Details

analyze270.0ms (3.7%)

Algorithm

1×	search
2×	egg-herbie

Rules

744×	`distribute-lft-out_binary64_3098`
629×	`associate-/l/_binary64_3094`
586×	`associate-/l*_binary64_3092`
496×	`associate-/r*_binary64_3091`
430×	`distribute-rgt-in_binary64_3097`
425×	`*-commutative_binary64_3078`
381×	`unswap-sqr_binary64_3115`
332×	`distribute-rgt-out_binary64_3100`
281×	`associate-+l+_binary64_3080`
273×	`associate-*r/_binary64_3089`
213×	`associate-*l/_binary64_3090`
183×	`*-lft-identity_binary64_3136`
179×	`associate-l_binary64_3088`
165×	`distribute-lft-in_binary64_3096`
157×	`associate-r_binary64_3087`
133×	`*-rgt-identity_binary64_3137`
126×	`sqr-pow_binary64_3119`
109×	`+-commutative_binary64_3077`
105×	`associate-+r+_binary64_3079`
68×	`associate-/r/_binary64_3093`
32×	`pow-sqr_binary64_3120`
21×	`cube-prod_binary64_3175`
20×	`pow-plus_binary64_3210`
11×	`unpow3_binary64_3213`
9×	`cube-unmult_binary64_3184`
8×	`cube-mult_binary64_3177`
6×	`/-rgt-identity_binary64_3138`
4×	`unpow2_binary64_3212`
3×	`unpow1_binary64_3205`
2×	`unpow1/2_binary64_3211` `rem-sqrt-square_binary64_3160`
1×	`1-exp_binary64_3191` `sqr-abs_binary64_3162`
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_3410` `erf-erfc_binary64_3409` `erf-odd_binary64_3408` `if-if-and-not_binary64_3407` `if-if-and_binary64_3406` `if-if-or-not_binary64_3405` `if-if-or_binary64_3404` `if-not_binary64_3403` `if-same_binary64_3402` `if-false_binary64_3401` `if-true_binary64_3400` `not-gte_binary64_3399` `not-lte_binary64_3398` `not-gt_binary64_3397` `not-lt_binary64_3396` `gte-same_binary64_3395` `lte-same_binary64_3394` `gt-same_binary64_3393` `lt-same_binary64_3392` `sinh---cosh_binary64_3339` `sinh-+-cosh_binary64_3338` `sinh-cosh_binary64_3337` `tanh-def-c_binary64_3336` `tanh-def-b_binary64_3335` `tanh-def-a_binary64_3334` `cosh-def_binary64_3333` `sinh-def_binary64_3332` `tan-neg_binary64_3279` `cos-neg_binary64_3278` `sin-neg_binary64_3277` `tan-0_binary64_3276` `cos-0_binary64_3275` `sin-0_binary64_3274` `hang-m-tan_binary64_3273` `hang-p-tan_binary64_3272` `hang-m0-tan_binary64_3271` `hang-p0-tan_binary64_3270` `hang-0m-tan_binary64_3269` `hang-0p-tan_binary64_3268` `tan-+PI/2_binary64_3267` `tan-+PI_binary64_3266` `tan-PI_binary64_3265` `tan-PI/3_binary64_3264` `tan-PI/4_binary64_3263` `tan-PI/6_binary64_3262` `cos-+PI/2_binary64_3261` `cos-+PI_binary64_3260` `cos-PI_binary64_3259` `cos-PI/2_binary64_3258` `cos-PI/3_binary64_3257` `cos-PI/4_binary64_3256` `cos-PI/6_binary64_3255` `sin-+PI/2_binary64_3254` `sin-+PI_binary64_3253` `sin-PI_binary64_3252` `sin-PI/2_binary64_3251` `sin-PI/3_binary64_3250` `sin-PI/4_binary64_3249` `sin-PI/6_binary64_3248` `sub-1-sin_binary64_3247` `sub-1-cos_binary64_3246` `-1-add-sin_binary64_3245` `-1-add-cos_binary64_3244` `1-sub-sin_binary64_3243` `1-sub-cos_binary64_3242` `cos-sin-sum_binary64_3241` `log-E_binary64_3237` `log-pow_binary64_3236` `log-rec_binary64_3235` `log-div_binary64_3234` `log-prod_binary64_3233` `pow-base-0_binary64_3231` `unpow1/3_binary64_3214` `exp-to-pow_binary64_3209` `pow-base-1_binary64_3207` `unpow0_binary64_3206` `unpow-1_binary64_3204` `exp-lft-cube_binary64_3203` `exp-lft-sqr_binary64_3202` `exp-cbrt_binary64_3201` `exp-sqrt_binary64_3200` `exp-prod_binary64_3199` `div-exp_binary64_3198` `rec-exp_binary64_3197` `prod-exp_binary64_3196` `exp-diff_binary64_3195` `exp-neg_binary64_3194` `exp-sum_binary64_3193` `e-exp-1_binary64_3192` `exp-1-e_binary64_3190` `exp-0_binary64_3189` `rem-log-exp_binary64_3188` `rem-exp-log_binary64_3187` `cube-div_binary64_3176` `cube-neg_binary64_3174` `rem-3cbrt-rft_binary64_3173` `rem-3cbrt-lft_binary64_3172` `rem-cbrt-cube_binary64_3171` `rem-cube-cbrt_binary64_3170` `sqr-neg_binary64_3161` `rem-square-sqrt_binary64_3159` `times-frac_binary64_3153` `div-sub_binary64_3152` `neg-mul-1_binary64_3143` `neg-sub0_binary64_3142` `unsub-neg_binary64_3141` `sub-neg_binary64_3140` `mul-1-neg_binary64_3139` `remove-double-neg_binary64_3135` `sub0-neg_binary64_3134` `--rgt-identity_binary64_3133` `+-rgt-identity_binary64_3132` `+-lft-identity_binary64_3131` `mul0-rgt_binary64_3130` `mul0-lft_binary64_3129` `div0_binary64_3128` `*-inverses_binary64_3127` `+-inverses_binary64_3126` `lft-mult-inverse_binary64_3125` `rgt-mult-inverse_binary64_3124` `remove-double-div_binary64_3123` `difference-of-sqr--1_binary64_3118` `difference-of-sqr-1_binary64_3117` `difference-of-squares_binary64_3116` `swap-sqr_binary64_3114` `cancel-sign-sub-inv_binary64_3113` `cancel-sign-sub_binary64_3112` `distribute-neg-frac_binary64_3111` `distribute-frac-neg_binary64_3110` `distribute-neg-out_binary64_3109` `distribute-neg-in_binary64_3108` `distribute-rgt-neg-out_binary64_3107` `distribute-lft-neg-out_binary64_3106` `distribute-rgt-neg-in_binary64_3105` `distribute-lft-neg-in_binary64_3104` `distribute-rgt1-in_binary64_3103` `distribute-lft1-in_binary64_3102` `distribute-rgt-out--_binary64_3101` `distribute-lft-out--_binary64_3099` `count-2_binary64_3095` `associate--r-_binary64_3086` `associate--l-_binary64_3085` `associate--l+_binary64_3084` `associate--r+_binary64_3083` `associate-+l-_binary64_3082` `associate-+r-_binary64_3081`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	77
1	70	62
2	210	45
3	761	41
4	1373	41
5	3002	41
6	3334	41
7	3492	41
8	4100	41
9	4119	41
10	4206	41
11	4850	41
12	5050	41
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

Compiler

Compiled 70 to 33 computations (52.9% saved)

sample46.0ms (0.6%)

Algorithm

1×

intervals

Results

28.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 137 to 65 computations (52.6% saved)

simplify127.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

744×	`distribute-lft-out_binary64_3098`
629×	`associate-/l/_binary64_3094`
586×	`associate-/l*_binary64_3092`
496×	`associate-/r*_binary64_3091`
430×	`distribute-rgt-in_binary64_3097`
425×	`*-commutative_binary64_3078`
381×	`unswap-sqr_binary64_3115`
332×	`distribute-rgt-out_binary64_3100`
281×	`associate-+l+_binary64_3080`
273×	`associate-*r/_binary64_3089`
213×	`associate-*l/_binary64_3090`
183×	`*-lft-identity_binary64_3136`
179×	`associate-l_binary64_3088`
165×	`distribute-lft-in_binary64_3096`
157×	`associate-r_binary64_3087`
133×	`*-rgt-identity_binary64_3137`
126×	`sqr-pow_binary64_3119`
109×	`+-commutative_binary64_3077`
105×	`associate-+r+_binary64_3079`
68×	`associate-/r/_binary64_3093`
32×	`pow-sqr_binary64_3120`
21×	`cube-prod_binary64_3175`
20×	`pow-plus_binary64_3210`
11×	`unpow3_binary64_3213`
9×	`cube-unmult_binary64_3184`
8×	`cube-mult_binary64_3177`
6×	`/-rgt-identity_binary64_3138`
4×	`unpow2_binary64_3212`
3×	`unpow1_binary64_3205`
2×	`unpow1/2_binary64_3211` `rem-sqrt-square_binary64_3160`
1×	`1-exp_binary64_3191` `sqr-abs_binary64_3162`
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_3410` `erf-erfc_binary64_3409` `erf-odd_binary64_3408` `if-if-and-not_binary64_3407` `if-if-and_binary64_3406` `if-if-or-not_binary64_3405` `if-if-or_binary64_3404` `if-not_binary64_3403` `if-same_binary64_3402` `if-false_binary64_3401` `if-true_binary64_3400` `not-gte_binary64_3399` `not-lte_binary64_3398` `not-gt_binary64_3397` `not-lt_binary64_3396` `gte-same_binary64_3395` `lte-same_binary64_3394` `gt-same_binary64_3393` `lt-same_binary64_3392` `sinh---cosh_binary64_3339` `sinh-+-cosh_binary64_3338` `sinh-cosh_binary64_3337` `tanh-def-c_binary64_3336` `tanh-def-b_binary64_3335` `tanh-def-a_binary64_3334` `cosh-def_binary64_3333` `sinh-def_binary64_3332` `tan-neg_binary64_3279` `cos-neg_binary64_3278` `sin-neg_binary64_3277` `tan-0_binary64_3276` `cos-0_binary64_3275` `sin-0_binary64_3274` `hang-m-tan_binary64_3273` `hang-p-tan_binary64_3272` `hang-m0-tan_binary64_3271` `hang-p0-tan_binary64_3270` `hang-0m-tan_binary64_3269` `hang-0p-tan_binary64_3268` `tan-+PI/2_binary64_3267` `tan-+PI_binary64_3266` `tan-PI_binary64_3265` `tan-PI/3_binary64_3264` `tan-PI/4_binary64_3263` `tan-PI/6_binary64_3262` `cos-+PI/2_binary64_3261` `cos-+PI_binary64_3260` `cos-PI_binary64_3259` `cos-PI/2_binary64_3258` `cos-PI/3_binary64_3257` `cos-PI/4_binary64_3256` `cos-PI/6_binary64_3255` `sin-+PI/2_binary64_3254` `sin-+PI_binary64_3253` `sin-PI_binary64_3252` `sin-PI/2_binary64_3251` `sin-PI/3_binary64_3250` `sin-PI/4_binary64_3249` `sin-PI/6_binary64_3248` `sub-1-sin_binary64_3247` `sub-1-cos_binary64_3246` `-1-add-sin_binary64_3245` `-1-add-cos_binary64_3244` `1-sub-sin_binary64_3243` `1-sub-cos_binary64_3242` `cos-sin-sum_binary64_3241` `log-E_binary64_3237` `log-pow_binary64_3236` `log-rec_binary64_3235` `log-div_binary64_3234` `log-prod_binary64_3233` `pow-base-0_binary64_3231` `unpow1/3_binary64_3214` `exp-to-pow_binary64_3209` `pow-base-1_binary64_3207` `unpow0_binary64_3206` `unpow-1_binary64_3204` `exp-lft-cube_binary64_3203` `exp-lft-sqr_binary64_3202` `exp-cbrt_binary64_3201` `exp-sqrt_binary64_3200` `exp-prod_binary64_3199` `div-exp_binary64_3198` `rec-exp_binary64_3197` `prod-exp_binary64_3196` `exp-diff_binary64_3195` `exp-neg_binary64_3194` `exp-sum_binary64_3193` `e-exp-1_binary64_3192` `exp-1-e_binary64_3190` `exp-0_binary64_3189` `rem-log-exp_binary64_3188` `rem-exp-log_binary64_3187` `cube-div_binary64_3176` `cube-neg_binary64_3174` `rem-3cbrt-rft_binary64_3173` `rem-3cbrt-lft_binary64_3172` `rem-cbrt-cube_binary64_3171` `rem-cube-cbrt_binary64_3170` `sqr-neg_binary64_3161` `rem-square-sqrt_binary64_3159` `times-frac_binary64_3153` `div-sub_binary64_3152` `neg-mul-1_binary64_3143` `neg-sub0_binary64_3142` `unsub-neg_binary64_3141` `sub-neg_binary64_3140` `mul-1-neg_binary64_3139` `remove-double-neg_binary64_3135` `sub0-neg_binary64_3134` `--rgt-identity_binary64_3133` `+-rgt-identity_binary64_3132` `+-lft-identity_binary64_3131` `mul0-rgt_binary64_3130` `mul0-lft_binary64_3129` `div0_binary64_3128` `*-inverses_binary64_3127` `+-inverses_binary64_3126` `lft-mult-inverse_binary64_3125` `rgt-mult-inverse_binary64_3124` `remove-double-div_binary64_3123` `difference-of-sqr--1_binary64_3118` `difference-of-sqr-1_binary64_3117` `difference-of-squares_binary64_3116` `swap-sqr_binary64_3114` `cancel-sign-sub-inv_binary64_3113` `cancel-sign-sub_binary64_3112` `distribute-neg-frac_binary64_3111` `distribute-frac-neg_binary64_3110` `distribute-neg-out_binary64_3109` `distribute-neg-in_binary64_3108` `distribute-rgt-neg-out_binary64_3107` `distribute-lft-neg-out_binary64_3106` `distribute-rgt-neg-in_binary64_3105` `distribute-lft-neg-in_binary64_3104` `distribute-rgt1-in_binary64_3103` `distribute-lft1-in_binary64_3102` `distribute-rgt-out--_binary64_3101` `distribute-lft-out--_binary64_3099` `count-2_binary64_3095` `associate--r-_binary64_3086` `associate--l-_binary64_3085` `associate--l+_binary64_3084` `associate--r+_binary64_3083` `associate-+l-_binary64_3082` `associate-+r-_binary64_3081`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	77
1	70	62
2	210	45
3	761	41
4	1373	41
5	3002	41
6	3334	41
7	3492	41
8	4100	41
9	4119	41
10	4206	41
11	4850	41
12	5050	41

prune8.0ms (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

0.1b

Counts

2 → 2

Compiler

Compiled 119 to 75 computations (37% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64)))
0.1b	(*.f64 1/5 (pow.f64 x 4))
0.2b	(.f64 2/3 (.f64 x x))
1.0b	(sqrt.f64 PI.f64)

rewrite312.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

38×	`add-sqr-sqrt_binary64_3169`
30×	`associate-r_binary64_3087`
23×	`add-cube-cbrt_binary64_3182` `*-un-lft-identity_binary64_3147`
20×	`times-frac_binary64_3153`
19×	`add-exp-log_binary64_3185`
16×	`add-cbrt-cube_binary64_3183`
13×	`sqrt-prod_binary64_3163`
12×	`pow1_binary64_3208`
9×	`associate-l_binary64_3088`
8×	`prod-exp_binary64_3196`
7×	`unswap-sqr_binary64_3115`
6×	`cbrt-unprod_binary64_3180`
4×	`add-log-exp_binary64_3186` `pow-prod-down_binary64_3218` `unpow-prod-down_binary64_3226`
3×	`*-commutative_binary64_3078`
2×	`sqr-pow_binary64_3119`
1×	`pow1/2_binary64_3227` `sqrt-pow1_binary64_3165` `rem-sqrt-square_binary64_3160` `pow-to-exp_binary64_3216` `pow-exp_binary64_3215` `div-exp_binary64_3198` `cbrt-undiv_binary64_3181` `associate-*r/_binary64_3089` `div-inv_binary64_3144`

Counts

4 → 99

Calls

4 calls:

23.0ms	(.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64)))
6.0ms	(*.f64 1/5 (pow.f64 x 4))
6.0ms	(.f64 2/3 (.f64 x x))
2.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 3378 to 2265 computations (32.9% saved)

series338.0ms (4.7%)

Error

0.1b

Counts

4 → 18

Calls

4 calls:

227.0ms	(.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64)))
46.0ms	(*.f64 1/5 (pow.f64 x 4))
39.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1020 to 814 computations (20.2% saved)

simplify121.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

753×	`times-frac_binary64_3153`
570×	`distribute-lft-in_binary64_3096`
566×	`distribute-rgt-in_binary64_3097`
215×	`associate-*r/_binary64_3089`
209×	`associate-l_binary64_3088`
195×	`associate-/l*_binary64_3092`
193×	`associate-*l/_binary64_3090`
191×	`associate-r_binary64_3087`
106×	`*-commutative_binary64_3078`
81×	`log-prod_binary64_3233`
76×	`unswap-sqr_binary64_3115`
73×	`associate-/l/_binary64_3094`
69×	`exp-prod_binary64_3199`
63×	`cube-prod_binary64_3175`
54×	`associate-/r*_binary64_3091`
51×	`associate-/r/_binary64_3093`
37×	`sqr-pow_binary64_3119`
33×	`+-commutative_binary64_3077`
32×	`distribute-rgt-out_binary64_3100`
26×	`*-rgt-identity_binary64_3137` `swap-sqr_binary64_3114`
25×	`distribute-lft-out_binary64_3098`
23×	`*-lft-identity_binary64_3136`
20×	`associate-+r+_binary64_3079`
17×	`unpow3_binary64_3213` `associate-+l+_binary64_3080`
14×	`cube-unmult_binary64_3184`
12×	`log-div_binary64_3234` `pow-plus_binary64_3210` `cube-mult_binary64_3177`
10×	`log-pow_binary64_3236` `cube-div_binary64_3176`
8×	`rem-sqrt-square_binary64_3160`
7×	`pow-sqr_binary64_3120`
6×	`/-rgt-identity_binary64_3138`
5×	`sub-neg_binary64_3140`
4×	`unpow1/2_binary64_3211`
3×	`unpow2_binary64_3212` `unpow1_binary64_3205`
2×	`log-rec_binary64_3235` `rem-square-sqrt_binary64_3159` `count-2_binary64_3095`
1×	`unpow1/3_binary64_3214` `1-exp_binary64_3191` `exp-1-e_binary64_3190` `sqr-abs_binary64_3162` `neg-mul-1_binary64_3143` `neg-sub0_binary64_3142` `associate-+l-_binary64_3082` `associate-+r-_binary64_3081`
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_3410` `erf-erfc_binary64_3409` `erf-odd_binary64_3408` `if-if-and-not_binary64_3407` `if-if-and_binary64_3406` `if-if-or-not_binary64_3405` `if-if-or_binary64_3404` `if-not_binary64_3403` `if-same_binary64_3402` `if-false_binary64_3401` `if-true_binary64_3400` `not-gte_binary64_3399` `not-lte_binary64_3398` `not-gt_binary64_3397` `not-lt_binary64_3396` `gte-same_binary64_3395` `lte-same_binary64_3394` `gt-same_binary64_3393` `lt-same_binary64_3392` `sinh---cosh_binary64_3339` `sinh-+-cosh_binary64_3338` `sinh-cosh_binary64_3337` `tanh-def-c_binary64_3336` `tanh-def-b_binary64_3335` `tanh-def-a_binary64_3334` `cosh-def_binary64_3333` `sinh-def_binary64_3332` `tan-neg_binary64_3279` `cos-neg_binary64_3278` `sin-neg_binary64_3277` `tan-0_binary64_3276` `cos-0_binary64_3275` `sin-0_binary64_3274` `hang-m-tan_binary64_3273` `hang-p-tan_binary64_3272` `hang-m0-tan_binary64_3271` `hang-p0-tan_binary64_3270` `hang-0m-tan_binary64_3269` `hang-0p-tan_binary64_3268` `tan-+PI/2_binary64_3267` `tan-+PI_binary64_3266` `tan-PI_binary64_3265` `tan-PI/3_binary64_3264` `tan-PI/4_binary64_3263` `tan-PI/6_binary64_3262` `cos-+PI/2_binary64_3261` `cos-+PI_binary64_3260` `cos-PI_binary64_3259` `cos-PI/2_binary64_3258` `cos-PI/3_binary64_3257` `cos-PI/4_binary64_3256` `cos-PI/6_binary64_3255` `sin-+PI/2_binary64_3254` `sin-+PI_binary64_3253` `sin-PI_binary64_3252` `sin-PI/2_binary64_3251` `sin-PI/3_binary64_3250` `sin-PI/4_binary64_3249` `sin-PI/6_binary64_3248` `sub-1-sin_binary64_3247` `sub-1-cos_binary64_3246` `-1-add-sin_binary64_3245` `-1-add-cos_binary64_3244` `1-sub-sin_binary64_3243` `1-sub-cos_binary64_3242` `cos-sin-sum_binary64_3241` `log-E_binary64_3237` `pow-base-0_binary64_3231` `exp-to-pow_binary64_3209` `pow-base-1_binary64_3207` `unpow0_binary64_3206` `unpow-1_binary64_3204` `exp-lft-cube_binary64_3203` `exp-lft-sqr_binary64_3202` `exp-cbrt_binary64_3201` `exp-sqrt_binary64_3200` `div-exp_binary64_3198` `rec-exp_binary64_3197` `prod-exp_binary64_3196` `exp-diff_binary64_3195` `exp-neg_binary64_3194` `exp-sum_binary64_3193` `e-exp-1_binary64_3192` `exp-0_binary64_3189` `rem-log-exp_binary64_3188` `rem-exp-log_binary64_3187` `cube-neg_binary64_3174` `rem-3cbrt-rft_binary64_3173` `rem-3cbrt-lft_binary64_3172` `rem-cbrt-cube_binary64_3171` `rem-cube-cbrt_binary64_3170` `sqr-neg_binary64_3161` `div-sub_binary64_3152` `unsub-neg_binary64_3141` `mul-1-neg_binary64_3139` `remove-double-neg_binary64_3135` `sub0-neg_binary64_3134` `--rgt-identity_binary64_3133` `+-rgt-identity_binary64_3132` `+-lft-identity_binary64_3131` `mul0-rgt_binary64_3130` `mul0-lft_binary64_3129` `div0_binary64_3128` `*-inverses_binary64_3127` `+-inverses_binary64_3126` `lft-mult-inverse_binary64_3125` `rgt-mult-inverse_binary64_3124` `remove-double-div_binary64_3123` `difference-of-sqr--1_binary64_3118` `difference-of-sqr-1_binary64_3117` `difference-of-squares_binary64_3116` `cancel-sign-sub-inv_binary64_3113` `cancel-sign-sub_binary64_3112` `distribute-neg-frac_binary64_3111` `distribute-frac-neg_binary64_3110` `distribute-neg-out_binary64_3109` `distribute-neg-in_binary64_3108` `distribute-rgt-neg-out_binary64_3107` `distribute-lft-neg-out_binary64_3106` `distribute-rgt-neg-in_binary64_3105` `distribute-lft-neg-in_binary64_3104` `distribute-rgt1-in_binary64_3103` `distribute-lft1-in_binary64_3102` `distribute-rgt-out--_binary64_3101` `distribute-lft-out--_binary64_3099` `associate--r-_binary64_3086` `associate--l-_binary64_3085` `associate--l+_binary64_3084` `associate--r+_binary64_3083`

Counts

117 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	194	3302
1	429	2953
2	1450	2813
3	4711	2794
4	5630	2794

prune103.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	54	5	59
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	55	6	61

Error

Counts

61 → 6

Compiler

Compiled 1275 to 889 computations (30.3% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 1/21 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (pow.f64 (fabs.f64 x) 7)))
0.1b	(.f64 (sqrt.f64 (/.f64 1 PI.f64)) (.f64 (fabs.f64 x) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))))
0.1b	(*.f64 1/5 (pow.f64 x 4))
0.2b	(.f64 2/3 (.f64 x x))

rewrite368.0ms (5.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

29×	`add-exp-log_binary64_3185`
25×	`associate-l_binary64_3088`
23×	`add-sqr-sqrt_binary64_3169`
21×	`add-cbrt-cube_binary64_3183`
17×	`add-cube-cbrt_binary64_3182` `*-un-lft-identity_binary64_3147`
16×	`pow1_binary64_3208` `prod-exp_binary64_3196`
13×	`sqrt-prod_binary64_3163`
10×	`cbrt-unprod_binary64_3180` `associate-r_binary64_3087`
9×	`times-frac_binary64_3153`
7×	`pow-prod-down_binary64_3218` `associate-*r/_binary64_3089`
4×	`add-log-exp_binary64_3186` `unswap-sqr_binary64_3115` `*-commutative_binary64_3078` `unpow-prod-down_binary64_3226` `sqrt-div_binary64_3164` `distribute-rgt-in_binary64_3097` `distribute-lft-in_binary64_3096`
2×	`pow-to-exp_binary64_3216` `pow-exp_binary64_3215` `sqr-pow_binary64_3119` `flip3-+_binary64_3150` `frac-times_binary64_3157` `flip-+_binary64_3121` `associate-*l/_binary64_3090`
1×	`div-inv_binary64_3144`

Counts

4 → 104

Calls

4 calls:

17.0ms	(.f64 (sqrt.f64 (/.f64 1 PI.f64)) (.f64 (fabs.f64 x) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))))
10.0ms	(.f64 1/21 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (pow.f64 (fabs.f64 x) 7)))
6.0ms	(.f64 2/3 (.f64 x x))
6.0ms	(*.f64 1/5 (pow.f64 x 4))

Compiler

Compiled 4011 to 2881 computations (28.2% saved)

series659.0ms (9.1%)

Error

Counts

4 → 18

Calls

4 calls:

355.0ms	(.f64 (sqrt.f64 (/.f64 1 PI.f64)) (.f64 (fabs.f64 x) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))))
190.0ms	(.f64 1/21 (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (pow.f64 (fabs.f64 x) 7)))
48.0ms	(*.f64 1/5 (pow.f64 x 4))
42.0ms	(.f64 2/3 (.f64 x x))

Compiler

Compiled 1394 to 1116 computations (19.9% saved)

simplify142.0ms (2%)

Algorithm

1×	egg-herbie

Rules

596×	`unswap-sqr_binary64_3115`
336×	`associate-r_binary64_3087`
317×	`associate-l_binary64_3088`
169×	`*-commutative_binary64_3078`
167×	`exp-prod_binary64_3199`
150×	`sqr-pow_binary64_3119`
148×	`log-prod_binary64_3233`
131×	`+-commutative_binary64_3077`
124×	`distribute-rgt-in_binary64_3097`
117×	`distribute-lft-in_binary64_3096`
104×	`associate-+l+_binary64_3080` `associate-+r+_binary64_3079`
103×	`cube-prod_binary64_3175`
75×	`cancel-sign-sub-inv_binary64_3113`
68×	`sub-neg_binary64_3140`
54×	`neg-mul-1_binary64_3143` `neg-sub0_binary64_3142` `distribute-rgt-neg-in_binary64_3105`
50×	`distribute-lft-neg-in_binary64_3104` `associate-*l/_binary64_3090`
48×	`swap-sqr_binary64_3114`
43×	`exp-sum_binary64_3193`
42×	`unpow3_binary64_3213`
39×	`associate-/l*_binary64_3092`
38×	`unsub-neg_binary64_3141`
30×	`*-lft-identity_binary64_3136`
27×	`*-rgt-identity_binary64_3137`
25×	`pow-sqr_binary64_3120` `associate-*r/_binary64_3089`
23×	`associate--r+_binary64_3083`
20×	`log-pow_binary64_3236` `distribute-rgt-out_binary64_3100` `associate--l+_binary64_3084`
19×	`cube-mult_binary64_3177`
17×	`cube-unmult_binary64_3184`
16×	`distribute-neg-in_binary64_3108`
12×	`pow-plus_binary64_3210`
10×	`distribute-lft-neg-out_binary64_3106`
7×	`associate-+l-_binary64_3082`
6×	`distribute-rgt-neg-out_binary64_3107`
5×	`rem-sqrt-square_binary64_3160` `distribute-lft-out_binary64_3098`
4×	`associate-+r-_binary64_3081`
3×	`unpow2_binary64_3212` `unpow1/2_binary64_3211` `unpow1_binary64_3205` `sub0-neg_binary64_3134` `+-rgt-identity_binary64_3132` `count-2_binary64_3095`
2×	`unpow1/3_binary64_3214` `exp-lft-sqr_binary64_3202` `rem-square-sqrt_binary64_3159` `distribute-rgt-out--_binary64_3101`
1×	`1-exp_binary64_3191` `exp-1-e_binary64_3190` `sqr-abs_binary64_3162` `/-rgt-identity_binary64_3138`
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_3410` `erf-erfc_binary64_3409` `erf-odd_binary64_3408` `if-if-and-not_binary64_3407` `if-if-and_binary64_3406` `if-if-or-not_binary64_3405` `if-if-or_binary64_3404` `if-not_binary64_3403` `if-same_binary64_3402` `if-false_binary64_3401` `if-true_binary64_3400` `not-gte_binary64_3399` `not-lte_binary64_3398` `not-gt_binary64_3397` `not-lt_binary64_3396` `gte-same_binary64_3395` `lte-same_binary64_3394` `gt-same_binary64_3393` `lt-same_binary64_3392` `sinh---cosh_binary64_3339` `sinh-+-cosh_binary64_3338` `sinh-cosh_binary64_3337` `tanh-def-c_binary64_3336` `tanh-def-b_binary64_3335` `tanh-def-a_binary64_3334` `cosh-def_binary64_3333` `sinh-def_binary64_3332` `tan-neg_binary64_3279` `cos-neg_binary64_3278` `sin-neg_binary64_3277` `tan-0_binary64_3276` `cos-0_binary64_3275` `sin-0_binary64_3274` `hang-m-tan_binary64_3273` `hang-p-tan_binary64_3272` `hang-m0-tan_binary64_3271` `hang-p0-tan_binary64_3270` `hang-0m-tan_binary64_3269` `hang-0p-tan_binary64_3268` `tan-+PI/2_binary64_3267` `tan-+PI_binary64_3266` `tan-PI_binary64_3265` `tan-PI/3_binary64_3264` `tan-PI/4_binary64_3263` `tan-PI/6_binary64_3262` `cos-+PI/2_binary64_3261` `cos-+PI_binary64_3260` `cos-PI_binary64_3259` `cos-PI/2_binary64_3258` `cos-PI/3_binary64_3257` `cos-PI/4_binary64_3256` `cos-PI/6_binary64_3255` `sin-+PI/2_binary64_3254` `sin-+PI_binary64_3253` `sin-PI_binary64_3252` `sin-PI/2_binary64_3251` `sin-PI/3_binary64_3250` `sin-PI/4_binary64_3249` `sin-PI/6_binary64_3248` `sub-1-sin_binary64_3247` `sub-1-cos_binary64_3246` `-1-add-sin_binary64_3245` `-1-add-cos_binary64_3244` `1-sub-sin_binary64_3243` `1-sub-cos_binary64_3242` `cos-sin-sum_binary64_3241` `log-E_binary64_3237` `log-rec_binary64_3235` `log-div_binary64_3234` `pow-base-0_binary64_3231` `exp-to-pow_binary64_3209` `pow-base-1_binary64_3207` `unpow0_binary64_3206` `unpow-1_binary64_3204` `exp-lft-cube_binary64_3203` `exp-cbrt_binary64_3201` `exp-sqrt_binary64_3200` `div-exp_binary64_3198` `rec-exp_binary64_3197` `prod-exp_binary64_3196` `exp-diff_binary64_3195` `exp-neg_binary64_3194` `e-exp-1_binary64_3192` `exp-0_binary64_3189` `rem-log-exp_binary64_3188` `rem-exp-log_binary64_3187` `cube-div_binary64_3176` `cube-neg_binary64_3174` `rem-3cbrt-rft_binary64_3173` `rem-3cbrt-lft_binary64_3172` `rem-cbrt-cube_binary64_3171` `rem-cube-cbrt_binary64_3170` `sqr-neg_binary64_3161` `times-frac_binary64_3153` `div-sub_binary64_3152` `mul-1-neg_binary64_3139` `remove-double-neg_binary64_3135` `--rgt-identity_binary64_3133` `+-lft-identity_binary64_3131` `mul0-rgt_binary64_3130` `mul0-lft_binary64_3129` `div0_binary64_3128` `-inverses_binary64_3127` `+-inverses_binary64_3126` `lft-mult-inverse_binary64_3125` `rgt-mult-inverse_binary64_3124` `remove-double-div_binary64_3123` `difference-of-sqr--1_binary64_3118` `difference-of-sqr-1_binary64_3117` `difference-of-squares_binary64_3116` `cancel-sign-sub_binary64_3112` `distribute-neg-frac_binary64_3111` `distribute-frac-neg_binary64_3110` `distribute-neg-out_binary64_3109` `distribute-rgt1-in_binary64_3103` `distribute-lft1-in_binary64_3102` `distribute-lft-out--_binary64_3099` `associate-/l/_binary64_3094` `associate-/r/_binary64_3093` `associate-/r_binary64_3091` `associate--r-_binary64_3086` `associate--l-_binary64_3085`

Counts

122 → 76

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	228	3244
1	530	2637
2	2003	2614
3	3230	2596
4	4940	2596
5	4924	2596

prune149.0ms (2.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	78	4	82

Error

Counts

82 → 4

Compiler

Compiled 2047 to 1473 computations (28% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 2/3 (.f64 x x))
0.3b	(.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 PI.f64))) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 (sqrt.f64 PI.f64))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite422.0ms (5.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

104×	`add-sqr-sqrt_binary64_3169`
84×	`sqrt-prod_binary64_3163`
78×	`times-frac_binary64_3153`
45×	`add-cube-cbrt_binary64_3182` `*-un-lft-identity_binary64_3147`
34×	`associate-l_binary64_3088`
32×	`associate-r_binary64_3087`
21×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
17×	`unswap-sqr_binary64_3115`
13×	`pow1_binary64_3208`
7×	`prod-exp_binary64_3196` `cbrt-unprod_binary64_3180`
4×	`add-log-exp_binary64_3186` `pow-prod-down_binary64_3218` `div-exp_binary64_3198` `cbrt-undiv_binary64_3181`
2×	`pow1/2_binary64_3227` `sqrt-pow1_binary64_3165` `rem-sqrt-square_binary64_3160` `div-inv_binary64_3144` `*-commutative_binary64_3078`
1×	`frac-times_binary64_3157` `associate-l/_binary64_3090` `associate-r/_binary64_3089`

Counts

4 → 143

Calls

4 calls:

41.0ms	(.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 PI.f64))) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 (sqrt.f64 PI.f64))))
6.0ms	(.f64 2/3 (.f64 x x))
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 5199 to 2930 computations (43.6% saved)

series274.0ms (3.8%)

Error

Counts

4 → 15

Calls

4 calls:

212.0ms	(.f64 (/.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 PI.f64))) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 (sqrt.f64 PI.f64))))
43.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 873 to 678 computations (22.3% saved)

simplify280.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

642×	`associate-/l*_binary64_3092`
303×	`associate-/l/_binary64_3094`
234×	`times-frac_binary64_3153`
210×	`unswap-sqr_binary64_3115`
178×	`associate-l_binary64_3088`
161×	`associate-r_binary64_3087`
160×	`associate-/r/_binary64_3093`
152×	`*-commutative_binary64_3078`
149×	`associate-*r/_binary64_3089`
143×	`associate-/r*_binary64_3091`
140×	`distribute-lft-out_binary64_3098`
137×	`associate-*l/_binary64_3090`
114×	`+-commutative_binary64_3077`
97×	`distribute-rgt-in_binary64_3097` `distribute-lft-in_binary64_3096`
95×	`associate-+l+_binary64_3080`
84×	`associate-+r+_binary64_3079`
77×	`exp-prod_binary64_3199`
76×	`sqr-pow_binary64_3119`
66×	`distribute-rgt-out_binary64_3100`
59×	`log-div_binary64_3234`
58×	`exp-sum_binary64_3193`
54×	`/-rgt-identity_binary64_3138`
51×	`log-prod_binary64_3233`
50×	`swap-sqr_binary64_3114`
37×	`*-rgt-identity_binary64_3137`
36×	`cube-div_binary64_3176`
31×	`cube-prod_binary64_3175` `*-lft-identity_binary64_3136`
30×	`sub-neg_binary64_3140`
24×	`unpow3_binary64_3213`
19×	`distribute-neg-in_binary64_3108`
14×	`pow-sqr_binary64_3120`
12×	`log-rec_binary64_3235`
11×	`pow-plus_binary64_3210`
10×	`cube-unmult_binary64_3184` `associate-+l-_binary64_3082` `associate-+r-_binary64_3081`
9×	`cube-mult_binary64_3177` `neg-mul-1_binary64_3143` `neg-sub0_binary64_3142`
7×	`associate--r+_binary64_3083`
5×	`rem-sqrt-square_binary64_3160` `unsub-neg_binary64_3141` `remove-double-div_binary64_3123`
4×	`log-pow_binary64_3236` `unpow1/2_binary64_3211` `cancel-sign-sub-inv_binary64_3113`
3×	`unpow2_binary64_3212` `rem-square-sqrt_binary64_3159` `+-rgt-identity_binary64_3132` `count-2_binary64_3095` `associate--r-_binary64_3086`
2×	`unpow1/3_binary64_3214` `remove-double-neg_binary64_3135` `associate--l+_binary64_3084`
1×	`unpow1_binary64_3205` `1-exp_binary64_3191` `exp-1-e_binary64_3190` `sqr-abs_binary64_3162` `--rgt-identity_binary64_3133` `distribute-neg-out_binary64_3109` `distribute-lft-neg-in_binary64_3104`
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_3410` `erf-erfc_binary64_3409` `erf-odd_binary64_3408` `if-if-and-not_binary64_3407` `if-if-and_binary64_3406` `if-if-or-not_binary64_3405` `if-if-or_binary64_3404` `if-not_binary64_3403` `if-same_binary64_3402` `if-false_binary64_3401` `if-true_binary64_3400` `not-gte_binary64_3399` `not-lte_binary64_3398` `not-gt_binary64_3397` `not-lt_binary64_3396` `gte-same_binary64_3395` `lte-same_binary64_3394` `gt-same_binary64_3393` `lt-same_binary64_3392` `sinh---cosh_binary64_3339` `sinh-+-cosh_binary64_3338` `sinh-cosh_binary64_3337` `tanh-def-c_binary64_3336` `tanh-def-b_binary64_3335` `tanh-def-a_binary64_3334` `cosh-def_binary64_3333` `sinh-def_binary64_3332` `tan-neg_binary64_3279` `cos-neg_binary64_3278` `sin-neg_binary64_3277` `tan-0_binary64_3276` `cos-0_binary64_3275` `sin-0_binary64_3274` `hang-m-tan_binary64_3273` `hang-p-tan_binary64_3272` `hang-m0-tan_binary64_3271` `hang-p0-tan_binary64_3270` `hang-0m-tan_binary64_3269` `hang-0p-tan_binary64_3268` `tan-+PI/2_binary64_3267` `tan-+PI_binary64_3266` `tan-PI_binary64_3265` `tan-PI/3_binary64_3264` `tan-PI/4_binary64_3263` `tan-PI/6_binary64_3262` `cos-+PI/2_binary64_3261` `cos-+PI_binary64_3260` `cos-PI_binary64_3259` `cos-PI/2_binary64_3258` `cos-PI/3_binary64_3257` `cos-PI/4_binary64_3256` `cos-PI/6_binary64_3255` `sin-+PI/2_binary64_3254` `sin-+PI_binary64_3253` `sin-PI_binary64_3252` `sin-PI/2_binary64_3251` `sin-PI/3_binary64_3250` `sin-PI/4_binary64_3249` `sin-PI/6_binary64_3248` `sub-1-sin_binary64_3247` `sub-1-cos_binary64_3246` `-1-add-sin_binary64_3245` `-1-add-cos_binary64_3244` `1-sub-sin_binary64_3243` `1-sub-cos_binary64_3242` `cos-sin-sum_binary64_3241` `log-E_binary64_3237` `pow-base-0_binary64_3231` `exp-to-pow_binary64_3209` `pow-base-1_binary64_3207` `unpow0_binary64_3206` `unpow-1_binary64_3204` `exp-lft-cube_binary64_3203` `exp-lft-sqr_binary64_3202` `exp-cbrt_binary64_3201` `exp-sqrt_binary64_3200` `div-exp_binary64_3198` `rec-exp_binary64_3197` `prod-exp_binary64_3196` `exp-diff_binary64_3195` `exp-neg_binary64_3194` `e-exp-1_binary64_3192` `exp-0_binary64_3189` `rem-log-exp_binary64_3188` `rem-exp-log_binary64_3187` `cube-neg_binary64_3174` `rem-3cbrt-rft_binary64_3173` `rem-3cbrt-lft_binary64_3172` `rem-cbrt-cube_binary64_3171` `rem-cube-cbrt_binary64_3170` `sqr-neg_binary64_3161` `div-sub_binary64_3152` `mul-1-neg_binary64_3139` `sub0-neg_binary64_3134` `+-lft-identity_binary64_3131` `mul0-rgt_binary64_3130` `mul0-lft_binary64_3129` `div0_binary64_3128` `*-inverses_binary64_3127` `+-inverses_binary64_3126` `lft-mult-inverse_binary64_3125` `rgt-mult-inverse_binary64_3124` `difference-of-sqr--1_binary64_3118` `difference-of-sqr-1_binary64_3117` `difference-of-squares_binary64_3116` `cancel-sign-sub_binary64_3112` `distribute-neg-frac_binary64_3111` `distribute-frac-neg_binary64_3110` `distribute-rgt-neg-out_binary64_3107` `distribute-lft-neg-out_binary64_3106` `distribute-rgt-neg-in_binary64_3105` `distribute-rgt1-in_binary64_3103` `distribute-lft1-in_binary64_3102` `distribute-rgt-out--_binary64_3101` `distribute-lft-out--_binary64_3099` `associate--l-_binary64_3085`

Counts

158 → 111

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	214	7437
1	564	6616
2	2002	6424
3	4189	6154
4	4875	6154
5	4999	6154
6	4950	6154

prune168.0ms (2.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	111	4	115

Error

Counts

115 → 4

Compiler

Compiled 2710 to 1600 computations (41% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/5 (pow.f64 x 4))
0.2b	(.f64 2/3 (.f64 x x))
0.3b	(/.f64 (.f64 (fabs.f64 x) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)

rewrite254.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

20×	`add-sqr-sqrt_binary64_3169`
19×	`add-exp-log_binary64_3185`
16×	`add-cbrt-cube_binary64_3183`
13×	`add-cube-cbrt_binary64_3182` `*-un-lft-identity_binary64_3147`
10×	`pow1_binary64_3208`
9×	`sqrt-prod_binary64_3163`
8×	`associate-r_binary64_3087`
7×	`prod-exp_binary64_3196`
6×	`times-frac_binary64_3153` `associate-/r_binary64_3091` `associate-l*_binary64_3088`
5×	`cbrt-unprod_binary64_3180`
4×	`add-log-exp_binary64_3186` `unswap-sqr_binary64_3115` `unpow-prod-down_binary64_3226`
3×	`pow-prod-down_binary64_3218`
2×	`div-exp_binary64_3198` `cbrt-undiv_binary64_3181` `associate-r/_binary64_3089` `associate-/l/_binary64_3094` `-commutative_binary64_3078` `sqr-pow_binary64_3119`
1×	`pow1/2_binary64_3227` `sqrt-pow1_binary64_3165` `rem-sqrt-square_binary64_3160` `frac-2neg_binary64_3158` `clear-num_binary64_3146` `div-inv_binary64_3144` `flip3-+_binary64_3150` `flip-+_binary64_3121` `associate-/l*_binary64_3092` `pow-to-exp_binary64_3216` `pow-exp_binary64_3215`

Counts

4 → 86

Calls

4 calls:

12.0ms	(/.f64 (.f64 (fabs.f64 x) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64))
6.0ms	(.f64 2/3 (.f64 x x))
6.0ms	(*.f64 1/5 (pow.f64 x 4))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 3122 to 2071 computations (33.7% saved)

series470.0ms (6.5%)

Error

Counts

4 → 15

Calls

4 calls:

351.0ms	(/.f64 (.f64 (fabs.f64 x) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64))
54.0ms	(*.f64 1/5 (pow.f64 x 4))
45.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1162 to 919 computations (20.9% saved)

simplify69.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

603×	`distribute-rgt-in_binary64_3097`
581×	`distribute-lft-in_binary64_3096`
423×	`associate-/l*_binary64_3092`
349×	`times-frac_binary64_3153`
156×	`associate-/l/_binary64_3094`
150×	`associate-l_binary64_3088`
139×	`associate-r_binary64_3087`
86×	`*-commutative_binary64_3078`
85×	`associate-/r/_binary64_3093`
65×	`cancel-sign-sub-inv_binary64_3113`
58×	`unswap-sqr_binary64_3115`
45×	`distribute-rgt-neg-in_binary64_3105`
42×	`distribute-lft-neg-in_binary64_3104`
31×	`sub-neg_binary64_3140`
30×	`log-prod_binary64_3233`
29×	`sqr-pow_binary64_3119`
28×	`associate-*l/_binary64_3090`
26×	`exp-prod_binary64_3199`
22×	`distribute-neg-in_binary64_3108` `associate-*r/_binary64_3089` `+-commutative_binary64_3077`
21×	`swap-sqr_binary64_3114`
20×	`cube-prod_binary64_3175`
17×	`neg-mul-1_binary64_3143` `neg-sub0_binary64_3142` `associate-/r*_binary64_3091`
16×	`distribute-rgt-out_binary64_3100`
15×	`log-div_binary64_3234`
10×	`cube-div_binary64_3176` `*-rgt-identity_binary64_3137` `associate-+l+_binary64_3080`
9×	`cube-unmult_binary64_3184` `distribute-lft-neg-out_binary64_3106`
8×	`unsub-neg_binary64_3141` `associate--r+_binary64_3083`
7×	`distribute-neg-frac_binary64_3111` `associate-+r+_binary64_3079`
6×	`pow-plus_binary64_3210` `rem-sqrt-square_binary64_3160` `distribute-rgt-neg-out_binary64_3107` `associate--l+_binary64_3084`
5×	`pow-sqr_binary64_3120`
3×	`log-pow_binary64_3236` `unpow2_binary64_3212` `unpow1_binary64_3205` `distribute-lft-out_binary64_3098`
2×	`rem-square-sqrt_binary64_3159` `div-sub_binary64_3152` `/-rgt-identity_binary64_3138` `distribute-rgt-out--_binary64_3101` `count-2_binary64_3095`
1×	`log-rec_binary64_3235` `unpow1/2_binary64_3211` `1-exp_binary64_3191` `sqr-abs_binary64_3162` `*-lft-identity_binary64_3136` `associate-+l-_binary64_3082` `associate-+r-_binary64_3081`
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_3410` `erf-erfc_binary64_3409` `erf-odd_binary64_3408` `if-if-and-not_binary64_3407` `if-if-and_binary64_3406` `if-if-or-not_binary64_3405` `if-if-or_binary64_3404` `if-not_binary64_3403` `if-same_binary64_3402` `if-false_binary64_3401` `if-true_binary64_3400` `not-gte_binary64_3399` `not-lte_binary64_3398` `not-gt_binary64_3397` `not-lt_binary64_3396` `gte-same_binary64_3395` `lte-same_binary64_3394` `gt-same_binary64_3393` `lt-same_binary64_3392` `sinh---cosh_binary64_3339` `sinh-+-cosh_binary64_3338` `sinh-cosh_binary64_3337` `tanh-def-c_binary64_3336` `tanh-def-b_binary64_3335` `tanh-def-a_binary64_3334` `cosh-def_binary64_3333` `sinh-def_binary64_3332` `tan-neg_binary64_3279` `cos-neg_binary64_3278` `sin-neg_binary64_3277` `tan-0_binary64_3276` `cos-0_binary64_3275` `sin-0_binary64_3274` `hang-m-tan_binary64_3273` `hang-p-tan_binary64_3272` `hang-m0-tan_binary64_3271` `hang-p0-tan_binary64_3270` `hang-0m-tan_binary64_3269` `hang-0p-tan_binary64_3268` `tan-+PI/2_binary64_3267` `tan-+PI_binary64_3266` `tan-PI_binary64_3265` `tan-PI/3_binary64_3264` `tan-PI/4_binary64_3263` `tan-PI/6_binary64_3262` `cos-+PI/2_binary64_3261` `cos-+PI_binary64_3260` `cos-PI_binary64_3259` `cos-PI/2_binary64_3258` `cos-PI/3_binary64_3257` `cos-PI/4_binary64_3256` `cos-PI/6_binary64_3255` `sin-+PI/2_binary64_3254` `sin-+PI_binary64_3253` `sin-PI_binary64_3252` `sin-PI/2_binary64_3251` `sin-PI/3_binary64_3250` `sin-PI/4_binary64_3249` `sin-PI/6_binary64_3248` `sub-1-sin_binary64_3247` `sub-1-cos_binary64_3246` `-1-add-sin_binary64_3245` `-1-add-cos_binary64_3244` `1-sub-sin_binary64_3243` `1-sub-cos_binary64_3242` `cos-sin-sum_binary64_3241` `log-E_binary64_3237` `pow-base-0_binary64_3231` `unpow1/3_binary64_3214` `unpow3_binary64_3213` `exp-to-pow_binary64_3209` `pow-base-1_binary64_3207` `unpow0_binary64_3206` `unpow-1_binary64_3204` `exp-lft-cube_binary64_3203` `exp-lft-sqr_binary64_3202` `exp-cbrt_binary64_3201` `exp-sqrt_binary64_3200` `div-exp_binary64_3198` `rec-exp_binary64_3197` `prod-exp_binary64_3196` `exp-diff_binary64_3195` `exp-neg_binary64_3194` `exp-sum_binary64_3193` `e-exp-1_binary64_3192` `exp-1-e_binary64_3190` `exp-0_binary64_3189` `rem-log-exp_binary64_3188` `rem-exp-log_binary64_3187` `cube-mult_binary64_3177` `cube-neg_binary64_3174` `rem-3cbrt-rft_binary64_3173` `rem-3cbrt-lft_binary64_3172` `rem-cbrt-cube_binary64_3171` `rem-cube-cbrt_binary64_3170` `sqr-neg_binary64_3161` `mul-1-neg_binary64_3139` `remove-double-neg_binary64_3135` `sub0-neg_binary64_3134` `--rgt-identity_binary64_3133` `+-rgt-identity_binary64_3132` `+-lft-identity_binary64_3131` `mul0-rgt_binary64_3130` `mul0-lft_binary64_3129` `div0_binary64_3128` `*-inverses_binary64_3127` `+-inverses_binary64_3126` `lft-mult-inverse_binary64_3125` `rgt-mult-inverse_binary64_3124` `remove-double-div_binary64_3123` `difference-of-sqr--1_binary64_3118` `difference-of-sqr-1_binary64_3117` `difference-of-squares_binary64_3116` `cancel-sign-sub_binary64_3112` `distribute-frac-neg_binary64_3110` `distribute-neg-out_binary64_3109` `distribute-rgt1-in_binary64_3103` `distribute-lft1-in_binary64_3102` `distribute-lft-out--_binary64_3099` `associate--r-_binary64_3086` `associate--l-_binary64_3085`

Counts

101 → 53

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	2088
1	383	1801
2	1346	1725
3	5135	1725

prune74.0ms (1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	53	4	57

Error

Counts

57 → 4

Compiler

Compiled 1110 to 750 computations (32.4% saved)

regimes1.2s (16.2%)

Accuracy

Total 0.1b remaining (93%)

Threshold costs 0.1b (93%)

Compiler

Compiled 14469 to 10871 computations (24.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64_3078`
3×	`+-commutative_binary64_3077`
1×	`1-exp_binary64_3191`
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_3407` `if-if-and_binary64_3406` `if-if-or-not_binary64_3405` `if-if-or_binary64_3404` `if-not_binary64_3403` `if-same_binary64_3402` `if-false_binary64_3401` `if-true_binary64_3400` `tan-0_binary64_3276` `cos-0_binary64_3275` `sin-0_binary64_3274` `unpow1_binary64_3205` `e-exp-1_binary64_3192` `exp-1-e_binary64_3190` `exp-0_binary64_3189` `sqr-abs_binary64_3162` `sqr-neg_binary64_3161` `neg-mul-1_binary64_3143` `neg-sub0_binary64_3142` `unsub-neg_binary64_3141` `sub-neg_binary64_3140` `mul-1-neg_binary64_3139` `/-rgt-identity_binary64_3138` `-rgt-identity_binary64_3137` `-lft-identity_binary64_3136` `remove-double-neg_binary64_3135` `sub0-neg_binary64_3134` `--rgt-identity_binary64_3133` `+-rgt-identity_binary64_3132` `+-lft-identity_binary64_3131` `cancel-sign-sub-inv_binary64_3113` `cancel-sign-sub_binary64_3112` `distribute-neg-frac_binary64_3111` `distribute-frac-neg_binary64_3110` `distribute-neg-out_binary64_3109` `distribute-neg-in_binary64_3108` `distribute-rgt-neg-out_binary64_3107` `distribute-lft-neg-out_binary64_3106` `distribute-rgt-neg-in_binary64_3105` `distribute-lft-neg-in_binary64_3104`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	54
1	37	54
2	36	54

end2.0ms (0%)

Compiler: Compiled 33 to 26 computations (21.2% saved)

sample1.3s (18.5%)

Algorithm

1×

intervals

Results

786.0ms	8000×	body	128	valid
92.0ms	8001×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 228 to 164 computations (28.1% saved)

Details

analyze270.0ms (3.7%)

sample46.0ms (0.6%)

simplify127.0ms (1.7%)

prune8.0ms (0.1%)

localize19.0ms (0.3%)

rewrite312.0ms (4.3%)

series338.0ms (4.7%)

simplify121.0ms (1.7%)

prune103.0ms (1.4%)

localize25.0ms (0.3%)

rewrite368.0ms (5.1%)

series659.0ms (9.1%)

simplify142.0ms (2%)

prune149.0ms (2.1%)

localize21.0ms (0.3%)

rewrite422.0ms (5.8%)

series274.0ms (3.8%)

simplify280.0ms (3.8%)

prune168.0ms (2.3%)

localize22.0ms (0.3%)

rewrite254.0ms (3.5%)

series470.0ms (6.5%)

simplify69.0ms (0.9%)

prune74.0ms (1%)

regimes1.2s (16.2%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end2.0ms (0%)

sample1.3s (18.5%)

Profiling