Details

analyze3.9s (12.8%)

Algorithm

1×	search
2×	egg-herbie

Rules

966×	`distribute-rgt-in_binary64_2756`
910×	`unsub-neg_binary64_2800`
843×	`distribute-lft-in_binary64_2755`
580×	`distribute-rgt-neg-out_binary64_2766`
450×	`distribute-lft-neg-out_binary64_2765`
437×	`neg-sub0_binary64_2801`
376×	`neg-mul-1_binary64_2802`
344×	`distribute-rgt-neg-in_binary64_2764`
295×	`sub-neg_binary64_2799`
276×	`*-commutative_binary64_2737`
230×	`cancel-sign-sub-inv_binary64_2772`
180×	`distribute-neg-out_binary64_2768`
165×	`distribute-lft-neg-in_binary64_2763`
160×	`associate-l_binary64_2747` `associate-r_binary64_2746` `associate--r+_binary64_2742`
137×	`remove-double-neg_binary64_2794`
130×	`distribute-neg-in_binary64_2767`
113×	`+-commutative_binary64_2736`
100×	`associate-+l-_binary64_2741`
73×	`*-lft-identity_binary64_2795`
67×	`mul0-rgt_binary64_2789` `mul0-lft_binary64_2788`
60×	`+-lft-identity_binary64_2790`
55×	`sub0-neg_binary64_2793`
51×	`*-rgt-identity_binary64_2796`
50×	`associate--r-_binary64_2745`
30×	`distribute-lft-out_binary64_2757`
25×	`--rgt-identity_binary64_2792`
20×	`cancel-sign-sub_binary64_2771` `associate--l+_binary64_2743`
10×	`associate-+r-_binary64_2740` `associate-+l+_binary64_2739` `associate-+r+_binary64_2738`
6×	`distribute-rgt-out--_binary64_2760`
5×	`+-rgt-identity_binary64_2791`
4×	`distribute-lft-out--_binary64_2758`
1×	`1-exp_binary64_2850`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_3069` `erf-erfc_binary64_3068` `erf-odd_binary64_3067` `if-if-and-not_binary64_3066` `if-if-and_binary64_3065` `if-if-or-not_binary64_3064` `if-if-or_binary64_3063` `if-not_binary64_3062` `if-same_binary64_3061` `if-false_binary64_3060` `if-true_binary64_3059` `not-gte_binary64_3058` `not-lte_binary64_3057` `not-gt_binary64_3056` `not-lt_binary64_3055` `gte-same_binary64_3054` `lte-same_binary64_3053` `gt-same_binary64_3052` `lt-same_binary64_3051` `sinh---cosh_binary64_2998` `sinh-+-cosh_binary64_2997` `sinh-cosh_binary64_2996` `tanh-def-c_binary64_2995` `tanh-def-b_binary64_2994` `tanh-def-a_binary64_2993` `cosh-def_binary64_2992` `sinh-def_binary64_2991` `tan-neg_binary64_2938` `cos-neg_binary64_2937` `sin-neg_binary64_2936` `tan-0_binary64_2935` `cos-0_binary64_2934` `sin-0_binary64_2933` `hang-m-tan_binary64_2932` `hang-p-tan_binary64_2931` `hang-m0-tan_binary64_2930` `hang-p0-tan_binary64_2929` `hang-0m-tan_binary64_2928` `hang-0p-tan_binary64_2927` `tan-+PI/2_binary64_2926` `tan-+PI_binary64_2925` `tan-PI_binary64_2924` `tan-PI/3_binary64_2923` `tan-PI/4_binary64_2922` `tan-PI/6_binary64_2921` `cos-+PI/2_binary64_2920` `cos-+PI_binary64_2919` `cos-PI_binary64_2918` `cos-PI/2_binary64_2917` `cos-PI/3_binary64_2916` `cos-PI/4_binary64_2915` `cos-PI/6_binary64_2914` `sin-+PI/2_binary64_2913` `sin-+PI_binary64_2912` `sin-PI_binary64_2911` `sin-PI/2_binary64_2910` `sin-PI/3_binary64_2909` `sin-PI/4_binary64_2908` `sin-PI/6_binary64_2907` `sub-1-sin_binary64_2906` `sub-1-cos_binary64_2905` `-1-add-sin_binary64_2904` `-1-add-cos_binary64_2903` `1-sub-sin_binary64_2902` `1-sub-cos_binary64_2901` `cos-sin-sum_binary64_2900` `log-E_binary64_2896` `log-pow_binary64_2895` `log-rec_binary64_2894` `log-div_binary64_2893` `log-prod_binary64_2892` `pow-base-0_binary64_2890` `unpow1/3_binary64_2873` `unpow3_binary64_2872` `unpow2_binary64_2871` `unpow1/2_binary64_2870` `pow-plus_binary64_2869` `exp-to-pow_binary64_2868` `pow-base-1_binary64_2866` `unpow0_binary64_2865` `unpow1_binary64_2864` `unpow-1_binary64_2863` `exp-lft-cube_binary64_2862` `exp-lft-sqr_binary64_2861` `exp-cbrt_binary64_2860` `exp-sqrt_binary64_2859` `exp-prod_binary64_2858` `div-exp_binary64_2857` `rec-exp_binary64_2856` `prod-exp_binary64_2855` `exp-diff_binary64_2854` `exp-neg_binary64_2853` `exp-sum_binary64_2852` `e-exp-1_binary64_2851` `exp-1-e_binary64_2849` `exp-0_binary64_2848` `rem-log-exp_binary64_2847` `rem-exp-log_binary64_2846` `cube-unmult_binary64_2843` `cube-mult_binary64_2836` `cube-div_binary64_2835` `cube-prod_binary64_2834` `cube-neg_binary64_2833` `rem-3cbrt-rft_binary64_2832` `rem-3cbrt-lft_binary64_2831` `rem-cbrt-cube_binary64_2830` `rem-cube-cbrt_binary64_2829` `sqr-abs_binary64_2821` `sqr-neg_binary64_2820` `rem-sqrt-square_binary64_2819` `rem-square-sqrt_binary64_2818` `times-frac_binary64_2812` `div-sub_binary64_2811` `mul-1-neg_binary64_2798` `/-rgt-identity_binary64_2797` `div0_binary64_2787` `-inverses_binary64_2786` `+-inverses_binary64_2785` `lft-mult-inverse_binary64_2784` `rgt-mult-inverse_binary64_2783` `remove-double-div_binary64_2782` `pow-sqr_binary64_2779` `sqr-pow_binary64_2778` `difference-of-sqr--1_binary64_2777` `difference-of-sqr-1_binary64_2776` `difference-of-squares_binary64_2775` `unswap-sqr_binary64_2774` `swap-sqr_binary64_2773` `distribute-neg-frac_binary64_2770` `distribute-frac-neg_binary64_2769` `distribute-rgt1-in_binary64_2762` `distribute-lft1-in_binary64_2761` `distribute-rgt-out_binary64_2759` `count-2_binary64_2754` `associate-/l/_binary64_2753` `associate-/r/_binary64_2752` `associate-/l_binary64_2751` `associate-/r_binary64_2750` `associate-l/_binary64_2749` `associate-*r/_binary64_2748` `associate--l-_binary64_2744`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	131	605
1	263	605
2	417	605
3	512	605
4	598	605
5	1028	605
6	994	605
7	1659	605
8	2449	605
9	2458	605
10	2534	605
11	2537	605
12	2537	605
13	2903	605
14	2948	605
15	2948	605
16	4374	605
17	4909	605
0	5	5
1	5	5

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
1.2%	98.6%	0.2%	11
1.4%	98.4%	0.2%	12
10.8%	88.9%	0.2%	13
10.8%	88.9%	0.2%	14

Compiler

Compiled 34 to 24 computations (29.4% saved)

sample234.0ms (0.8%)

Algorithm

1×

intervals

Results

155.0ms	127×	body	1024	valid
33.0ms	45×	body	512	valid
13.0ms	64×	body	128	valid
9.0ms	19×	body	256	valid
2.0ms	1×	body	2048	valid

Compiler

Compiled 67 to 52 computations (22.4% saved)

simplify47.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

103×	`unsub-neg_binary64_2800`
90×	`associate-l_binary64_2747`
88×	`distribute-rgt-in_binary64_2756`
82×	`cancel-sign-sub-inv_binary64_2772`
80×	`associate-r_binary64_2746`
70×	`distribute-rgt-neg-in_binary64_2764`
58×	`distribute-lft-neg-out_binary64_2765`
57×	`distribute-lft-in_binary64_2755`
56×	`distribute-rgt-neg-out_binary64_2766`
49×	`sub-neg_binary64_2799`
41×	`neg-sub0_binary64_2801`
40×	`distribute-lft-neg-in_binary64_2763`
34×	`neg-mul-1_binary64_2802`
33×	`associate--r+_binary64_2742`
28×	`*-commutative_binary64_2737`
25×	`distribute-neg-in_binary64_2767`
21×	`mul0-rgt_binary64_2789` `mul0-lft_binary64_2788`
17×	`+-commutative_binary64_2736`
14×	`associate-+l-_binary64_2741`
13×	`*-lft-identity_binary64_2795`
12×	`remove-double-neg_binary64_2794`
8×	`sub0-neg_binary64_2793` `+-lft-identity_binary64_2790`
7×	`*-rgt-identity_binary64_2796`
5×	`associate--l+_binary64_2743` `associate-+l+_binary64_2739`
4×	`mul-1-neg_binary64_2798`
3×	`--rgt-identity_binary64_2792` `associate--r-_binary64_2745` `associate--l-_binary64_2744` `associate-+r+_binary64_2738`
2×	`+-rgt-identity_binary64_2791`
1×	`1-exp_binary64_2850` `cancel-sign-sub_binary64_2771` `associate-+r-_binary64_2740`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_3069` `erf-erfc_binary64_3068` `erf-odd_binary64_3067` `if-if-and-not_binary64_3066` `if-if-and_binary64_3065` `if-if-or-not_binary64_3064` `if-if-or_binary64_3063` `if-not_binary64_3062` `if-same_binary64_3061` `if-false_binary64_3060` `if-true_binary64_3059` `not-gte_binary64_3058` `not-lte_binary64_3057` `not-gt_binary64_3056` `not-lt_binary64_3055` `gte-same_binary64_3054` `lte-same_binary64_3053` `gt-same_binary64_3052` `lt-same_binary64_3051` `sinh---cosh_binary64_2998` `sinh-+-cosh_binary64_2997` `sinh-cosh_binary64_2996` `tanh-def-c_binary64_2995` `tanh-def-b_binary64_2994` `tanh-def-a_binary64_2993` `cosh-def_binary64_2992` `sinh-def_binary64_2991` `tan-neg_binary64_2938` `cos-neg_binary64_2937` `sin-neg_binary64_2936` `tan-0_binary64_2935` `cos-0_binary64_2934` `sin-0_binary64_2933` `hang-m-tan_binary64_2932` `hang-p-tan_binary64_2931` `hang-m0-tan_binary64_2930` `hang-p0-tan_binary64_2929` `hang-0m-tan_binary64_2928` `hang-0p-tan_binary64_2927` `tan-+PI/2_binary64_2926` `tan-+PI_binary64_2925` `tan-PI_binary64_2924` `tan-PI/3_binary64_2923` `tan-PI/4_binary64_2922` `tan-PI/6_binary64_2921` `cos-+PI/2_binary64_2920` `cos-+PI_binary64_2919` `cos-PI_binary64_2918` `cos-PI/2_binary64_2917` `cos-PI/3_binary64_2916` `cos-PI/4_binary64_2915` `cos-PI/6_binary64_2914` `sin-+PI/2_binary64_2913` `sin-+PI_binary64_2912` `sin-PI_binary64_2911` `sin-PI/2_binary64_2910` `sin-PI/3_binary64_2909` `sin-PI/4_binary64_2908` `sin-PI/6_binary64_2907` `sub-1-sin_binary64_2906` `sub-1-cos_binary64_2905` `-1-add-sin_binary64_2904` `-1-add-cos_binary64_2903` `1-sub-sin_binary64_2902` `1-sub-cos_binary64_2901` `cos-sin-sum_binary64_2900` `log-E_binary64_2896` `log-pow_binary64_2895` `log-rec_binary64_2894` `log-div_binary64_2893` `log-prod_binary64_2892` `pow-base-0_binary64_2890` `unpow1/3_binary64_2873` `unpow3_binary64_2872` `unpow2_binary64_2871` `unpow1/2_binary64_2870` `pow-plus_binary64_2869` `exp-to-pow_binary64_2868` `pow-base-1_binary64_2866` `unpow0_binary64_2865` `unpow1_binary64_2864` `unpow-1_binary64_2863` `exp-lft-cube_binary64_2862` `exp-lft-sqr_binary64_2861` `exp-cbrt_binary64_2860` `exp-sqrt_binary64_2859` `exp-prod_binary64_2858` `div-exp_binary64_2857` `rec-exp_binary64_2856` `prod-exp_binary64_2855` `exp-diff_binary64_2854` `exp-neg_binary64_2853` `exp-sum_binary64_2852` `e-exp-1_binary64_2851` `exp-1-e_binary64_2849` `exp-0_binary64_2848` `rem-log-exp_binary64_2847` `rem-exp-log_binary64_2846` `cube-unmult_binary64_2843` `cube-mult_binary64_2836` `cube-div_binary64_2835` `cube-prod_binary64_2834` `cube-neg_binary64_2833` `rem-3cbrt-rft_binary64_2832` `rem-3cbrt-lft_binary64_2831` `rem-cbrt-cube_binary64_2830` `rem-cube-cbrt_binary64_2829` `sqr-abs_binary64_2821` `sqr-neg_binary64_2820` `rem-sqrt-square_binary64_2819` `rem-square-sqrt_binary64_2818` `times-frac_binary64_2812` `div-sub_binary64_2811` `/-rgt-identity_binary64_2797` `div0_binary64_2787` `-inverses_binary64_2786` `+-inverses_binary64_2785` `lft-mult-inverse_binary64_2784` `rgt-mult-inverse_binary64_2783` `remove-double-div_binary64_2782` `pow-sqr_binary64_2779` `sqr-pow_binary64_2778` `difference-of-sqr--1_binary64_2777` `difference-of-sqr-1_binary64_2776` `difference-of-squares_binary64_2775` `unswap-sqr_binary64_2774` `swap-sqr_binary64_2773` `distribute-neg-frac_binary64_2770` `distribute-frac-neg_binary64_2769` `distribute-neg-out_binary64_2768` `distribute-rgt1-in_binary64_2762` `distribute-lft1-in_binary64_2761` `distribute-rgt-out--_binary64_2760` `distribute-rgt-out_binary64_2759` `distribute-lft-out--_binary64_2758` `distribute-lft-out_binary64_2757` `count-2_binary64_2754` `associate-/l/_binary64_2753` `associate-/r/_binary64_2752` `associate-/l_binary64_2751` `associate-/r_binary64_2750` `associate-l/_binary64_2749` `associate-*r/_binary64_2748`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	55
1	39	55
2	61	55
3	72	55
4	83	55
5	107	55
6	134	55
7	164	55
8	217	55
9	216	55
10	240	55
11	275	55
12	317	55
13	431	55
14	486	55
15	534	55
16	567	55
17	521	55
18	523	55
19	525	55
20	526	55
21	463	55

prune5.0ms (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

0.1b

Counts

2 → 1

Compiler

Compiled 66 to 46 computations (30.3% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (sin.f64 theta) (sin.f64 delta))
0.3b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.5b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))

rewrite161.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

12×	`add-sqr-sqrt_binary64_2828`
8×	`pow1_binary64_2867` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `add-cube-cbrt_binary64_2841` `*-un-lft-identity_binary64_2806`
6×	`add-log-exp_binary64_2845` `associate-l_binary64_2747` `associate-r_binary64_2746`
2×	`sin-mult_binary64_2961` `pow-prod-down_binary64_2877` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `unswap-sqr_binary64_2774` `*-commutative_binary64_2737`
1×	`diff-log_binary64_2898` `flip3--_binary64_2810` `sub-neg_binary64_2799` `flip--_binary64_2781` `cancel-sign-sub-inv_binary64_2772` `asin-acos_binary64_2986`

Counts

4 → 58

Calls

4 calls:

9.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
6.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
6.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
2.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

Compiler

Compiled 2653 to 371 computations (86% saved)

series1.5s (4.9%)

Error

0.1b

Counts

4 → 39

Calls

4 calls:

639.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
548.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
155.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
113.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

Compiler

Compiled 3878 to 1832 computations (52.8% saved)

simplify164.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

560×	`unsub-neg_binary64_2800`
445×	`distribute-rgt-in_binary64_2756`
337×	`distribute-rgt-neg-in_binary64_2764`
331×	`distribute-lft-in_binary64_2755`
292×	`distribute-lft-neg-in_binary64_2763`
267×	`cancel-sign-sub-inv_binary64_2772`
247×	`*-commutative_binary64_2737`
239×	`neg-mul-1_binary64_2802`
218×	`neg-sub0_binary64_2801`
186×	`sub-neg_binary64_2799`
147×	`+-commutative_binary64_2736`
130×	`sqr-pow_binary64_2778`
128×	`times-frac_binary64_2812`
109×	`associate-l_binary64_2747`
98×	`associate-r_binary64_2746`
81×	`associate-+l-_binary64_2741`
78×	`associate--r+_binary64_2742`
71×	`distribute-neg-in_binary64_2767`
59×	`associate-+l+_binary64_2739`
57×	`distribute-lft-neg-out_binary64_2765` `associate-+r+_binary64_2738`
49×	`exp-prod_binary64_2858`
47×	`distribute-rgt-neg-out_binary64_2766`
42×	`distribute-rgt-out_binary64_2759`
38×	`associate-/l*_binary64_2751`
34×	`exp-sum_binary64_2852`
33×	`distribute-neg-out_binary64_2768`
32×	`unswap-sqr_binary64_2774`
30×	`associate-+r-_binary64_2740`
29×	`mul0-rgt_binary64_2789` `mul0-lft_binary64_2788`
28×	`sub0-neg_binary64_2793` `pow-sqr_binary64_2779` `associate-/r*_binary64_2750`
27×	`cube-prod_binary64_2834`
26×	`rem-sqrt-square_binary64_2819`
21×	`swap-sqr_binary64_2773` `associate--l+_binary64_2743`
20×	`log-prod_binary64_2892` `distribute-rgt-out--_binary64_2760`
19×	`div-sub_binary64_2811` `+-rgt-identity_binary64_2791`
18×	`difference-of-squares_binary64_2775`
17×	`*-lft-identity_binary64_2795` `associate-/l/_binary64_2753`
16×	`exp-diff_binary64_2854`
15×	`cube-unmult_binary64_2843` `-rgt-identity_binary64_2796` `associate-r/_binary64_2748`
11×	`unpow3_binary64_2872` `unpow1/2_binary64_2870`
10×	`associate--r-_binary64_2745`
9×	`distribute-lft-out_binary64_2757`
6×	`associate-*l/_binary64_2749`
5×	`cube-mult_binary64_2836` `remove-double-neg_binary64_2794`
4×	`sqr-neg_binary64_2820` `+-lft-identity_binary64_2790` `associate-/r/_binary64_2752`
3×	`cos-neg_binary64_2937` `cube-neg_binary64_2833` `--rgt-identity_binary64_2792` `cancel-sign-sub_binary64_2771` `distribute-frac-neg_binary64_2769` `distribute-rgt1-in_binary64_2762` `distribute-lft-out--_binary64_2758` `associate--l-_binary64_2744`
2×	`distribute-lft1-in_binary64_2761`
1×	`sin-neg_binary64_2936` `unpow2_binary64_2871` `pow-plus_binary64_2869` `unpow1_binary64_2864` `div-exp_binary64_2857` `1-exp_binary64_2850` `exp-1-e_binary64_2849` `count-2_binary64_2754`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_3069` `erf-erfc_binary64_3068` `erf-odd_binary64_3067` `if-if-and-not_binary64_3066` `if-if-and_binary64_3065` `if-if-or-not_binary64_3064` `if-if-or_binary64_3063` `if-not_binary64_3062` `if-same_binary64_3061` `if-false_binary64_3060` `if-true_binary64_3059` `not-gte_binary64_3058` `not-lte_binary64_3057` `not-gt_binary64_3056` `not-lt_binary64_3055` `gte-same_binary64_3054` `lte-same_binary64_3053` `gt-same_binary64_3052` `lt-same_binary64_3051` `sinh---cosh_binary64_2998` `sinh-+-cosh_binary64_2997` `sinh-cosh_binary64_2996` `tanh-def-c_binary64_2995` `tanh-def-b_binary64_2994` `tanh-def-a_binary64_2993` `cosh-def_binary64_2992` `sinh-def_binary64_2991` `tan-neg_binary64_2938` `tan-0_binary64_2935` `cos-0_binary64_2934` `sin-0_binary64_2933` `hang-m-tan_binary64_2932` `hang-p-tan_binary64_2931` `hang-m0-tan_binary64_2930` `hang-p0-tan_binary64_2929` `hang-0m-tan_binary64_2928` `hang-0p-tan_binary64_2927` `tan-+PI/2_binary64_2926` `tan-+PI_binary64_2925` `tan-PI_binary64_2924` `tan-PI/3_binary64_2923` `tan-PI/4_binary64_2922` `tan-PI/6_binary64_2921` `cos-+PI/2_binary64_2920` `cos-+PI_binary64_2919` `cos-PI_binary64_2918` `cos-PI/2_binary64_2917` `cos-PI/3_binary64_2916` `cos-PI/4_binary64_2915` `cos-PI/6_binary64_2914` `sin-+PI/2_binary64_2913` `sin-+PI_binary64_2912` `sin-PI_binary64_2911` `sin-PI/2_binary64_2910` `sin-PI/3_binary64_2909` `sin-PI/4_binary64_2908` `sin-PI/6_binary64_2907` `sub-1-sin_binary64_2906` `sub-1-cos_binary64_2905` `-1-add-sin_binary64_2904` `-1-add-cos_binary64_2903` `1-sub-sin_binary64_2902` `1-sub-cos_binary64_2901` `cos-sin-sum_binary64_2900` `log-E_binary64_2896` `log-pow_binary64_2895` `log-rec_binary64_2894` `log-div_binary64_2893` `pow-base-0_binary64_2890` `unpow1/3_binary64_2873` `exp-to-pow_binary64_2868` `pow-base-1_binary64_2866` `unpow0_binary64_2865` `unpow-1_binary64_2863` `exp-lft-cube_binary64_2862` `exp-lft-sqr_binary64_2861` `exp-cbrt_binary64_2860` `exp-sqrt_binary64_2859` `rec-exp_binary64_2856` `prod-exp_binary64_2855` `exp-neg_binary64_2853` `e-exp-1_binary64_2851` `exp-0_binary64_2848` `rem-log-exp_binary64_2847` `rem-exp-log_binary64_2846` `cube-div_binary64_2835` `rem-3cbrt-rft_binary64_2832` `rem-3cbrt-lft_binary64_2831` `rem-cbrt-cube_binary64_2830` `rem-cube-cbrt_binary64_2829` `sqr-abs_binary64_2821` `rem-square-sqrt_binary64_2818` `mul-1-neg_binary64_2798` `/-rgt-identity_binary64_2797` `div0_binary64_2787` `*-inverses_binary64_2786` `+-inverses_binary64_2785` `lft-mult-inverse_binary64_2784` `rgt-mult-inverse_binary64_2783` `remove-double-div_binary64_2782` `difference-of-sqr--1_binary64_2777` `difference-of-sqr-1_binary64_2776` `distribute-neg-frac_binary64_2770`

Counts

97 → 73

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	3100
1	318	2935
2	806	2872
3	1428	2872
4	2518	2872
5	4253	2872
6	4919	2872

prune168.0ms (0.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	63	10	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	10	74

Error

0.0b

Counts

74 → 10

Compiler

Compiled 3434 to 593 computations (82.7% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))
0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
0.5b	(-.f64 (cos.f64 delta) (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))))))
2.1b	(log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))))

rewrite158.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

13×	`add-sqr-sqrt_binary64_2828`
12×	`*-un-lft-identity_binary64_2806`
9×	`pow1_binary64_2867` `add-cube-cbrt_binary64_2841`
7×	`add-log-exp_binary64_2845` `log-pow_binary64_2895`
6×	`log-prod_binary64_2892` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `cancel-sign-sub-inv_binary64_2772`
3×	`associate--r+_binary64_2742` `associate-l_binary64_2747` `associate-r_binary64_2746`
2×	`exp-to-pow_binary64_2868` `exp-prod_binary64_2858` `distribute-lft-out--_binary64_2758`
1×	`rem-log-exp_binary64_2847` `diff-log_binary64_2898` `flip3--_binary64_2810` `sub-neg_binary64_2799` `flip--_binary64_2781` `difference-of-squares_binary64_2775` `asin-acos_binary64_2986` `sin-mult_binary64_2961` `pow-prod-down_binary64_2877` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `unswap-sqr_binary64_2774` `*-commutative_binary64_2737`

Counts

4 → 64

Calls

4 calls:

10.0ms	(-.f64 (cos.f64 delta) (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))))))
6.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))
3.0ms	(log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))))
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))

Compiler

Compiled 3270 to 427 computations (86.9% saved)

series3.5s (11.4%)

Error

0.0b

Counts

4 → 41

Calls

4 calls:

1.4s	(-.f64 (cos.f64 delta) (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))))))
1.4s	(log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))))
523.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))
113.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))

Compiler

Compiled 4346 to 2057 computations (52.7% saved)

simplify234.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

621×	`unsub-neg_binary64_2800`
377×	`distribute-rgt-in_binary64_2756`
329×	`distribute-lft-in_binary64_2755`
313×	`associate-l_binary64_2747`
286×	`sub-neg_binary64_2799`
262×	`associate-r_binary64_2746`
252×	`sqr-pow_binary64_2778`
242×	`neg-mul-1_binary64_2802`
221×	`neg-sub0_binary64_2801`
210×	`cancel-sign-sub-inv_binary64_2772` `distribute-rgt-neg-in_binary64_2764`
195×	`distribute-lft-neg-in_binary64_2763`
148×	`times-frac_binary64_2812`
106×	`exp-prod_binary64_2858`
93×	`log-pow_binary64_2895` `log-prod_binary64_2892`
84×	`distribute-lft-neg-out_binary64_2765`
81×	`*-commutative_binary64_2737`
77×	`exp-sum_binary64_2852`
76×	`pow-sqr_binary64_2779`
71×	`associate-+r+_binary64_2738`
69×	`distribute-rgt-neg-out_binary64_2766`
59×	`associate-+l+_binary64_2739`
55×	`+-commutative_binary64_2736`
51×	`mul0-rgt_binary64_2789` `mul0-lft_binary64_2788`
46×	`cube-prod_binary64_2834`
40×	`sub0-neg_binary64_2793` `associate-+l-_binary64_2741`
37×	`unswap-sqr_binary64_2774`
34×	`rem-sqrt-square_binary64_2819` `*-lft-identity_binary64_2795`
33×	`*-rgt-identity_binary64_2796`
30×	`+-rgt-identity_binary64_2791`
29×	`distribute-rgt-out_binary64_2759` `associate--r+_binary64_2742`
28×	`exp-diff_binary64_2854`
27×	`div-sub_binary64_2811`
23×	`remove-double-neg_binary64_2794`
20×	`cube-unmult_binary64_2843` `distribute-lft-out_binary64_2757` `associate-+r-_binary64_2740`
19×	`unpow3_binary64_2872` `associate--l+_binary64_2743`
18×	`+-lft-identity_binary64_2790` `swap-sqr_binary64_2773`
16×	`exp-to-pow_binary64_2868`
11×	`pow-plus_binary64_2869`
9×	`cube-mult_binary64_2836` `associate-/r*_binary64_2750`
8×	`unpow1/2_binary64_2870` `sqr-neg_binary64_2820` `--rgt-identity_binary64_2792` `difference-of-squares_binary64_2775`
7×	`rem-log-exp_binary64_2847` `mul-1-neg_binary64_2798` `distribute-neg-in_binary64_2767`
6×	`rem-exp-log_binary64_2846` `distribute-lft-out--_binary64_2758` `count-2_binary64_2754`
5×	`distribute-rgt-out--_binary64_2760`
4×	`exp-sqrt_binary64_2859`
3×	`log-div_binary64_2893` `div-exp_binary64_2857` `cube-div_binary64_2835` `distribute-rgt1-in_binary64_2762` `associate-/l/_binary64_2753` `associate-*r/_binary64_2748`
2×	`cos-neg_binary64_2937` `sin-neg_binary64_2936` `unpow2_binary64_2871` `rec-exp_binary64_2856` `cube-neg_binary64_2833` `associate-/l*_binary64_2751`
1×	`log-E_binary64_2896` `unpow1_binary64_2864` `1-exp_binary64_2850` `exp-1-e_binary64_2849` `rem-3cbrt-lft_binary64_2831` `rem-square-sqrt_binary64_2818` `difference-of-sqr-1_binary64_2776` `distribute-lft1-in_binary64_2761` `associate-/r/_binary64_2752` `associate--r-_binary64_2745` `associate--l-_binary64_2744`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_3069` `erf-erfc_binary64_3068` `erf-odd_binary64_3067` `if-if-and-not_binary64_3066` `if-if-and_binary64_3065` `if-if-or-not_binary64_3064` `if-if-or_binary64_3063` `if-not_binary64_3062` `if-same_binary64_3061` `if-false_binary64_3060` `if-true_binary64_3059` `not-gte_binary64_3058` `not-lte_binary64_3057` `not-gt_binary64_3056` `not-lt_binary64_3055` `gte-same_binary64_3054` `lte-same_binary64_3053` `gt-same_binary64_3052` `lt-same_binary64_3051` `sinh---cosh_binary64_2998` `sinh-+-cosh_binary64_2997` `sinh-cosh_binary64_2996` `tanh-def-c_binary64_2995` `tanh-def-b_binary64_2994` `tanh-def-a_binary64_2993` `cosh-def_binary64_2992` `sinh-def_binary64_2991` `tan-neg_binary64_2938` `tan-0_binary64_2935` `cos-0_binary64_2934` `sin-0_binary64_2933` `hang-m-tan_binary64_2932` `hang-p-tan_binary64_2931` `hang-m0-tan_binary64_2930` `hang-p0-tan_binary64_2929` `hang-0m-tan_binary64_2928` `hang-0p-tan_binary64_2927` `tan-+PI/2_binary64_2926` `tan-+PI_binary64_2925` `tan-PI_binary64_2924` `tan-PI/3_binary64_2923` `tan-PI/4_binary64_2922` `tan-PI/6_binary64_2921` `cos-+PI/2_binary64_2920` `cos-+PI_binary64_2919` `cos-PI_binary64_2918` `cos-PI/2_binary64_2917` `cos-PI/3_binary64_2916` `cos-PI/4_binary64_2915` `cos-PI/6_binary64_2914` `sin-+PI/2_binary64_2913` `sin-+PI_binary64_2912` `sin-PI_binary64_2911` `sin-PI/2_binary64_2910` `sin-PI/3_binary64_2909` `sin-PI/4_binary64_2908` `sin-PI/6_binary64_2907` `sub-1-sin_binary64_2906` `sub-1-cos_binary64_2905` `-1-add-sin_binary64_2904` `-1-add-cos_binary64_2903` `1-sub-sin_binary64_2902` `1-sub-cos_binary64_2901` `cos-sin-sum_binary64_2900` `log-rec_binary64_2894` `pow-base-0_binary64_2890` `unpow1/3_binary64_2873` `pow-base-1_binary64_2866` `unpow0_binary64_2865` `unpow-1_binary64_2863` `exp-lft-cube_binary64_2862` `exp-lft-sqr_binary64_2861` `exp-cbrt_binary64_2860` `prod-exp_binary64_2855` `exp-neg_binary64_2853` `e-exp-1_binary64_2851` `exp-0_binary64_2848` `rem-3cbrt-rft_binary64_2832` `rem-cbrt-cube_binary64_2830` `rem-cube-cbrt_binary64_2829` `sqr-abs_binary64_2821` `/-rgt-identity_binary64_2797` `div0_binary64_2787` `-inverses_binary64_2786` `+-inverses_binary64_2785` `lft-mult-inverse_binary64_2784` `rgt-mult-inverse_binary64_2783` `remove-double-div_binary64_2782` `difference-of-sqr--1_binary64_2777` `cancel-sign-sub_binary64_2771` `distribute-neg-frac_binary64_2770` `distribute-frac-neg_binary64_2769` `distribute-neg-out_binary64_2768` `associate-l/_binary64_2749`

Counts

105 → 70

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	131	4124
1	249	3928
2	565	3841
3	1636	3812
4	3658	3812
5	4202	3737
6	4985	3737
7	4855	3737

prune136.0ms (0.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	71	9	80

Error

0.0b

Counts

80 → 9

Compiler

Compiled 3224 to 478 computations (85.2% saved)

localize46.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (cos.f64 delta) 3)
0.5b	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3)
0.8b	(pow.f64 (cbrt.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))) 6)
4.0b	(cbrt.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))))

rewrite303.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

10×	`add-cube-cbrt_binary64_2841` `add-sqr-sqrt_binary64_2828` `*-un-lft-identity_binary64_2806`
9×	`pow1_binary64_2867` `add-exp-log_binary64_2844` `pow-unpow_binary64_2883`
8×	`add-cbrt-cube_binary64_2842` `unpow-prod-down_binary64_2885`
5×	`pow-pow_binary64_2878`
4×	`add-log-exp_binary64_2845` `pow-exp_binary64_2874` `cube-prod_binary64_2834`
3×	`pow-to-exp_binary64_2875` `sqr-pow_binary64_2778` `rem-cube-cbrt_binary64_2829`
2×	`pow1/3_binary64_2888` `sin-mult_binary64_2961` `cbrt-prod_binary64_2837` `unpow3_binary64_2872` `cube-mult_binary64_2836`
1×	`cbrt-div_binary64_2838` `pow-prod-down_binary64_2877` `prod-exp_binary64_2855` `cube-div_binary64_2835` `cbrt-unprod_binary64_2839`

Counts

4 → 75

Calls

4 calls:

6.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3)
4.0ms	(cbrt.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))))
4.0ms	(pow.f64 (cbrt.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))) 6)
3.0ms	(pow.f64 (cos.f64 delta) 3)

Compiler

Compiled 7322 to 1090 computations (85.1% saved)

series4.9s (15.9%)

Error

0.0b

Counts

4 → 32

Calls

4 calls:

2.2s	(pow.f64 (cbrt.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))) 6)
1.4s	(cbrt.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))))
1.1s	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3)
65.0ms	(pow.f64 (cos.f64 delta) 3)

Compiler

Compiled 8374 to 2771 computations (66.9% saved)

simplify155.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

493×	`log-prod_binary64_2892`
402×	`sqr-pow_binary64_2778`
386×	`distribute-rgt-in_binary64_2756`
327×	`exp-prod_binary64_2858`
307×	`*-commutative_binary64_2737`
281×	`cube-prod_binary64_2834`
196×	`swap-sqr_binary64_2773`
158×	`log-pow_binary64_2895`
124×	`pow-sqr_binary64_2779`
101×	`associate-r_binary64_2746`
98×	`associate-l_binary64_2747`
86×	`unpow3_binary64_2872`
74×	`cube-mult_binary64_2836` `distribute-lft-out_binary64_2757`
73×	`distribute-rgt-neg-in_binary64_2764`
71×	`distribute-lft-neg-in_binary64_2763`
61×	`distribute-rgt-out_binary64_2759`
41×	`distribute-lft-in_binary64_2755`
39×	`cancel-sign-sub-inv_binary64_2772`
38×	`pow-plus_binary64_2869`
33×	`rem-sqrt-square_binary64_2819` `unswap-sqr_binary64_2774`
29×	`neg-mul-1_binary64_2802` `neg-sub0_binary64_2801`
24×	`sub-neg_binary64_2799`
19×	`associate-+l+_binary64_2739` `associate-+r+_binary64_2738`
13×	`cube-unmult_binary64_2843`
12×	`distribute-rgt-neg-out_binary64_2766` `distribute-lft-neg-out_binary64_2765`
11×	`exp-sum_binary64_2852` `*-rgt-identity_binary64_2796`
9×	`*-lft-identity_binary64_2795`
8×	`count-2_binary64_2754` `+-commutative_binary64_2736`
6×	`unpow1/3_binary64_2873` `unpow1/2_binary64_2870` `unpow1_binary64_2864` `prod-exp_binary64_2855` `associate-/l/_binary64_2753` `associate-*r/_binary64_2748`
4×	`rem-cube-cbrt_binary64_2829` `unsub-neg_binary64_2800` `sub0-neg_binary64_2793` `associate-+l-_binary64_2741`
3×	`unpow2_binary64_2871` `rem-cbrt-cube_binary64_2830` `+-rgt-identity_binary64_2791` `associate-+r-_binary64_2740`
2×	`exp-to-pow_binary64_2868` `rem-exp-log_binary64_2846` `distribute-rgt-out--_binary64_2760` `associate-/r/_binary64_2752` `associate-/l*_binary64_2751`
1×	`cos-neg_binary64_2937` `1-exp_binary64_2850` `rem-3cbrt-rft_binary64_2832` `rem-3cbrt-lft_binary64_2831` `sqr-neg_binary64_2820` `rem-square-sqrt_binary64_2818` `distribute-rgt1-in_binary64_2762` `distribute-lft-out--_binary64_2758`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_3069` `erf-erfc_binary64_3068` `erf-odd_binary64_3067` `if-if-and-not_binary64_3066` `if-if-and_binary64_3065` `if-if-or-not_binary64_3064` `if-if-or_binary64_3063` `if-not_binary64_3062` `if-same_binary64_3061` `if-false_binary64_3060` `if-true_binary64_3059` `not-gte_binary64_3058` `not-lte_binary64_3057` `not-gt_binary64_3056` `not-lt_binary64_3055` `gte-same_binary64_3054` `lte-same_binary64_3053` `gt-same_binary64_3052` `lt-same_binary64_3051` `sinh---cosh_binary64_2998` `sinh-+-cosh_binary64_2997` `sinh-cosh_binary64_2996` `tanh-def-c_binary64_2995` `tanh-def-b_binary64_2994` `tanh-def-a_binary64_2993` `cosh-def_binary64_2992` `sinh-def_binary64_2991` `tan-neg_binary64_2938` `sin-neg_binary64_2936` `tan-0_binary64_2935` `cos-0_binary64_2934` `sin-0_binary64_2933` `hang-m-tan_binary64_2932` `hang-p-tan_binary64_2931` `hang-m0-tan_binary64_2930` `hang-p0-tan_binary64_2929` `hang-0m-tan_binary64_2928` `hang-0p-tan_binary64_2927` `tan-+PI/2_binary64_2926` `tan-+PI_binary64_2925` `tan-PI_binary64_2924` `tan-PI/3_binary64_2923` `tan-PI/4_binary64_2922` `tan-PI/6_binary64_2921` `cos-+PI/2_binary64_2920` `cos-+PI_binary64_2919` `cos-PI_binary64_2918` `cos-PI/2_binary64_2917` `cos-PI/3_binary64_2916` `cos-PI/4_binary64_2915` `cos-PI/6_binary64_2914` `sin-+PI/2_binary64_2913` `sin-+PI_binary64_2912` `sin-PI_binary64_2911` `sin-PI/2_binary64_2910` `sin-PI/3_binary64_2909` `sin-PI/4_binary64_2908` `sin-PI/6_binary64_2907` `sub-1-sin_binary64_2906` `sub-1-cos_binary64_2905` `-1-add-sin_binary64_2904` `-1-add-cos_binary64_2903` `1-sub-sin_binary64_2902` `1-sub-cos_binary64_2901` `cos-sin-sum_binary64_2900` `log-E_binary64_2896` `log-rec_binary64_2894` `log-div_binary64_2893` `pow-base-0_binary64_2890` `pow-base-1_binary64_2866` `unpow0_binary64_2865` `unpow-1_binary64_2863` `exp-lft-cube_binary64_2862` `exp-lft-sqr_binary64_2861` `exp-cbrt_binary64_2860` `exp-sqrt_binary64_2859` `div-exp_binary64_2857` `rec-exp_binary64_2856` `exp-diff_binary64_2854` `exp-neg_binary64_2853` `e-exp-1_binary64_2851` `exp-1-e_binary64_2849` `exp-0_binary64_2848` `rem-log-exp_binary64_2847` `cube-div_binary64_2835` `cube-neg_binary64_2833` `sqr-abs_binary64_2821` `times-frac_binary64_2812` `div-sub_binary64_2811` `mul-1-neg_binary64_2798` `/-rgt-identity_binary64_2797` `remove-double-neg_binary64_2794` `--rgt-identity_binary64_2792` `+-lft-identity_binary64_2790` `mul0-rgt_binary64_2789` `mul0-lft_binary64_2788` `div0_binary64_2787` `-inverses_binary64_2786` `+-inverses_binary64_2785` `lft-mult-inverse_binary64_2784` `rgt-mult-inverse_binary64_2783` `remove-double-div_binary64_2782` `difference-of-sqr--1_binary64_2777` `difference-of-sqr-1_binary64_2776` `difference-of-squares_binary64_2775` `cancel-sign-sub_binary64_2771` `distribute-neg-frac_binary64_2770` `distribute-frac-neg_binary64_2769` `distribute-neg-out_binary64_2768` `distribute-neg-in_binary64_2767` `distribute-lft1-in_binary64_2761` `associate-/r_binary64_2750` `associate-*l/_binary64_2749` `associate--r-_binary64_2745` `associate--l-_binary64_2744` `associate--l+_binary64_2743` `associate--r+_binary64_2742`

Counts

107 → 73

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	137	3312
1	294	3158
2	964	3034
3	2303	3026
4	4839	3026
5	4999	3026

prune246.0ms (0.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	73	9	82

Error

0.0b

Counts

82 → 9

Compiler

Compiled 6895 to 1083 computations (84.3% saved)

localize37.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (sin.f64 phi1) (sin.f64 (log.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))))
0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
0.5b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (log.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))))))
3.2b	(log.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))))

rewrite176.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

15×	`log-prod_binary64_2892`
14×	`add-sqr-sqrt_binary64_2828`
12×	`add-cube-cbrt_binary64_2841` `*-un-lft-identity_binary64_2806` `sin-sum_binary64_2939`
7×	`pow1_binary64_2867`
6×	`add-log-exp_binary64_2845` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `distribute-rgt-in_binary64_2756` `associate--r+_binary64_2742` `distribute-lft-in_binary64_2755`
4×	`log-pow_binary64_2895`
3×	`exp-prod_binary64_2858` `associate-l_binary64_2747` `associate-r_binary64_2746`
2×	`asin-acos_binary64_2986`
1×	`exp-diff_binary64_2854` `log-div_binary64_2893` `rem-log-exp_binary64_2847` `diff-log_binary64_2898` `flip3--_binary64_2810` `sub-neg_binary64_2799` `flip--_binary64_2781` `cancel-sign-sub-inv_binary64_2772` `sin-mult_binary64_2961` `pow-prod-down_binary64_2877` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `unswap-sqr_binary64_2774` `*-commutative_binary64_2737`

Counts

4 → 67

Calls

4 calls:

8.0ms	(.f64 (sin.f64 phi1) (sin.f64 (log.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))))
5.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (log.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))))))
3.0ms	(log.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))))
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))

Compiler

Compiled 4020 to 499 computations (87.6% saved)

series3.3s (10.6%)

Error

0.0b

Counts

4 → 40

Calls

4 calls:

1.2s	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (log.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))))))
1.1s	(.f64 (sin.f64 phi1) (sin.f64 (log.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))))
737.0ms	(log.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))))
117.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))

Compiler

Compiled 4225 to 2008 computations (52.5% saved)

simplify259.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

479×	`neg-mul-1_binary64_2802`
461×	`neg-sub0_binary64_2801`
419×	`unsub-neg_binary64_2800`
410×	`distribute-rgt-neg-in_binary64_2764`
403×	`cancel-sign-sub-inv_binary64_2772`
308×	`associate-l_binary64_2747`
253×	`associate-r_binary64_2746`
232×	`distribute-rgt-in_binary64_2756`
210×	`distribute-lft-neg-in_binary64_2763`
192×	`distribute-lft-in_binary64_2755`
182×	`distribute-lft-neg-out_binary64_2765`
176×	`sub-neg_binary64_2799`
160×	`distribute-rgt-neg-out_binary64_2766`
120×	`*-commutative_binary64_2737`
96×	`sqr-pow_binary64_2778`
94×	`times-frac_binary64_2812`
84×	`distribute-neg-in_binary64_2767`
83×	`distribute-neg-out_binary64_2768`
57×	`exp-prod_binary64_2858`
54×	`unswap-sqr_binary64_2774`
53×	`log-prod_binary64_2892` `associate-+r+_binary64_2738`
49×	`+-commutative_binary64_2736`
47×	`associate-+l+_binary64_2739`
44×	`*-rgt-identity_binary64_2796`
42×	`*-lft-identity_binary64_2795`
41×	`mul0-rgt_binary64_2789` `mul0-lft_binary64_2788`
36×	`exp-sum_binary64_2852`
30×	`associate-+l-_binary64_2741`
26×	`sub0-neg_binary64_2793`
24×	`cube-prod_binary64_2834` `distribute-rgt-out_binary64_2759`
21×	`pow-sqr_binary64_2779`
20×	`associate--r+_binary64_2742`
19×	`log-pow_binary64_2895` `rem-sqrt-square_binary64_2819` `difference-of-squares_binary64_2775`
18×	`exp-diff_binary64_2854` `cube-unmult_binary64_2843`
16×	`+-rgt-identity_binary64_2791` `associate-+r-_binary64_2740`
15×	`div-sub_binary64_2811`
14×	`unpow3_binary64_2872` `distribute-lft-out_binary64_2757`
12×	`associate--l+_binary64_2743`
11×	`distribute-rgt-out--_binary64_2760`
10×	`swap-sqr_binary64_2773`
8×	`unpow1/2_binary64_2870` `remove-double-neg_binary64_2794`
7×	`rem-log-exp_binary64_2847` `+-lft-identity_binary64_2790`
6×	`cube-neg_binary64_2833` `sqr-neg_binary64_2820` `--rgt-identity_binary64_2792` `distribute-lft-out--_binary64_2758` `associate-/r*_binary64_2750`
5×	`pow-plus_binary64_2869` `mul-1-neg_binary64_2798`
3×	`exp-sqrt_binary64_2859` `rem-exp-log_binary64_2846` `cube-mult_binary64_2836` `distribute-frac-neg_binary64_2769` `distribute-rgt1-in_binary64_2762` `count-2_binary64_2754` `associate--r-_binary64_2745`
2×	`cos-neg_binary64_2937` `sin-neg_binary64_2936` `exp-neg_binary64_2853` `associate-/l/_binary64_2753` `associate-/l_binary64_2751` `associate-r/_binary64_2748`
1×	`unpow2_binary64_2871` `unpow1_binary64_2864` `div-exp_binary64_2857` `1-exp_binary64_2850` `exp-1-e_binary64_2849` `cancel-sign-sub_binary64_2771` `distribute-lft1-in_binary64_2761` `associate--l-_binary64_2744`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_3069` `erf-erfc_binary64_3068` `erf-odd_binary64_3067` `if-if-and-not_binary64_3066` `if-if-and_binary64_3065` `if-if-or-not_binary64_3064` `if-if-or_binary64_3063` `if-not_binary64_3062` `if-same_binary64_3061` `if-false_binary64_3060` `if-true_binary64_3059` `not-gte_binary64_3058` `not-lte_binary64_3057` `not-gt_binary64_3056` `not-lt_binary64_3055` `gte-same_binary64_3054` `lte-same_binary64_3053` `gt-same_binary64_3052` `lt-same_binary64_3051` `sinh---cosh_binary64_2998` `sinh-+-cosh_binary64_2997` `sinh-cosh_binary64_2996` `tanh-def-c_binary64_2995` `tanh-def-b_binary64_2994` `tanh-def-a_binary64_2993` `cosh-def_binary64_2992` `sinh-def_binary64_2991` `tan-neg_binary64_2938` `tan-0_binary64_2935` `cos-0_binary64_2934` `sin-0_binary64_2933` `hang-m-tan_binary64_2932` `hang-p-tan_binary64_2931` `hang-m0-tan_binary64_2930` `hang-p0-tan_binary64_2929` `hang-0m-tan_binary64_2928` `hang-0p-tan_binary64_2927` `tan-+PI/2_binary64_2926` `tan-+PI_binary64_2925` `tan-PI_binary64_2924` `tan-PI/3_binary64_2923` `tan-PI/4_binary64_2922` `tan-PI/6_binary64_2921` `cos-+PI/2_binary64_2920` `cos-+PI_binary64_2919` `cos-PI_binary64_2918` `cos-PI/2_binary64_2917` `cos-PI/3_binary64_2916` `cos-PI/4_binary64_2915` `cos-PI/6_binary64_2914` `sin-+PI/2_binary64_2913` `sin-+PI_binary64_2912` `sin-PI_binary64_2911` `sin-PI/2_binary64_2910` `sin-PI/3_binary64_2909` `sin-PI/4_binary64_2908` `sin-PI/6_binary64_2907` `sub-1-sin_binary64_2906` `sub-1-cos_binary64_2905` `-1-add-sin_binary64_2904` `-1-add-cos_binary64_2903` `1-sub-sin_binary64_2902` `1-sub-cos_binary64_2901` `cos-sin-sum_binary64_2900` `log-E_binary64_2896` `log-rec_binary64_2894` `log-div_binary64_2893` `pow-base-0_binary64_2890` `unpow1/3_binary64_2873` `exp-to-pow_binary64_2868` `pow-base-1_binary64_2866` `unpow0_binary64_2865` `unpow-1_binary64_2863` `exp-lft-cube_binary64_2862` `exp-lft-sqr_binary64_2861` `exp-cbrt_binary64_2860` `rec-exp_binary64_2856` `prod-exp_binary64_2855` `e-exp-1_binary64_2851` `exp-0_binary64_2848` `cube-div_binary64_2835` `rem-3cbrt-rft_binary64_2832` `rem-3cbrt-lft_binary64_2831` `rem-cbrt-cube_binary64_2830` `rem-cube-cbrt_binary64_2829` `sqr-abs_binary64_2821` `rem-square-sqrt_binary64_2818` `/-rgt-identity_binary64_2797` `div0_binary64_2787` `-inverses_binary64_2786` `+-inverses_binary64_2785` `lft-mult-inverse_binary64_2784` `rgt-mult-inverse_binary64_2783` `remove-double-div_binary64_2782` `difference-of-sqr--1_binary64_2777` `difference-of-sqr-1_binary64_2776` `distribute-neg-frac_binary64_2770` `associate-/r/_binary64_2752` `associate-l/_binary64_2749`

Counts

107 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	157	4917
1	313	4544
2	769	4486
3	1617	4486
4	2952	4486
5	4106	4486
6	4988	4486
7	4878	4486

prune131.0ms (0.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	80	9	89

Error

0.0b

Counts

89 → 9

Compiler

Compiled 3816 to 409 computations (89.3% saved)

regimes1.6s (5.2%)

Accuracy

Total 0.1b remaining (69.7%)

Threshold costs 0.1b (69.7%)

Compiler

Compiled 22566 to 12047 computations (46.6% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64_2737`
4×	`+-commutative_binary64_2736`
2×	`sub-neg_binary64_2799`
1×	`neg-mul-1_binary64_2802` `neg-sub0_binary64_2801`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `if-if-and-not_binary64_3066` `if-if-and_binary64_3065` `if-if-or-not_binary64_3064` `if-if-or_binary64_3063` `if-not_binary64_3062` `if-same_binary64_3061` `if-false_binary64_3060` `if-true_binary64_3059` `tan-0_binary64_2935` `cos-0_binary64_2934` `sin-0_binary64_2933` `unpow1_binary64_2864` `e-exp-1_binary64_2851` `1-exp_binary64_2850` `exp-1-e_binary64_2849` `exp-0_binary64_2848` `sqr-abs_binary64_2821` `sqr-neg_binary64_2820` `unsub-neg_binary64_2800` `mul-1-neg_binary64_2798` `/-rgt-identity_binary64_2797` `-rgt-identity_binary64_2796` `-lft-identity_binary64_2795` `remove-double-neg_binary64_2794` `sub0-neg_binary64_2793` `--rgt-identity_binary64_2792` `+-rgt-identity_binary64_2791` `+-lft-identity_binary64_2790` `cancel-sign-sub-inv_binary64_2772` `cancel-sign-sub_binary64_2771` `distribute-neg-frac_binary64_2770` `distribute-frac-neg_binary64_2769` `distribute-neg-out_binary64_2768` `distribute-neg-in_binary64_2767` `distribute-rgt-neg-out_binary64_2766` `distribute-lft-neg-out_binary64_2765` `distribute-rgt-neg-in_binary64_2764` `distribute-lft-neg-in_binary64_2763`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	59
1	35	59
2	40	59
3	42	59
4	43	59
5	43	59

end0.0ms (0%)

sample9.3s (30.3%)

Algorithm

1×

intervals

Results

4.9s	3930×	body	1024	valid
1.0s	1323×	body	512	valid
495.0ms	2208×	body	128	valid
241.0ms	527×	body	256	valid
28.0ms	12×	body	2048	valid

Compiler

Compiled 3273 to 1755 computations (46.4% saved)

Iter	Nodes	Cost
0	23	55
1	39	55
2	61	55
3	72	55
4	83	55
5	107	55
6	134	55
7	164	55
8	217	55
9	216	55
10	240	55
11	275	55
12	317	55
13	431	55
14	486	55
15	534	55
16	567	55
17	521	55
18	523	55
19	525	55
20	526	55
21	463	55

Iter	Nodes	Cost
0	23	55
1	39	55
2	61	55
3	72	55
4	83	55
5	107	55
6	134	55
7	164	55
8	217	55
9	216	55
10	240	55
11	275	55
12	317	55
13	431	55
14	486	55
15	534	55
16	567	55
17	521	55
18	523	55
19	525	55
20	526	55
21	463	55

Details

analyze3.9s (12.8%)

sample234.0ms (0.8%)

simplify47.0ms (0.2%)

prune5.0ms (0%)

localize28.0ms (0.1%)

rewrite161.0ms (0.5%)

series1.5s (4.9%)

simplify164.0ms (0.5%)

prune168.0ms (0.5%)

localize30.0ms (0.1%)

rewrite158.0ms (0.5%)

series3.5s (11.4%)

simplify234.0ms (0.8%)

prune136.0ms (0.4%)

localize46.0ms (0.1%)

rewrite303.0ms (1%)

series4.9s (15.9%)

simplify155.0ms (0.5%)

prune246.0ms (0.8%)

localize37.0ms (0.1%)

rewrite176.0ms (0.6%)

series3.3s (10.6%)

simplify259.0ms (0.8%)

prune131.0ms (0.4%)

regimes1.6s (5.2%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample9.3s (30.3%)

Profiling

Iter	Nodes	Cost
0	23	55
1	39	55
2	61	55
3	72	55
4	83	55
5	107	55
6	134	55
7	164	55
8	217	55
9	216	55
10	240	55
11	275	55
12	317	55
13	431	55
14	486	55
15	534	55
16	567	55
17	521	55
18	523	55
19	525	55
20	526	55
21	463	55