Details

analyze2.7s (15.6%)

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
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)

sample212.0ms (1.2%)

Algorithm

1×

intervals

Results

148.0ms	174×	body	1024	valid
27.0ms	39×	body	512	valid
12.0ms	6×	body	2048	valid
5.0ms	12×	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

14.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	14.3b	(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)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.2b	(cos.f64 (-.f64 lambda1 lambda2))
4.2b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite139.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

6.1b

Rules

11×	`add-sqr-sqrt_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
6×	`cancel-sign-sub-inv_binary64` `associate-r_binary64`
4×	`sin-sum_binary64` `add-log-exp_binary64` `cos-sum_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `associate-l_binary64`
3×	`cos-diff_binary64`

Counts

4 → 64

Calls

4 calls:

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

Compiler

Compiled 1966 to 330 computations (83.2% saved)

series265.0ms (1.5%)

Error

11.1b

Counts

4 → 64

Calls

4 calls:

88.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
53.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
24.0ms	(cos.f64 (-.f64 lambda1 lambda2))
22.0ms	(sin.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 4674 to 2223 computations (52.4% saved)

simplify120.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

782×	`cancel-sign-sub-inv_binary64`
532×	`sub-neg_binary64`
388×	`associate-r_binary64`
378×	`associate-l_binary64`
373×	`distribute-rgt-neg-in_binary64`

Counts

128 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	279	2703
1	747	2437
2	2302	2265
3	4171	2263
4	5178	2263

prune138.0ms (0.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	66	12	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	12	79

Error

6.1b

Counts

79 → 12

Alt Table

Status	Error	Program
	14.5b	(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)))))
	19.7b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (sin.f64 phi1)))))
	14.2b	(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))))))
	26.2b	(atan2.f64 (.f64 (-.f64 (sin.f64 lambda1) (+.f64 (.f64 lambda2 (cos.f64 lambda1)) (.f64 1/2 (.f64 (sin.f64 lambda1) (.f64 lambda2 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)))))
	14.5b	(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)))))))
	20.8b	(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))))
	28.6b	(atan2.f64 (.f64 (+.f64 (-.f64 (-.f64 (.f64 lambda1 (cos.f64 lambda2)) (sin.f64 lambda2)) (.f64 (.f64 (.f64 lambda1 lambda1) -1/2) (sin.f64 lambda2))) (.f64 (.f64 (cos.f64 lambda2) (pow.f64 lambda1 3)) -1/6)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	15.0b	(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))))))
▶	6.4b	(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)))))
	26.8b	(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)) (+.f64 (.f64 lambda2 (sin.f64 lambda1)) (.f64 (+.f64 (.f64 (.f64 lambda2 lambda2) -1/2) 1) (cos.f64 lambda1))))))
	17.7b	(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)))))
	40.4b	(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)))))

Compiler

Compiled 2801 to 947 computations (66.2% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
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)))
4.2b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite175.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

14×	`add-sqr-sqrt_binary64`
13×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
9×	`associate-r_binary64`
7×	`associate-l_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))
5.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 2666 to 378 computations (85.8% saved)

series358.0ms (2.1%)

Error

5.7b

Counts

4 → 61

Calls

4 calls:

98.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
89.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
38.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
26.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 5553 to 2761 computations (50.3% saved)

simplify162.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

806×	`cancel-sign-sub-inv_binary64`
477×	`associate-r_binary64`
453×	`associate-l_binary64`
432×	`distribute-rgt-neg-in_binary64`
377×	`distribute-lft-neg-in_binary64`

Counts

132 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	318	3166
1	870	2847
2	2837	2845
3	4143	2845
4	4956	2845
5	4953	2845

prune166.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	88	5	93
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	97	8	105

Error

0.1b

Counts

105 → 8

Alt Table

Status	Error	Program
	14.5b	(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)))))
	10.3b	(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)))))
	14.5b	(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)))))))
▶	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))))))
	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))))))
	7.0b	(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))))))
	40.4b	(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)))))
	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)))))

Compiler

Compiled 3423 to 855 computations (75% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
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))))
0.3b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite245.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

17×	`add-sqr-sqrt_binary64`
15×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-r_binary64`
11×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
10×	`associate-l_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))))
7.0ms	(.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))
4.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 3785 to 478 computations (87.4% saved)

series400.0ms (2.3%)

Error

0.1b

Counts

4 → 59

Calls

4 calls:

149.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
85.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
34.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
34.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 6484 to 2979 computations (54.1% saved)

simplify127.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

743×	`associate-r_binary64`
666×	`associate-l_binary64`
512×	`distribute-rgt-neg-in_binary64`
355×	`*-commutative_binary64`
205×	`sub-neg_binary64`

Counts

143 → 112

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	379	4159
1	1106	3681
2	4189	3681
3	5213	3681

prune245.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	107	5	112
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	111	9	120

Error

0.0b

Counts

120 → 9

Alt Table

Status	Error	Program
	10.3b	(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)))))
	0.5b	(atan2.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (.f64 (cos.f64 phi2) (cbrt.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))) (-.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))))))
	6.3b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda2) (cos.f64 lambda1))))) (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))))))
	0.3b	(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 (cbrt.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 phi1) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))) (cbrt.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 phi1) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) (cbrt.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 phi1) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))
	7.0b	(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 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (.f64 (sin.f64 lambda2) (cbrt.f64 (sin.f64 lambda1))))))))
	40.4b	(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)))))
	26.2b	(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 (sqrt.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1))) (sqrt.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
	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)))))

Compiler

Compiled 5255 to 1153 computations (78.1% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1)))
0.6b	(cbrt.f64 (sin.f64 lambda1))
0.6b	(cbrt.f64 (sin.f64 lambda1))
0.6b	(cbrt.f64 (sin.f64 lambda1))

rewrite497.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
11×	`pow1_binary64`
9×	`pow1/3_binary64`

Counts

4 → 73

Calls

4 calls:

7.0ms	(*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1)))
2.0ms	(cbrt.f64 (sin.f64 lambda1))
1.0ms	(cbrt.f64 (sin.f64 lambda1))
1.0ms	(cbrt.f64 (sin.f64 lambda1))

Compiler

Compiled 3588 to 521 computations (85.5% saved)

series115.0ms (0.7%)

Error

0.0b

Counts

4 → 16

Calls

4 calls:

23.0ms	(*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1)))
22.0ms	(cbrt.f64 (sin.f64 lambda1))
19.0ms	(cbrt.f64 (sin.f64 lambda1))
19.0ms	(cbrt.f64 (sin.f64 lambda1))

Compiler

Compiled 2124 to 1052 computations (50.5% saved)

simplify107.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

574×	`log-prod_binary64`
569×	`distribute-rgt-in_binary64`
530×	`distribute-lft-in_binary64`
471×	`unswap-sqr_binary64`
251×	`associate-l_binary64`

Counts

89 → 70

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	63	890
1	130	820
2	336	798
3	771	780
4	1729	620
5	4212	620
6	4929	620
7	4924	620

prune115.0ms (0.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	70	9	79

Error

0.0b

Counts

79 → 9

Alt Table

Status	Error	Program
	10.3b	(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)))))
	0.5b	(atan2.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (.f64 (cos.f64 phi2) (cbrt.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))) (-.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)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1)))) (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 lambda1))) 4)) (*.f64 (sin.f64 lambda2) (cbrt.f64 (sin.f64 lambda1))))))))
	0.3b	(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 (cbrt.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 phi1) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))) (cbrt.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 phi1) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) (cbrt.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 phi1) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))
	7.0b	(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 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (.f64 (sin.f64 lambda2) (cbrt.f64 (sin.f64 lambda1))))))))
	40.4b	(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)))))
	26.2b	(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 (sqrt.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1))) (sqrt.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
	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)))))

Compiler

Compiled 2223 to 575 computations (74.1% saved)

regimes3.8s (22.2%)

Accuracy

Total 0.1b remaining (52.7%)

Threshold costs 0.1b (52.7%)

Compiler

Compiled 81333 to 46637 computations (42.7% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

22×	`*-commutative_binary64`
16×	`+-commutative_binary64`
15×	`sub-neg_binary64`
13×	`neg-mul-1_binary64` `neg-sub0_binary64`
12×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	73
1	43	73
2	60	73
3	85	73
4	116	73
5	133	73
6	144	73
7	148	73
8	148	73

end1.0ms (0%)

Compiler: Compiled 48 to 25 computations (47.9% saved)

sample6.9s (40.3%)

Algorithm

1×

intervals

Results

4.8s	5388×	body	1024	valid
705.0ms	1253×	body	512	valid
343.0ms	175×	body	2048	valid
142.0ms	794×	body	128	valid
142.0ms	390×	body	256	valid

Compiler

Compiled 576 to 293 computations (49.1% 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 (15.6%)

sample212.0ms (1.2%)

simplify24.0ms (0.1%)

prune4.0ms (0%)

localize25.0ms (0.1%)

rewrite139.0ms (0.8%)

series265.0ms (1.5%)

simplify120.0ms (0.7%)

prune138.0ms (0.8%)

localize31.0ms (0.2%)

rewrite175.0ms (1%)

series358.0ms (2.1%)

simplify162.0ms (0.9%)

prune166.0ms (1%)

localize32.0ms (0.2%)

rewrite245.0ms (1.4%)

series400.0ms (2.3%)

simplify127.0ms (0.7%)

prune245.0ms (1.4%)

localize37.0ms (0.2%)

rewrite497.0ms (2.9%)

series115.0ms (0.7%)

simplify107.0ms (0.6%)

prune115.0ms (0.7%)

regimes3.8s (22.2%)

simplify7.0ms (0%)

end1.0ms (0%)

sample6.9s (40.3%)

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