Details

analyze6.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample22.0ms (0.9%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify649.0ms (25.7%)

Algorithm

1×	egg-herbie

Rules

804×	`exp-prod_binary64_2858`
474×	`unsub-neg_binary64_2800`
472×	`associate-/l*_binary64_2751`
309×	`exp-sum_binary64_2852` `distribute-rgt-in_binary64_2756`
274×	`swap-sqr_binary64_2773`
178×	`exp-diff_binary64_2854`
176×	`distribute-rgt-neg-in_binary64_2764`
160×	`neg-mul-1_binary64_2802`
153×	`neg-sub0_binary64_2801`
127×	`associate-+l-_binary64_2741`
115×	`distribute-lft-in_binary64_2755`
109×	`associate-r_binary64_2746`
105×	`associate-+l+_binary64_2739` `*-commutative_binary64_2737`
100×	`associate--r+_binary64_2742`
99×	`distribute-rgt1-in_binary64_2762`
98×	`distribute-rgt-out_binary64_2759`
95×	`associate-+r+_binary64_2738`
93×	`sub-neg_binary64_2799` `associate-+r-_binary64_2740`
91×	`pow-plus_binary64_2869`
79×	`associate-l_binary64_2747`
74×	`associate--l+_binary64_2743`
72×	`cancel-sign-sub-inv_binary64_2772`
70×	`distribute-lft-neg-in_binary64_2763` `distribute-rgt-out--_binary64_2760`
65×	`sqr-neg_binary64_2820` `associate--r-_binary64_2745`
56×	`distribute-rgt-neg-out_binary64_2766`
54×	`associate--l-_binary64_2744`
50×	`distribute-lft-neg-out_binary64_2765`
49×	`exp-neg_binary64_2853`
46×	`distribute-neg-in_binary64_2767` `distribute-lft-out_binary64_2757`
41×	`distribute-lft-out--_binary64_2758`
33×	`+-commutative_binary64_2736`
20×	`distribute-neg-out_binary64_2768`
17×	`div-sub_binary64_2811` `associate-/r*_binary64_2750`
13×	`sqr-pow_binary64_2778`
12×	`exp-lft-sqr_binary64_2861`
11×	`cube-prod_binary64_2834`
10×	`distribute-lft1-in_binary64_2761`
9×	`pow-base-1_binary64_2866`
8×	`cube-div_binary64_2835` `+-inverses_binary64_2785` `count-2_binary64_2754`
6×	`cube-unmult_binary64_2843` `*-rgt-identity_binary64_2796` `sub0-neg_binary64_2793` `distribute-frac-neg_binary64_2769`
5×	`+-rgt-identity_binary64_2791` `pow-sqr_binary64_2779`
4×	`--rgt-identity_binary64_2792` `+-lft-identity_binary64_2790` `mul0-lft_binary64_2788`
3×	`cube-neg_binary64_2833` `/-rgt-identity_binary64_2797` `remove-double-neg_binary64_2794` `difference-of-squares_binary64_2775`
2×	`div-exp_binary64_2857` `times-frac_binary64_2812` `*-lft-identity_binary64_2795` `mul0-rgt_binary64_2789` `div0_binary64_2787` `unswap-sqr_binary64_2774` `associate-/r/_binary64_2752`
1×	`exp-sqrt_binary64_2859` `1-exp_binary64_2850` `exp-1-e_binary64_2849` `mul-1-neg_binary64_2798` `difference-of-sqr-1_binary64_2776`
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` `exp-to-pow_binary64_2868` `unpow0_binary64_2865` `unpow1_binary64_2864` `unpow-1_binary64_2863` `exp-lft-cube_binary64_2862` `exp-cbrt_binary64_2860` `rec-exp_binary64_2856` `prod-exp_binary64_2855` `e-exp-1_binary64_2851` `exp-0_binary64_2848` `rem-log-exp_binary64_2847` `rem-exp-log_binary64_2846` `cube-mult_binary64_2836` `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-sqrt-square_binary64_2819` `rem-square-sqrt_binary64_2818` `-inverses_binary64_2786` `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` `associate-/l/_binary64_2753` `associate-l/_binary64_2749` `associate-*r/_binary64_2748`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	24	20
3	32	20
4	50	20
5	75	20
6	176	20
7	877	20
8	3104	20

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

Counts

1 → 1

Compiler

Compiled 13 to 10 computations (23.1% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
0.0b	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

rewrite163.0ms (6.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

45×	`*-un-lft-identity_binary64_2806`
37×	`times-frac_binary64_2812`
34×	`add-sqr-sqrt_binary64_2828`
28×	`sqrt-prod_binary64_2822`
25×	`add-cube-cbrt_binary64_2841`
10×	`difference-of-squares_binary64_2775`
8×	`distribute-lft-out_binary64_2757` `associate-/l*_binary64_2751`
7×	`div-inv_binary64_2803`
5×	`add-log-exp_binary64_2845` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
4×	`pow1_binary64_2867` `sqrt-div_binary64_2823`
3×	`distribute-rgt-out_binary64_2759` `associate-/r*_binary64_2750`
2×	`flip3--_binary64_2810` `associate-/l/_binary64_2753` `flip--_binary64_2781`
1×	`sum-log_binary64_2897` `frac-add_binary64_2814` `flip3-+_binary64_2809` `flip-+_binary64_2780` `distribute-rgt1-in_binary64_2762` `+-commutative_binary64_2736` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `pow1/2_binary64_2886` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819`

Counts

3 → 90

Calls

3 calls:

24.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
7.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 2001 to 1256 computations (37.2% saved)

series169.0ms (6.7%)

Error

Counts

3 → 18

Calls

3 calls:

58.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
54.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
40.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 552 to 471 computations (14.7% saved)

simplify569.0ms (22.6%)

Algorithm

1×	egg-herbie

Rules

293×	`times-frac_binary64_2812`
289×	`distribute-rgt-out_binary64_2759`
248×	`distribute-rgt-neg-in_binary64_2764`
209×	`sub-neg_binary64_2799`
205×	`distribute-lft-neg-in_binary64_2763`
179×	`unswap-sqr_binary64_2774`
170×	`associate-r_binary64_2746`
169×	`cancel-sign-sub-inv_binary64_2772`
166×	`associate-l_binary64_2747`
153×	`distribute-rgt-out--_binary64_2760`
144×	`associate-/l*_binary64_2751`
126×	`associate-/r*_binary64_2750`
120×	`div-sub_binary64_2811`
117×	`associate-*l/_binary64_2749`
100×	`sqr-pow_binary64_2778` `distribute-neg-frac_binary64_2770`
96×	`associate-*r/_binary64_2748`
94×	`associate-/r/_binary64_2752`
83×	`*-commutative_binary64_2737`
82×	`distribute-rgt-in_binary64_2756`
79×	`associate-/l/_binary64_2753`
65×	`pow-sqr_binary64_2779`
62×	`unsub-neg_binary64_2800` `distribute-lft-neg-out_binary64_2765`
59×	`neg-sub0_binary64_2801`
56×	`+-commutative_binary64_2736`
55×	`neg-mul-1_binary64_2802`
53×	`distribute-lft-in_binary64_2755`
47×	`cube-prod_binary64_2834`
43×	`log-prod_binary64_2892`
40×	`distribute-rgt-neg-out_binary64_2766` `associate--r+_binary64_2742` `associate-+l+_binary64_2739`
38×	`distribute-rgt1-in_binary64_2762`
37×	`exp-prod_binary64_2858` `associate-+l-_binary64_2741`
36×	`cube-div_binary64_2835`
35×	`distribute-neg-in_binary64_2767`
33×	`pow-plus_binary64_2869` `swap-sqr_binary64_2773`
32×	`log-div_binary64_2893`
25×	`/-rgt-identity_binary64_2797` `distribute-neg-out_binary64_2768`
24×	`*-rgt-identity_binary64_2796`
23×	`*-lft-identity_binary64_2795` `sub0-neg_binary64_2793`
22×	`associate-+r-_binary64_2740`
21×	`associate--l+_binary64_2743`
20×	`difference-of-squares_binary64_2775`
17×	`prod-exp_binary64_2855`
16×	`div-exp_binary64_2857`
15×	`log-pow_binary64_2895` `associate-+r+_binary64_2738`
12×	`+-rgt-identity_binary64_2791`
11×	`cube-unmult_binary64_2843` `cancel-sign-sub_binary64_2771`
9×	`unpow3_binary64_2872`
8×	`exp-sqrt_binary64_2859` `associate--l-_binary64_2744`
7×	`rem-sqrt-square_binary64_2819` `remove-double-div_binary64_2782` `difference-of-sqr-1_binary64_2776`
6×	`log-rec_binary64_2894` `pow-base-1_binary64_2866` `cube-mult_binary64_2836` `distribute-lft1-in_binary64_2761`
5×	`mul0-lft_binary64_2788`
4×	`exp-lft-sqr_binary64_2861` `rec-exp_binary64_2856` `mul0-rgt_binary64_2789` `distribute-frac-neg_binary64_2769`
3×	`mul-1-neg_binary64_2798` `*-inverses_binary64_2786` `distribute-lft-out--_binary64_2758` `distribute-lft-out_binary64_2757`
2×	`exp-sum_binary64_2852` `associate--r-_binary64_2745`
1×	`unpow2_binary64_2871` `unpow1_binary64_2864` `exp-diff_binary64_2854` `1-exp_binary64_2850` `exp-1-e_binary64_2849` `rem-log-exp_binary64_2847` `rem-square-sqrt_binary64_2818` `div0_binary64_2787` `+-inverses_binary64_2785` `difference-of-sqr--1_binary64_2777` `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-E_binary64_2896` `pow-base-0_binary64_2890` `unpow1/3_binary64_2873` `unpow1/2_binary64_2870` `exp-to-pow_binary64_2868` `unpow0_binary64_2865` `unpow-1_binary64_2863` `exp-lft-cube_binary64_2862` `exp-cbrt_binary64_2860` `exp-neg_binary64_2853` `e-exp-1_binary64_2851` `exp-0_binary64_2848` `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-abs_binary64_2821` `sqr-neg_binary64_2820` `remove-double-neg_binary64_2794` `--rgt-identity_binary64_2792` `+-lft-identity_binary64_2790` `lft-mult-inverse_binary64_2784` `rgt-mult-inverse_binary64_2783`

Counts

108 → 99

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	180	2021
1	380	1958
2	1025	1952
3	2867	1952

prune138.0ms (5.5%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	99	1	100

Error

Counts

100 → 1

Compiler

Compiled 2311 to 1565 computations (32.3% saved)

regimes47.0ms (1.9%)

Accuracy

Total 0.0b remaining (1.1%)

Threshold costs 0.0b (1.1%)

Compiler

Compiled 187 to 157 computations (16% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64_2736`
3×	`sub-neg_binary64_2799`
2×	`neg-mul-1_binary64_2802` `neg-sub0_binary64_2801` `*-commutative_binary64_2737`
1×	`1-exp_binary64_2850` `cancel-sign-sub-inv_binary64_2772` `distribute-lft-neg-out_binary64_2765` `distribute-rgt-neg-in_binary64_2764`
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` `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_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-in_binary64_2763`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	24	20
3	28	20
4	30	20

Proof

(log f64 (+ f64 (/ f64 1 h0) (/ f64 (sqrt f64 (- f64 1 (* f64 h0 h0))) h0)))

end0.0ms (0%)

sample741.0ms (29.4%)

Algorithm

1×

intervals

Results

441.0ms	8000×	body	128	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 72 to 61 computations (15.3% saved)

Details

analyze6.0ms (0.2%)

sample22.0ms (0.9%)

simplify649.0ms (25.7%)

prune3.0ms (0.1%)

localize10.0ms (0.4%)

rewrite163.0ms (6.5%)

series169.0ms (6.7%)

simplify569.0ms (22.6%)

prune138.0ms (5.5%)

regimes47.0ms (1.9%)

bsearch0.0ms (0%)

simplify4.0ms (0.2%)

end0.0ms (0%)

sample741.0ms (29.4%)

Profiling