Details

analyze224.0ms (1.4%)

Algorithm

1×	search
2×	egg-herbie

Rules

847×	`unswap-sqr_binary64_2774`
640×	`associate-*l/_binary64_2749`
462×	`associate-*r/_binary64_2748`
372×	`associate-/l*_binary64_2751`
366×	`distribute-rgt-out_binary64_2759`
344×	`distribute-rgt-in_binary64_2756`
324×	`distribute-lft-in_binary64_2755`
294×	`associate-+l+_binary64_2739`
262×	`distribute-lft-out_binary64_2757`
258×	`associate-+r+_binary64_2738`
240×	`*-commutative_binary64_2737`
183×	`associate-l_binary64_2747`
178×	`associate-r_binary64_2746`
126×	`associate-/l/_binary64_2753`
105×	`+-commutative_binary64_2736`
78×	`-rgt-identity_binary64_2796` `-lft-identity_binary64_2795`
73×	`associate-/r*_binary64_2750`
68×	`sqr-pow_binary64_2778`
61×	`associate-/r/_binary64_2752`
52×	`times-frac_binary64_2812`
31×	`pow-sqr_binary64_2779`
22×	`distribute-rgt1-in_binary64_2762`
14×	`distribute-lft1-in_binary64_2761`
12×	`pow-plus_binary64_2869`
7×	`cube-div_binary64_2835` `/-rgt-identity_binary64_2797`
4×	`unpow3_binary64_2872` `cube-unmult_binary64_2843`
2×	`unpow2_binary64_2871` `exp-prod_binary64_2858` `cube-prod_binary64_2834` `swap-sqr_binary64_2773`
1×	`unpow1/2_binary64_2870` `unpow1_binary64_2864` `1-exp_binary64_2850` `cube-mult_binary64_2836` `sqr-abs_binary64_2821`
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` `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` `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-neg_binary64_2833` `rem-3cbrt-rft_binary64_2832` `rem-3cbrt-lft_binary64_2831` `rem-cbrt-cube_binary64_2830` `rem-cube-cbrt_binary64_2829` `sqr-neg_binary64_2820` `rem-sqrt-square_binary64_2819` `rem-square-sqrt_binary64_2818` `div-sub_binary64_2811` `neg-mul-1_binary64_2802` `neg-sub0_binary64_2801` `unsub-neg_binary64_2800` `sub-neg_binary64_2799` `mul-1-neg_binary64_2798` `remove-double-neg_binary64_2794` `sub0-neg_binary64_2793` `--rgt-identity_binary64_2792` `+-rgt-identity_binary64_2791` `+-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-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` `distribute-rgt-out--_binary64_2760` `distribute-lft-out--_binary64_2758` `count-2_binary64_2754` `associate--r-_binary64_2745` `associate--l-_binary64_2744` `associate--l+_binary64_2743` `associate--r+_binary64_2742` `associate-+l-_binary64_2741` `associate-+r-_binary64_2740`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	152
1	91	86
2	261	60
3	1006	52
4	3215	49
5	3806	47
6	4565	47
7	5512	47
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

Compiler

Compiled 106 to 71 computations (33% saved)

sample76.0ms (0.5%)

Algorithm

1×

intervals

Results

55.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify75.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

847×	`unswap-sqr_binary64_2774`
640×	`associate-*l/_binary64_2749`
462×	`associate-*r/_binary64_2748`
372×	`associate-/l*_binary64_2751`
366×	`distribute-rgt-out_binary64_2759`
344×	`distribute-rgt-in_binary64_2756`
324×	`distribute-lft-in_binary64_2755`
294×	`associate-+l+_binary64_2739`
262×	`distribute-lft-out_binary64_2757`
258×	`associate-+r+_binary64_2738`
240×	`*-commutative_binary64_2737`
183×	`associate-l_binary64_2747`
178×	`associate-r_binary64_2746`
126×	`associate-/l/_binary64_2753`
105×	`+-commutative_binary64_2736`
78×	`-rgt-identity_binary64_2796` `-lft-identity_binary64_2795`
73×	`associate-/r*_binary64_2750`
68×	`sqr-pow_binary64_2778`
61×	`associate-/r/_binary64_2752`
52×	`times-frac_binary64_2812`
31×	`pow-sqr_binary64_2779`
22×	`distribute-rgt1-in_binary64_2762`
14×	`distribute-lft1-in_binary64_2761`
12×	`pow-plus_binary64_2869`
7×	`cube-div_binary64_2835` `/-rgt-identity_binary64_2797`
4×	`unpow3_binary64_2872` `cube-unmult_binary64_2843`
2×	`unpow2_binary64_2871` `exp-prod_binary64_2858` `cube-prod_binary64_2834` `swap-sqr_binary64_2773`
1×	`unpow1/2_binary64_2870` `unpow1_binary64_2864` `1-exp_binary64_2850` `cube-mult_binary64_2836` `sqr-abs_binary64_2821`
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` `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` `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-neg_binary64_2833` `rem-3cbrt-rft_binary64_2832` `rem-3cbrt-lft_binary64_2831` `rem-cbrt-cube_binary64_2830` `rem-cube-cbrt_binary64_2829` `sqr-neg_binary64_2820` `rem-sqrt-square_binary64_2819` `rem-square-sqrt_binary64_2818` `div-sub_binary64_2811` `neg-mul-1_binary64_2802` `neg-sub0_binary64_2801` `unsub-neg_binary64_2800` `sub-neg_binary64_2799` `mul-1-neg_binary64_2798` `remove-double-neg_binary64_2794` `sub0-neg_binary64_2793` `--rgt-identity_binary64_2792` `+-rgt-identity_binary64_2791` `+-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-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` `distribute-rgt-out--_binary64_2760` `distribute-lft-out--_binary64_2758` `count-2_binary64_2754` `associate--r-_binary64_2745` `associate--l-_binary64_2744` `associate--l+_binary64_2743` `associate--r+_binary64_2742` `associate-+l-_binary64_2741` `associate-+r-_binary64_2740`

Counts

1 → 1

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	35	152
1	91	86
2	261	60
3	1006	52
4	3215	49
5	3806	47
6	4565	47
7	5512	47

prune10.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

2.7b

Counts

2 → 2

Compiler

Compiled 163 to 111 computations (31.9% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
0.5b	(/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x))
1.0b	(sqrt.f64 PI.f64)
2.4b	(exp.f64 (*.f64 x x))

rewrite373.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

142×	`times-frac_binary64_2812`
86×	`*-un-lft-identity_binary64_2806`
83×	`add-sqr-sqrt_binary64_2828`
82×	`add-cube-cbrt_binary64_2841`
39×	`sqrt-prod_binary64_2822`
26×	`associate-/l*_binary64_2751`
14×	`add-cbrt-cube_binary64_2842`
13×	`add-exp-log_binary64_2844`
6×	`add-log-exp_binary64_2845` `div-inv_binary64_2803`
5×	`pow1_binary64_2867` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840`
4×	`associate-/r*_binary64_2750`
3×	`associate-/l/_binary64_2753`
2×	`frac-2neg_binary64_2817` `clear-num_binary64_2805` `distribute-lft-out_binary64_2757`
1×	`exp-to-pow_binary64_2868` `exp-prod_binary64_2858` `rem-exp-log_binary64_2846` `pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `flip3-+_binary64_2809` `flip-+_binary64_2780`

Counts

4 → 154

Calls

4 calls:

10.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
10.0ms	(/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x))
4.0ms	(sqrt.f64 PI.f64)
2.0ms	(exp.f64 (*.f64 x x))

Compiler

Compiled 6494 to 2669 computations (58.9% saved)

series335.0ms (2%)

Error

2.6b

Counts

4 → 18

Calls

4 calls:

160.0ms	(/.f64 (/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64)) (fabs.f64 x))
109.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
32.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1486 to 1083 computations (27.1% saved)

simplify202.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

620×	`times-frac_binary64_2812`
595×	`associate-/r*_binary64_2750`
562×	`associate-/l*_binary64_2751`
333×	`associate-*l/_binary64_2749`
263×	`associate-*r/_binary64_2748`
205×	`associate-/l/_binary64_2753`
202×	`associate-/r/_binary64_2752`
172×	`div-sub_binary64_2811`
100×	`distribute-rgt-in_binary64_2756`
89×	`distribute-lft-in_binary64_2755`
80×	`*-commutative_binary64_2737`
56×	`associate-l_binary64_2747`
50×	`sub-neg_binary64_2799`
49×	`sqr-pow_binary64_2778`
38×	`unswap-sqr_binary64_2774`
35×	`log-div_binary64_2893`
32×	`associate-r_binary64_2746`
31×	`/-rgt-identity_binary64_2797`
29×	`neg-mul-1_binary64_2802` `neg-sub0_binary64_2801`
28×	`log-prod_binary64_2892`
27×	`+-commutative_binary64_2736`
26×	`exp-prod_binary64_2858` `*-rgt-identity_binary64_2796`
25×	`distribute-lft-out_binary64_2757`
22×	`cube-div_binary64_2835`
20×	`cube-prod_binary64_2834`
17×	`distribute-rgt-out_binary64_2759`
16×	`associate-+r+_binary64_2738`
15×	`log-pow_binary64_2895` `unsub-neg_binary64_2800`
14×	`associate-+l+_binary64_2739`
13×	`distribute-neg-frac_binary64_2770`
12×	`cube-unmult_binary64_2843`
11×	`*-lft-identity_binary64_2795` `cancel-sign-sub-inv_binary64_2772`
10×	`pow-sqr_binary64_2779`
8×	`distribute-rgt-neg-in_binary64_2764` `distribute-lft-neg-in_binary64_2763`
7×	`unpow3_binary64_2872`
5×	`pow-plus_binary64_2869` `rem-sqrt-square_binary64_2819` `distribute-neg-in_binary64_2767` `count-2_binary64_2754`
3×	`prod-exp_binary64_2855` `rem-log-exp_binary64_2847` `swap-sqr_binary64_2773` `distribute-rgt-neg-out_binary64_2766` `distribute-lft-neg-out_binary64_2765`
2×	`exp-to-pow_binary64_2868` `rec-exp_binary64_2856` `exp-diff_binary64_2854` `exp-sum_binary64_2852` `cube-mult_binary64_2836` `distribute-rgt1-in_binary64_2762` `associate--r+_binary64_2742` `associate-+l-_binary64_2741`
1×	`log-rec_binary64_2894` `unpow2_binary64_2871` `unpow1/2_binary64_2870` `unpow1_binary64_2864` `1-exp_binary64_2850` `exp-1-e_binary64_2849` `rem-exp-log_binary64_2846` `sqr-abs_binary64_2821` `rem-square-sqrt_binary64_2818` `remove-double-neg_binary64_2794` `mul0-rgt_binary64_2789` `mul0-lft_binary64_2788` `div0_binary64_2787` `*-inverses_binary64_2786` `distribute-neg-out_binary64_2768` `distribute-lft1-in_binary64_2761` `distribute-rgt-out--_binary64_2760` `associate--l-_binary64_2744` `associate--l+_binary64_2743` `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` `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` `exp-sqrt_binary64_2859` `div-exp_binary64_2857` `exp-neg_binary64_2853` `e-exp-1_binary64_2851` `exp-0_binary64_2848` `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-neg_binary64_2820` `mul-1-neg_binary64_2798` `sub0-neg_binary64_2793` `--rgt-identity_binary64_2792` `+-rgt-identity_binary64_2791` `+-lft-identity_binary64_2790` `+-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-frac-neg_binary64_2769` `distribute-lft-out--_binary64_2758` `associate--r-_binary64_2745`

Counts

172 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	273	4788
1	629	4525
2	1618	4480
3	4431	4477
4	4995	4477
5	4940	4477

prune229.0ms (1.4%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	66	20	86
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	67	21	88

Error

1.8b

Counts

88 → 21

Compiler

Compiled 4293 to 2024 computations (52.9% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (exp.f64 (-.f64 (.f64 x x) (log.f64 (.f64 (fabs.f64 x) (sqrt.f64 PI.f64))))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
0.5b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
1.0b	(sqrt.f64 PI.f64)
2.4b	(exp.f64 (-.f64 (.f64 x x) (log.f64 (.f64 (fabs.f64 x) (sqrt.f64 PI.f64)))))

rewrite269.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

1.0b

Rules

21×	`*-un-lft-identity_binary64_2806`
16×	`add-sqr-sqrt_binary64_2828`
13×	`pow1_binary64_2867`
12×	`add-cube-cbrt_binary64_2841` `exp-sum_binary64_2852`
11×	`add-cbrt-cube_binary64_2842`
10×	`cancel-sign-sub-inv_binary64_2772` `add-exp-log_binary64_2844`
9×	`associate-l_binary64_2747`
6×	`add-log-exp_binary64_2845`
5×	`distribute-lft-out_binary64_2757` `associate-r_binary64_2746`
4×	`exp-prod_binary64_2858` `exp-diff_binary64_2854` `log-pow_binary64_2895` `times-frac_binary64_2812` `associate-/l*_binary64_2751`
3×	`pow-prod-down_binary64_2877` `sqrt-prod_binary64_2822` `flip3-+_binary64_2809` `flip-+_binary64_2780`
2×	`sub-neg_binary64_2799` `rem-exp-log_binary64_2846` `prod-exp_binary64_2855` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `cbrt-unprod_binary64_2839` `associate-/l/_binary64_2753` `frac-times_binary64_2816` `associate-*r/_binary64_2748`
1×	`difference-of-squares_binary64_2775` `diff-log_binary64_2898` `pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `div-inv_binary64_2803` `associate-/r_binary64_2750` `unswap-sqr_binary64_2774` `distribute-rgt-in_binary64_2756` `distribute-lft-in_binary64_2755` `associate-l/_binary64_2749` `*-commutative_binary64_2737`

Counts

4 → 91

Calls

4 calls:

40.0ms	(.f64 (exp.f64 (-.f64 (.f64 x x) (log.f64 (.f64 (fabs.f64 x) (sqrt.f64 PI.f64))))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
9.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
8.0ms	(exp.f64 (-.f64 (.f64 x x) (log.f64 (.f64 (fabs.f64 x) (sqrt.f64 PI.f64)))))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 3956 to 1845 computations (53.4% saved)

series505.0ms (3.1%)

Error

1.8b

Counts

4 → 24

Calls

4 calls:

236.0ms	(.f64 (exp.f64 (-.f64 (.f64 x x) (log.f64 (.f64 (fabs.f64 x) (sqrt.f64 PI.f64))))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
121.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
103.0ms	(exp.f64 (-.f64 (.f64 x x) (log.f64 (.f64 (fabs.f64 x) (sqrt.f64 PI.f64)))))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1935 to 1175 computations (39.3% saved)

simplify108.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

844×	`times-frac_binary64_2812`
702×	`distribute-rgt-in_binary64_2756`
671×	`distribute-lft-in_binary64_2755`
105×	`associate-l_binary64_2747`
92×	`*-commutative_binary64_2737`
88×	`associate-r_binary64_2746`
61×	`associate-/r*_binary64_2750`
59×	`sub-neg_binary64_2799`
58×	`associate-*r/_binary64_2748`
56×	`unswap-sqr_binary64_2774` `associate-*l/_binary64_2749`
48×	`+-commutative_binary64_2736`
43×	`distribute-rgt-out_binary64_2759`
41×	`sqr-pow_binary64_2778`
38×	`exp-prod_binary64_2858` `associate-/l*_binary64_2751`
35×	`associate-+r+_binary64_2738`
33×	`exp-sum_binary64_2852` `associate-+l+_binary64_2739`
31×	`cancel-sign-sub-inv_binary64_2772`
30×	`*-lft-identity_binary64_2795`
26×	`log-prod_binary64_2892`
25×	`neg-mul-1_binary64_2802` `*-rgt-identity_binary64_2796`
23×	`neg-sub0_binary64_2801` `distribute-rgt-neg-in_binary64_2764`
21×	`distribute-neg-in_binary64_2767`
17×	`distribute-neg-frac_binary64_2770`
14×	`swap-sqr_binary64_2773` `distribute-lft-neg-in_binary64_2763` `associate--r+_binary64_2742`
12×	`exp-diff_binary64_2854` `distribute-lft-out_binary64_2757`
11×	`log-div_binary64_2893` `distribute-lft-neg-out_binary64_2765`
10×	`cube-prod_binary64_2834`
9×	`cube-div_binary64_2835` `distribute-rgt-neg-out_binary64_2766` `distribute-rgt1-in_binary64_2762`
8×	`cube-unmult_binary64_2843` `unsub-neg_binary64_2800`
7×	`prod-exp_binary64_2855` `associate-/l/_binary64_2753`
6×	`pow-sqr_binary64_2779` `distribute-rgt-out--_binary64_2760` `associate--l+_binary64_2743`
5×	`associate-/r/_binary64_2752` `associate-+r-_binary64_2740`
4×	`exp-neg_binary64_2853` `associate-+l-_binary64_2741`
3×	`rem-exp-log_binary64_2846` `rem-sqrt-square_binary64_2819` `/-rgt-identity_binary64_2797`
2×	`log-pow_binary64_2895` `unpow3_binary64_2872` `rem-log-exp_binary64_2847` `rem-square-sqrt_binary64_2818` `distribute-lft1-in_binary64_2761` `count-2_binary64_2754`
1×	`unpow2_binary64_2871` `unpow1/2_binary64_2870` `pow-plus_binary64_2869` `exp-to-pow_binary64_2868` `unpow1_binary64_2864` `1-exp_binary64_2850` `exp-1-e_binary64_2849` `cube-mult_binary64_2836` `rem-3cbrt-lft_binary64_2831` `+-rgt-identity_binary64_2791` `difference-of-squares_binary64_2775`
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-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` `exp-sqrt_binary64_2859` `div-exp_binary64_2857` `rec-exp_binary64_2856` `e-exp-1_binary64_2851` `exp-0_binary64_2848` `cube-neg_binary64_2833` `rem-3cbrt-rft_binary64_2832` `rem-cbrt-cube_binary64_2830` `rem-cube-cbrt_binary64_2829` `sqr-abs_binary64_2821` `sqr-neg_binary64_2820` `div-sub_binary64_2811` `mul-1-neg_binary64_2798` `remove-double-neg_binary64_2794` `sub0-neg_binary64_2793` `--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` `cancel-sign-sub_binary64_2771` `distribute-frac-neg_binary64_2769` `distribute-neg-out_binary64_2768` `distribute-lft-out--_binary64_2758` `associate--r-_binary64_2745` `associate--l-_binary64_2744`

Counts

115 → 85

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	3941
1	556	3524
2	1695	3402
3	5002	3402

prune204.0ms (1.2%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	77	8	85
Fresh	8	12	20
Picked	0	1	1
Done	0	0	0
Total	85	21	106

Error

1.0b

Counts

106 → 21

Compiler

Compiled 4188 to 2057 computations (50.9% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (pow.f64 E.f64 (-.f64 (.f64 x x) (log.f64 (.f64 (fabs.f64 x) (sqrt.f64 PI.f64))))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
0.5b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
1.0b	(sqrt.f64 PI.f64)
2.6b	(pow.f64 E.f64 (-.f64 (.f64 x x) (log.f64 (.f64 (fabs.f64 x) (sqrt.f64 PI.f64)))))

rewrite297.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

23×	`*-un-lft-identity_binary64_2806`
21×	`add-sqr-sqrt_binary64_2828`
16×	`add-exp-log_binary64_2844`
14×	`add-cube-cbrt_binary64_2841`
13×	`associate-l_binary64_2747`
12×	`unpow-prod-up_binary64_2884` `pow1_binary64_2867`
11×	`add-cbrt-cube_binary64_2842`
10×	`cancel-sign-sub-inv_binary64_2772`
7×	`unpow-prod-down_binary64_2885`
5×	`prod-exp_binary64_2855` `distribute-lft-out_binary64_2757` `associate-r_binary64_2746`
4×	`log-pow_binary64_2895` `pow-unpow_binary64_2883` `pow-sub_binary64_2882` `pow-exp_binary64_2874` `add-log-exp_binary64_2845` `times-frac_binary64_2812` `associate-/l*_binary64_2751`
3×	`sqr-pow_binary64_2778` `sqrt-prod_binary64_2822` `flip3-+_binary64_2809` `flip-+_binary64_2780` `unswap-sqr_binary64_2774`
2×	`sub-neg_binary64_2799` `pow-prod-down_binary64_2877` `pow-to-exp_binary64_2875` `e-exp-1_binary64_2851` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `cbrt-unprod_binary64_2839` `associate-/l/_binary64_2753` `frac-times_binary64_2816` `associate-*r/_binary64_2748`
1×	`difference-of-squares_binary64_2775` `pow-pow_binary64_2878` `pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `div-inv_binary64_2803` `associate-/r_binary64_2750` `distribute-rgt-in_binary64_2756` `distribute-lft-in_binary64_2755` `associate-l/_binary64_2749` `*-commutative_binary64_2737`

Counts

4 → 105

Calls

4 calls:

33.0ms	(.f64 (pow.f64 E.f64 (-.f64 (.f64 x x) (log.f64 (.f64 (fabs.f64 x) (sqrt.f64 PI.f64))))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
12.0ms	(pow.f64 E.f64 (-.f64 (.f64 x x) (log.f64 (.f64 (fabs.f64 x) (sqrt.f64 PI.f64)))))
10.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 4747 to 2110 computations (55.6% saved)

series565.0ms (3.4%)

Error

1.0b

Counts

4 → 24

Calls

4 calls:

274.0ms	(.f64 (pow.f64 E.f64 (-.f64 (.f64 x x) (log.f64 (.f64 (fabs.f64 x) (sqrt.f64 PI.f64))))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (*.f64 x x)))))
136.0ms	(pow.f64 E.f64 (-.f64 (.f64 x x) (log.f64 (.f64 (fabs.f64 x) (sqrt.f64 PI.f64)))))
108.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1966 to 1359 computations (30.9% saved)

simplify136.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

810×	`distribute-rgt-in_binary64_2756`
777×	`distribute-lft-in_binary64_2755`
474×	`times-frac_binary64_2812`
170×	`associate-l_binary64_2747`
139×	`associate-r_binary64_2746`
122×	`*-commutative_binary64_2737`
85×	`sqr-pow_binary64_2778`
63×	`unswap-sqr_binary64_2774` `distribute-rgt-out_binary64_2759`
61×	`associate-/r*_binary64_2750`
59×	`associate-*r/_binary64_2748`
58×	`sub-neg_binary64_2799`
54×	`distribute-lft-out_binary64_2757`
53×	`associate-*l/_binary64_2749`
51×	`+-commutative_binary64_2736`
49×	`associate-/l*_binary64_2751`
43×	`exp-prod_binary64_2858`
38×	`*-lft-identity_binary64_2795`
33×	`*-rgt-identity_binary64_2796`
32×	`associate-+r+_binary64_2738`
31×	`exp-sum_binary64_2852` `cancel-sign-sub-inv_binary64_2772`
28×	`pow-sqr_binary64_2779` `associate-+l+_binary64_2739`
27×	`log-prod_binary64_2892`
23×	`neg-mul-1_binary64_2802` `distribute-rgt-neg-in_binary64_2764`
20×	`neg-sub0_binary64_2801`
18×	`distribute-neg-in_binary64_2767`
17×	`distribute-neg-frac_binary64_2770`
16×	`div-sub_binary64_2811`
14×	`cube-prod_binary64_2834` `swap-sqr_binary64_2773` `distribute-lft-neg-in_binary64_2763` `associate--r+_binary64_2742`
13×	`distribute-lft-neg-out_binary64_2765`
12×	`distribute-rgt-neg-out_binary64_2766`
10×	`cube-unmult_binary64_2843`
8×	`log-div_binary64_2893` `unsub-neg_binary64_2800`
7×	`exp-diff_binary64_2854` `distribute-rgt1-in_binary64_2762`
6×	`cube-div_binary64_2835` `distribute-frac-neg_binary64_2769` `distribute-rgt-out--_binary64_2760` `associate-/l/_binary64_2753`
5×	`log-pow_binary64_2895` `rem-sqrt-square_binary64_2819` `associate-/r/_binary64_2752`
4×	`associate--l+_binary64_2743` `associate-+r-_binary64_2740`
3×	`pow-base-1_binary64_2866` `rem-exp-log_binary64_2846` `associate-+l-_binary64_2741`
2×	`unpow3_binary64_2872` `unpow1/2_binary64_2870` `pow-plus_binary64_2869` `exp-to-pow_binary64_2868` `unpow1_binary64_2864` `rem-square-sqrt_binary64_2818`
1×	`log-E_binary64_2896` `unpow2_binary64_2871` `prod-exp_binary64_2855` `e-exp-1_binary64_2851` `1-exp_binary64_2850` `cube-mult_binary64_2836` `rem-3cbrt-lft_binary64_2831` `/-rgt-identity_binary64_2797` `+-rgt-identity_binary64_2791` `difference-of-squares_binary64_2775` `distribute-lft1-in_binary64_2761` `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` `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-rec_binary64_2894` `pow-base-0_binary64_2890` `unpow1/3_binary64_2873` `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-neg_binary64_2853` `exp-1-e_binary64_2849` `exp-0_binary64_2848` `rem-log-exp_binary64_2847` `cube-neg_binary64_2833` `rem-3cbrt-rft_binary64_2832` `rem-cbrt-cube_binary64_2830` `rem-cube-cbrt_binary64_2829` `sqr-abs_binary64_2821` `sqr-neg_binary64_2820` `mul-1-neg_binary64_2798` `remove-double-neg_binary64_2794` `sub0-neg_binary64_2793` `--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` `cancel-sign-sub_binary64_2771` `distribute-neg-out_binary64_2768` `distribute-lft-out--_binary64_2758` `associate--r-_binary64_2745` `associate--l-_binary64_2744`

Counts

129 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	242	4976
1	656	4425
2	2014	4310
3	5513	4310

prune254.0ms (1.5%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	82	11	93
Fresh	2	17	19
Picked	1	0	1
Done	0	1	1
Total	85	29	114

Error

0.8b

Counts

114 → 29

Compiler

Compiled 5101 to 2517 computations (50.7% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) 3))
0.7b	(pow.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) 3)
1.0b	(sqrt.f64 PI.f64)
2.6b	(pow.f64 E.f64 (-.f64 (.f64 x x) (log.f64 (.f64 (fabs.f64 x) (sqrt.f64 PI.f64)))))

rewrite294.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

26×	`*-un-lft-identity_binary64_2806`
22×	`cbrt-prod_binary64_2837`
20×	`add-sqr-sqrt_binary64_2828`
19×	`unpow-prod-down_binary64_2885`
18×	`add-cube-cbrt_binary64_2841`
16×	`times-frac_binary64_2812` `cube-prod_binary64_2834`
11×	`add-exp-log_binary64_2844`
10×	`pow1_binary64_2867` `add-cbrt-cube_binary64_2842`
7×	`pow-unpow_binary64_2883`
6×	`unpow-prod-up_binary64_2884`
5×	`cancel-sign-sub-inv_binary64_2772` `pow-exp_binary64_2874`
4×	`add-log-exp_binary64_2845` `distribute-lft-out_binary64_2757` `div-inv_binary64_2803`
3×	`sqr-pow_binary64_2778` `sqrt-prod_binary64_2822` `rem-cube-cbrt_binary64_2829`
2×	`log-pow_binary64_2895` `pow-pow_binary64_2878` `pow-to-exp_binary64_2875` `div-exp_binary64_2857` `unpow3_binary64_2872` `cube-mult_binary64_2836` `cube-div_binary64_2835` `cbrt-undiv_binary64_2840`
1×	`sub-neg_binary64_2799` `pow-prod-down_binary64_2877` `difference-of-squares_binary64_2775` `pow-sub_binary64_2882` `e-exp-1_binary64_2851` `pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `pow1/3_binary64_2888` `cbrt-div_binary64_2838` `rem-cbrt-cube_binary64_2830`

Counts

4 → 109

Calls

4 calls:

11.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) 3))
11.0ms	(pow.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) 3)
8.0ms	(pow.f64 E.f64 (-.f64 (.f64 x x) (log.f64 (.f64 (fabs.f64 x) (sqrt.f64 PI.f64)))))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 4954 to 2495 computations (49.6% saved)

series396.0ms (2.4%)

Error

0.8b

Counts

4 → 24

Calls

4 calls:

125.0ms	(pow.f64 E.f64 (-.f64 (.f64 x x) (log.f64 (.f64 (fabs.f64 x) (sqrt.f64 PI.f64)))))
121.0ms	(pow.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) 3)
103.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x)) 3))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 2068 to 1531 computations (26% saved)

simplify142.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

376×	`unswap-sqr_binary64_2774`
348×	`log-div_binary64_2893`
316×	`times-frac_binary64_2812`
298×	`associate-*l/_binary64_2749`
292×	`associate-*r/_binary64_2748`
269×	`associate-/l*_binary64_2751`
265×	`associate-/r*_binary64_2750`
139×	`sqr-pow_binary64_2778`
95×	`distribute-rgt-in_binary64_2756`
93×	`distribute-lft-in_binary64_2755`
87×	`log-prod_binary64_2892`
82×	`exp-prod_binary64_2858`
60×	`log-pow_binary64_2895`
54×	`associate-l_binary64_2747`
49×	`associate-/l/_binary64_2753`
46×	`cube-prod_binary64_2834` `associate-r_binary64_2746`
40×	`pow-sqr_binary64_2779`
38×	`swap-sqr_binary64_2773`
34×	`*-commutative_binary64_2737`
30×	`associate-/r/_binary64_2752`
26×	`cube-div_binary64_2835`
22×	`sub-neg_binary64_2799`
18×	`unpow3_binary64_2872` `+-commutative_binary64_2736`
17×	`cube-mult_binary64_2836` `rem-sqrt-square_binary64_2819` `distribute-lft-out_binary64_2757`
16×	`div-sub_binary64_2811`
15×	`associate-+l+_binary64_2739` `associate-+r+_binary64_2738`
14×	`exp-sum_binary64_2852`
13×	`cube-unmult_binary64_2843`
12×	`rem-cbrt-cube_binary64_2830`
11×	`pow-plus_binary64_2869` `neg-mul-1_binary64_2802`
9×	`distribute-rgt-out_binary64_2759`
8×	`neg-sub0_binary64_2801`
7×	`exp-diff_binary64_2854` `-rgt-identity_binary64_2796` `-lft-identity_binary64_2795`
6×	`distribute-frac-neg_binary64_2769`
5×	`distribute-rgt-neg-out_binary64_2766` `distribute-lft-neg-out_binary64_2765` `count-2_binary64_2754` `associate--r+_binary64_2742`
4×	`rem-square-sqrt_binary64_2818` `distribute-rgt-neg-in_binary64_2764`
3×	`unpow1/2_binary64_2870` `pow-base-1_binary64_2866` `unpow1_binary64_2864` `rem-exp-log_binary64_2846` `unsub-neg_binary64_2800` `cancel-sign-sub-inv_binary64_2772` `distribute-neg-in_binary64_2767` `distribute-lft-neg-in_binary64_2763`
2×	`exp-to-pow_binary64_2868` `rem-3cbrt-lft_binary64_2831` `rem-cube-cbrt_binary64_2829`
1×	`log-E_binary64_2896` `unpow2_binary64_2871` `prod-exp_binary64_2855` `e-exp-1_binary64_2851` `1-exp_binary64_2850` `/-rgt-identity_binary64_2797` `+-rgt-identity_binary64_2791` `difference-of-squares_binary64_2775` `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-rec_binary64_2894` `pow-base-0_binary64_2890` `unpow1/3_binary64_2873` `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-neg_binary64_2853` `exp-1-e_binary64_2849` `exp-0_binary64_2848` `rem-log-exp_binary64_2847` `cube-neg_binary64_2833` `rem-3cbrt-rft_binary64_2832` `sqr-abs_binary64_2821` `sqr-neg_binary64_2820` `mul-1-neg_binary64_2798` `remove-double-neg_binary64_2794` `sub0-neg_binary64_2793` `--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` `cancel-sign-sub_binary64_2771` `distribute-neg-frac_binary64_2770` `distribute-neg-out_binary64_2768` `distribute-rgt1-in_binary64_2762` `distribute-lft1-in_binary64_2761` `distribute-rgt-out--_binary64_2760` `distribute-lft-out--_binary64_2758` `associate--r-_binary64_2745` `associate--l-_binary64_2744` `associate--l+_binary64_2743` `associate-+l-_binary64_2741`

Counts

133 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	3191
1	425	2899
2	1159	2843
3	4761	2843
4	5283	2843

prune171.0ms (1%)

Pruning

29 alts after pruning (27 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	27	27
Picked	0	1	1
Done	0	1	1
Total	91	29	120

Error

0.8b

Counts

120 → 29

Compiler

Compiled 3596 to 1799 computations (50% saved)

regimes2.6s (15.5%)

Accuracy

Total 0.8b remaining (59%)

Threshold costs 0.8b (59%)

Compiler

Compiled 33350 to 20349 computations (39% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64_2736`
1×	`1-exp_binary64_2850` `*-commutative_binary64_2737`
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` `exp-1-e_binary64_2849` `exp-0_binary64_2848` `sqr-abs_binary64_2821` `sqr-neg_binary64_2820` `neg-mul-1_binary64_2802` `neg-sub0_binary64_2801` `unsub-neg_binary64_2800` `sub-neg_binary64_2799` `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	23	47
1	29	47
2	28	47

end0.0ms (0%)

sample9.0s (54.5%)

Algorithm

1×

intervals

Results

1.6s	8000×	body	128	valid
104.0ms	8114×	pre	128	true
22.0ms	114×	body	128	invalid

Compiler

Compiled 11182 to 6829 computations (38.9% saved)

Details

analyze224.0ms (1.4%)

sample76.0ms (0.5%)

simplify75.0ms (0.5%)

prune10.0ms (0.1%)

localize18.0ms (0.1%)

rewrite373.0ms (2.3%)

series335.0ms (2%)

simplify202.0ms (1.2%)

prune229.0ms (1.4%)

localize20.0ms (0.1%)

rewrite269.0ms (1.6%)

series505.0ms (3.1%)

simplify108.0ms (0.7%)

prune204.0ms (1.2%)

localize22.0ms (0.1%)

rewrite297.0ms (1.8%)

series565.0ms (3.4%)

simplify136.0ms (0.8%)

prune254.0ms (1.5%)

localize25.0ms (0.2%)

rewrite294.0ms (1.8%)

series396.0ms (2.4%)

simplify142.0ms (0.9%)

prune171.0ms (1%)

regimes2.6s (15.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample9.0s (54.5%)

Profiling