f64 phi1)))))))
	13.6b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	26.9b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (sin.f64 lambda1) (.f64 lambda2 (cos.f64 lambda1)))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	13.8b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (sin.f64 phi1))) 3))))
	14.7b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))))
▶	6.2b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 2635 to 922 computations (65% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.2b	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.2b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite184.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

14×	`add-sqr-sqrt_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
13×	`pow1_binary64`
10×	`*-un-lft-identity_binary64`

Counts

4 → 71

Calls

4 calls:

8.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
7.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
4.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 2666 to 378 computations (85.8% saved)

series317.0ms (1.8%)

Error

5.4b

Counts

4 → 54

Calls

4 calls:

85.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
82.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
32.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
25.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 4901 to 2502 computations (48.9% saved)

simplify115.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

502×	`cancel-sign-sub-inv_binary64`
428×	`sub-neg_binary64`
396×	`associate-r_binary64`
390×	`associate-l_binary64`
343×	`distribute-rgt-neg-in_binary64`

Counts

125 → 83

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	2721
1	720	2450
2	2280	2348
3	4399	2348
4	5276	2348

prune164.0ms (0.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	76	7	83
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	85	12	97

Error

0.0b

Counts

97 → 12

Alt Table

Status	Error	Program
	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	39.5b	(atan2.f64 (.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	35.5b	(atan2.f64 (exp.f64 (log.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	7.1b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))))
▶	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	9.3b	(atan2.f64 (.f64 (-.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	13.9b	(atan2.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi2) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	13.8b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))))
	24.7b	(atan2.f64 (log.f64 (pow.f64 (exp.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cos.f64 phi2))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	13.8b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (sin.f64 phi1))))) (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (sin.f64 phi1)))))))
	9.7b	(atan2.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) 3)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	12.6b	(atan2.f64 (/.f64 (.f64 (cos.f64 phi2) (-.f64 (pow.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3) (pow.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) 3))) (+.f64 (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 3287 to 939 computations (71.4% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.2b	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite275.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

17×	`add-sqr-sqrt_binary64`
15×	`add-cbrt-cube_binary64`
15×	`add-exp-log_binary64`
15×	`pow1_binary64`
12×	`associate-r_binary64`

Counts

4 → 84

Calls

4 calls:

11.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
9.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))

Compiler

Compiled 3785 to 478 computations (87.4% saved)

series379.0ms (2.2%)

Error

0.0b

Counts

4 → 55

Calls

4 calls:

122.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
83.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
33.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
33.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))

Compiler

Compiled 5871 to 2720 computations (53.7% saved)

simplify178.0ms (1%)

Algorithm

1×	egg-herbie

Rules

845×	`cancel-sign-sub-inv_binary64`
633×	`associate-r_binary64`
607×	`associate-l_binary64`
307×	`*-commutative_binary64`
164×	`exp-prod_binary64`

Counts

139 → 113

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	336	3707
1	975	3298
2	3604	3298
3	4986	3298
4	4994	3298
5	5045	3298

prune267.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	116	9	125

Error

0.0b

Counts

125 → 9

Alt Table

Status	Error	Program
	0.4b	(atan2.f64 (.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (.f64 (cbrt.f64 (cos.f64 phi2)) (cbrt.f64 (cos.f64 phi2)))) (cbrt.f64 (cos.f64 phi2))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	3.7b	(atan2.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) 3)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	35.5b	(atan2.f64 (exp.f64 (log.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	9.3b	(atan2.f64 (.f64 (-.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	13.8b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))))
	39.7b	(atan2.f64 (.f64 (.f64 (sqrt.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) (sqrt.f64 (cos.f64 phi2))) (.f64 (sqrt.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) (sqrt.f64 (cos.f64 phi2)))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	24.7b	(atan2.f64 (log.f64 (pow.f64 (exp.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cos.f64 phi2))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
▶	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 phi1) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))) 3))))
	1.1b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1))) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))

Compiler

Compiled 4828 to 1040 computations (78.5% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (sin.f64 phi1) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))
0.2b	(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))
0.5b	(pow.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 phi1) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))) 3)
20.7b	(cbrt.f64 (pow.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 phi1) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))) 3))

rewrite291.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

15×	`associate-*r/_binary64`
14×	`add-sqr-sqrt_binary64`
14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow1_binary64`

Counts

4 → 90

Calls

4 calls:

12.0ms	(pow.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 phi1) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))) 3)
9.0ms	(.f64 (sin.f64 phi1) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))
6.0ms	(cbrt.f64 (pow.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 phi1) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))) 3))
5.0ms	(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))

Compiler

Compiled 4351 to 788 computations (81.9% saved)

series896.0ms (5.1%)

Error

0.0b

Counts

4 → 62

Calls

4 calls:

533.0ms	(pow.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 phi1) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))) 3)
122.0ms	(cbrt.f64 (pow.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 phi1) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))) 3))
81.0ms	(.f64 (sin.f64 phi1) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))
33.0ms	(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))

Compiler

Compiled 10746 to 5819 computations (45.8% saved)

simplify163.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

453×	`unswap-sqr_binary64`
337×	`*-commutative_binary64`
262×	`associate-r_binary64`
208×	`associate-+r+_binary64`
205×	`+-commutative_binary64`

Counts

152 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	589	6661
1	1592	5899
2	3552	5847
3	4964	5847

prune231.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	106	9	115

Error

0.0b

Counts

115 → 9

Alt Table

Status	Error	Program
	0.4b	(atan2.f64 (.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (.f64 (cbrt.f64 (cos.f64 phi2)) (cbrt.f64 (cos.f64 phi2)))) (cbrt.f64 (cos.f64 phi2))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	3.7b	(atan2.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) 3)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	35.5b	(atan2.f64 (exp.f64 (log.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	9.3b	(atan2.f64 (.f64 (-.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	13.8b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))))
	39.7b	(atan2.f64 (.f64 (.f64 (sqrt.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) (sqrt.f64 (cos.f64 phi2))) (.f64 (sqrt.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) (sqrt.f64 (cos.f64 phi2)))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 phi1) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))) 3))))
	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (sin.f64 phi1)))))
	1.1b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1))) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))

Compiler

Compiled 5040 to 1548 computations (69.3% saved)

regimes3.3s (18.6%)

Accuracy

Total 0.1b remaining (53%)

Threshold costs 0.1b (53%)

Compiler

Compiled 68109 to 40025 computations (41.2% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

21×	`*-commutative_binary64`
15×	`+-commutative_binary64`
14×	`sub-neg_binary64`
12×	`neg-sub0_binary64`
12×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	63
1	49	63
2	72	63
3	92	63
4	120	63
5	132	63
6	138	63
7	140	63
8	139	63

end4.0ms (0%)

Compiler: Compiled 42 to 24 computations (42.9% saved)

sample7.1s (40.5%)

Algorithm

1×

intervals

Results

4.8s	5363×	body	1024	valid
867.0ms	1275×	body	512	valid
381.0ms	189×	body	2048	valid
142.0ms	408×	body	256	valid
131.0ms	765×	body	128	valid

Compiler

Compiled 479 to 275 computations (42.6% saved)

Iter	Nodes	Cost
0	18	39
1	31	39
2	59	39
3	105	39
4	129	39
5	196	39
6	248	39
7	309	39
8	420	39
9	430	39
10	436	39
11	385	39

Iter	Nodes	Cost
0	18	39
1	31	39
2	59	39
3	105	39
4	129	39
5	196	39
6	248	39
7	309	39
8	420	39
9	430	39
10	436	39
11	385	39

Details

analyze2.7s (15.4%)

sample210.0ms (1.2%)

simplify24.0ms (0.1%)

prune4.0ms (0%)

localize21.0ms (0.1%)

rewrite157.0ms (0.9%)

series244.0ms (1.4%)

simplify130.0ms (0.7%)

prune119.0ms (0.7%)

localize30.0ms (0.2%)

rewrite184.0ms (1%)

series317.0ms (1.8%)

simplify115.0ms (0.7%)

prune164.0ms (0.9%)

localize29.0ms (0.2%)

rewrite275.0ms (1.6%)

series379.0ms (2.2%)

simplify178.0ms (1%)

prune267.0ms (1.5%)

localize33.0ms (0.2%)

rewrite291.0ms (1.7%)

series896.0ms (5.1%)

simplify163.0ms (0.9%)

prune231.0ms (1.3%)

regimes3.3s (18.6%)

simplify7.0ms (0%)

end4.0ms (0%)

sample7.1s (40.5%)

Profiling

Iter	Nodes	Cost
0	18	39
1	31	39
2	59	39
3	105	39
4	129	39
5	196	39
6	248	39
7	309	39
8	420	39
9	430	39
10	436	39
11	385	39