Details

analyze5.1s (13.1%)

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 25 to 18 computations (28% saved)

sample432.0ms (1.1%)

Algorithm

1×

intervals

Results

306.0ms	168×	body	1024	valid
57.0ms	51×	body	512	valid
25.0ms	4×	body	2048	valid
8.0ms	23×	body	128	valid
7.0ms	10×	body	256	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify213.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	385	39
1	385	39

prune7.0ms (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

15.0b

Counts

2 → 1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize44.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.3b	(sin.f64 (-.f64 lambda1 lambda2))
5.6b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite77.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_2828` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `pow1_binary64_2867`
9×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
6×	`cancel-sign-sub-inv_binary64_2772` `associate-r_binary64_2746`
4×	`associate-l_binary64_2747` `sin-sum_binary64_2939` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `add-log-exp_binary64_2845` `cos-sum_binary64_2940` `pow-prod-down_binary64_2877`
3×	`cos-diff_binary64_2943`
2×	`*-commutative_binary64_2737` `sub-neg_binary64_2799`
1×	`sin-diff_binary64_2942` `distribute-lft-in_binary64_2755` `distribute-rgt-in_binary64_2756` `associate-*l/_binary64_2749` `unswap-sqr_binary64_2774` `sin-cos-mult_binary64_2962`

Counts

4 → 63

Calls

4 calls:

21.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
18.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
14.0ms	(sin.f64 (-.f64 lambda1 lambda2))
11.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series1.2s (3.1%)

Counts

4 → 52

Calls

4 calls:

767.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
215.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
120.0ms	(sin.f64 (-.f64 lambda1 lambda2))
120.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 2355 to 1608 computations (31.7% saved)

simplify179.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (133.0ms)

Iter	Nodes	Cost
0	5110	1742

prune292.0ms (0.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	100	15	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	15	116

Error

7.4b

Counts

116 → 15

Compiler

Compiled 3717 to 790 computations (78.7% saved)

localize57.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.2b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.6b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite60.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2828`
13×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `pow1_binary64_2867`
10×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
9×	`associate-r_binary64_2746`
7×	`associate-l_binary64_2747`
5×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `pow-prod-down_binary64_2877`
4×	`add-log-exp_binary64_2845` `cos-sum_binary64_2940`
3×	`cos-diff_binary64_2943` `cancel-sign-sub-inv_binary64_2772` `*-commutative_binary64_2737`
2×	`unswap-sqr_binary64_2774`
1×	`distribute-lft-in_binary64_2755` `distribute-rgt-in_binary64_2756` `sub-neg_binary64_2799` `associate-*l/_binary64_2749` `sin-cos-mult_binary64_2962`

Counts

4 → 69

Calls

4 calls:

14.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
12.0ms	(cos.f64 (-.f64 lambda1 lambda2))
9.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
9.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

series1.3s (3.2%)

Counts

4 → 50

Calls

4 calls:

732.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
214.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
200.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
116.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 2845 to 2008 computations (29.4% saved)

simplify189.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (146.0ms)

Iter	Nodes	Cost
0	4949	1747
1	4949	1747

prune287.0ms (0.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	10	4	14
Picked	1	0	1
Done	0	0	0
Total	126	8	134

Error

0.1b

Counts

134 → 8

Compiler

Compiled 4466 to 710 computations (84.1% saved)

localize60.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite74.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_2828` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `pow1_binary64_2867`
9×	`-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841` `associate-r*_binary64_2746`
7×	`associate-l_binary64_2747`
6×	`add-log-exp_binary64_2845`
5×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `pow-prod-down_binary64_2877`
4×	`sin-mult_binary64_2961` `sin-cos-mult_binary64_2962`
3×	`frac-times_binary64_2816` `-commutative_binary64_2737` `flip-+_binary64_2780` `frac-add_binary64_2814` `cos-mult_binary64_2960` `flip3-+_binary64_2809` `associate-r/_binary64_2748`
2×	`unswap-sqr_binary64_2774`
1×	`distribute-lft-in_binary64_2755` `distribute-rgt-in_binary64_2756` `sum-log_binary64_2897` `associate-*l/_binary64_2749` `+-commutative_binary64_2736`

Counts

4 → 76

Calls

4 calls:

22.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
13.0ms	(+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
10.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
9.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))

series2.3s (5.8%)

Counts

4 → 53

Calls

4 calls:

1.5s	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
324.0ms	(+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
276.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
204.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 3571 to 2219 computations (37.9% saved)

simplify140.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5063	3234

prune390.0ms (1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	124	5	129
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	126	11	137

Error

0.0b

Counts

137 → 11

Compiler

Compiled 6251 to 984 computations (84.3% saved)

localize74.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
0.3b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
0.4b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))

rewrite250.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`pow1_binary64_2867`
78×	`cos-mult_binary64_2960` `sin-mult_binary64_2961`
74×	`associate-*r/_binary64_2748`
66×	`frac-times_binary64_2816`
44×	`associate-*l/_binary64_2749`
42×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
37×	`frac-sub_binary64_2815` `pow-prod-down_binary64_2877`
34×	`sin-cos-mult_binary64_2962`
33×	`associate-/l/_binary64_2753`
22×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839`
21×	`sub-div_binary64_2813`
8×	`pow-sqr_binary64_2779` `pow-prod-up_binary64_2876`
7×	`add-sqr-sqrt_binary64_2828` `*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
6×	`associate-r_binary64_2746`
5×	`flip3--_binary64_2810` `flip--_binary64_2781`
4×	`add-log-exp_binary64_2845` `associate-/r/_binary64_2752` `pow-plus_binary64_2869`
3×	`associate-l_binary64_2747` `times-frac_binary64_2812` `div-exp_binary64_2857` `-commutative_binary64_2737` `cbrt-undiv_binary64_2840` `associate-/r_binary64_2750`
2×	`cancel-sign-sub-inv_binary64_2772` `distribute-lft-in_binary64_2755` `distribute-rgt-in_binary64_2756` `sub-neg_binary64_2799` `swap-sqr_binary64_2773` `pow2_binary64_2887`
1×	`div-inv_binary64_2803` `clear-num_binary64_2805` `difference-of-squares_binary64_2775` `associate-/l*_binary64_2751` `frac-2neg_binary64_2817`

Counts

4 → 190

Calls

4 calls:

67.0ms	(/.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
48.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
22.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
20.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))

series6.8s (17.2%)

Counts

4 → 65

Calls

4 calls:

3.6s	(/.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
2.4s	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
405.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
326.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))

Compiler

Compiled 7134 to 4052 computations (43.2% saved)

simplify277.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

255 → 255

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4959	11070
1	4959	11070

prune1.0s (2.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	254	1	255
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	254	12	266

Error

0.0b

Counts

266 → 12

Compiler

Compiled 18376 to 3661 computations (80.1% saved)

regimes2.2s (5.6%)

Accuracy

Total 0.1b remaining (71%)

Threshold costs 0.1b (71%)

Compiler

Compiled 13954 to 8562 computations (38.6% saved)

bsearch0.0ms (0%)

simplify39.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	474	103
1	474	103

end0.0ms (0%)

sample16.2s (41.3%)

Algorithm

1×

intervals

Results

9.4s	5325×	body	1024	valid
1.4s	1321×	body	512	valid
692.0ms	181×	body	2048	valid
284.0ms	777×	body	128	valid
272.0ms	396×	body	256	valid

Compiler

Compiled 2316 to 1409 computations (39.2% saved)

Details

analyze5.1s (13.1%)

sample432.0ms (1.1%)

simplify213.0ms (0.5%)

prune7.0ms (0%)

localize44.0ms (0.1%)

rewrite77.0ms (0.2%)

series1.2s (3.1%)

simplify179.0ms (0.5%)

prune292.0ms (0.7%)

localize57.0ms (0.1%)

rewrite60.0ms (0.2%)

series1.3s (3.2%)

simplify189.0ms (0.5%)

prune287.0ms (0.7%)

localize60.0ms (0.2%)

rewrite74.0ms (0.2%)

series2.3s (5.8%)

simplify140.0ms (0.4%)

prune390.0ms (1%)

localize74.0ms (0.2%)

rewrite250.0ms (0.6%)

series6.8s (17.2%)

simplify277.0ms (0.7%)

prune1.0s (2.6%)

regimes2.2s (5.6%)

bsearch0.0ms (0%)

simplify39.0ms (0.1%)

end0.0ms (0%)

sample16.2s (41.3%)

Profiling