Details

analyze1.9s (11%)

Algorithm

1×	search
2×	egg-herbie

Rules

752×	`associate-*r/_binary64`
481×	`*-commutative_binary64`
271×	`cancel-sign-sub-inv_binary64`
230×	`associate-/l*_binary64`
224×	`neg-mul-1_binary64` `neg-sub0_binary64`
216×	`unswap-sqr_binary64`
205×	`distribute-rgt-neg-in_binary64`
185×	`distribute-lft-neg-in_binary64`
140×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64`
129×	`associate-l_binary64`
118×	`associate-/r/_binary64`
100×	`swap-sqr_binary64`
94×	`distribute-neg-frac_binary64`
87×	`sub-neg_binary64`
85×	`sqr-pow_binary64`
77×	`associate-r_binary64`
72×	`times-frac_binary64`
71×	`associate-/r*_binary64`
48×	`associate-*l/_binary64`
40×	`unsub-neg_binary64` `distribute-lft-neg-out_binary64`
29×	`-rgt-identity_binary64` `-lft-identity_binary64`
21×	`unpow1/2_binary64`
20×	`div-sub_binary64` `distribute-rgt-neg-out_binary64`
18×	`associate-/l/_binary64`
10×	`unpow2_binary64` `sub0-neg_binary64` `associate-+l-_binary64` `+-commutative_binary64`
9×	`unpow1_binary64` `rem-sqrt-square_binary64`
1×	`1-exp_binary64` `swap-M-D`
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` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow3_binary64` `pow-plus_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `exp-prod_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-unmult_binary64` `cube-mult_binary64` `cube-div_binary64` `cube-prod_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `remove-double-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `pow-sqr_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-rgt-out_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64` `count-2_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+r-_binary64` `associate-+l+_binary64` `associate-+r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	122	451
1	393	451
2	1448	451
3	4121	451
4	5362	451
0	5	5
1	5	5

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	81.1%	18.9%	7
0%	68.6%	31.4%	8
0%	59.2%	40.8%	9
0%	59.2%	40.8%	10
0%	59.2%	40.8%	11
0.4%	49.5%	50.1%	12
0.8%	44.4%	54.8%	13
1.4%	39.9%	58.7%	14

Symmetry

(sort M D)

Compiler

Compiled 36 to 32 computations (11.1% saved)

sample161.0ms (0.9%)

Algorithm

1×

intervals

Results

46.0ms	327×	body	128	nan
36.0ms	256×	body	128	valid
21.0ms	153×	body	128	invalid

Compiler

Compiled 71 to 68 computations (4.2% saved)

simplify39.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

679×	`distribute-neg-frac_binary64`
437×	`*-commutative_binary64`
425×	`associate-/l*_binary64`
347×	`cancel-sign-sub-inv_binary64`
263×	`associate-/l/_binary64`
212×	`associate-/r/_binary64`
203×	`associate-/r*_binary64`
201×	`neg-sub0_binary64`
200×	`neg-mul-1_binary64`
198×	`distribute-rgt-neg-in_binary64`
195×	`distribute-lft-neg-in_binary64`
188×	`times-frac_binary64`
160×	`associate-l_binary64`
141×	`associate-r_binary64`
136×	`unswap-sqr_binary64`
118×	`unsub-neg_binary64`
107×	`associate-*l/_binary64`
76×	`associate-*r/_binary64`
67×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64`
30×	`distribute-lft-neg-out_binary64`
29×	`sub-neg_binary64`
27×	`distribute-rgt-neg-out_binary64`
24×	`div-sub_binary64`
20×	`swap-sqr_binary64`
19×	`sqr-pow_binary64`
14×	`distribute-rgt-out_binary64` `distribute-lft-out_binary64`
12×	`mul0-rgt_binary64` `mul0-lft_binary64`
9×	`-rgt-identity_binary64` `-lft-identity_binary64`
6×	`cube-unmult_binary64`
4×	`pow-plus_binary64`
3×	`unpow1/2_binary64` `+-commutative_binary64`
2×	`div0_binary64`
1×	`unpow2_binary64` `unpow1_binary64` `1-exp_binary64` `rem-sqrt-square_binary64` `sub0-neg_binary64` `associate-+l-_binary64` `associate-+l+_binary64`
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` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `exp-prod_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-mult_binary64` `cube-div_binary64` `cube-prod_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `remove-double-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `pow-sqr_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `count-2_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+r-_binary64` `associate-+r+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	41
1	62	41
2	188	41
3	1060	41
4	3490	41
5	5205	41

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

27.8b

Counts

2 → 1

Compiler

Compiled 54 to 46 computations (14.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.3b	(/.f64 (.f64 M D) (.f64 d 2))
9.7b	(sqrt.f64 (/.f64 d h))
9.7b	(sqrt.f64 (/.f64 d l))
15.6b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite288.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

14.1b

Rules

84×	`add-exp-log_binary64`
42×	`prod-exp_binary64`
31×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
28×	`add-cbrt-cube_binary64`
26×	`sqrt-prod_binary64`
25×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
20×	`div-exp_binary64`
13×	`associate-r_binary64`
10×	`pow-exp_binary64` `cbrt-unprod_binary64`
8×	`pow1_binary64`
6×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `div-inv_binary64` `rem-sqrt-square_binary64`
2×	`pow-to-exp_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `associate-l_binary64` `-commutative_binary64` `frac-2neg_binary64` `clear-num_binary64` `associate-/l_binary64` `associate-/r_binary64`

Counts

4 → 115

Calls

4 calls:

10.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
6.0ms	(sqrt.f64 (/.f64 d h))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
3.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 3820 to 1753 computations (54.1% saved)

series217.0ms (1.2%)

Error

25.3b

Counts

4 → 36

Calls

4 calls:

134.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
39.0ms	(/.f64 (.f64 M D) (.f64 d 2))
21.0ms	(sqrt.f64 (/.f64 d h))
19.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 2196 to 1866 computations (15% saved)

simplify116.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

830×	`associate-/r*_binary64`
451×	`associate-/l/_binary64`
299×	`associate-/r/_binary64`
268×	`log-div_binary64`
224×	`associate-l_binary64`
203×	`times-frac_binary64`
162×	`associate-/l*_binary64`
158×	`associate-r_binary64`
106×	`associate-*r/_binary64`
103×	`*-commutative_binary64`
95×	`associate-*l/_binary64`
76×	`log-prod_binary64`
71×	`swap-sqr_binary64`
51×	`exp-prod_binary64`
47×	`cube-prod_binary64` `unswap-sqr_binary64`
37×	`sqr-pow_binary64`
30×	`cube-div_binary64`
29×	`sub-neg_binary64`
23×	`*-rgt-identity_binary64`
21×	`+-commutative_binary64`
17×	`*-lft-identity_binary64` `associate-+l+_binary64`
14×	`distribute-rgt-in_binary64`
12×	`neg-sub0_binary64` `distribute-lft-in_binary64`
11×	`cube-unmult_binary64` `distribute-rgt-neg-in_binary64`
10×	`log-pow_binary64` `rem-sqrt-square_binary64`
9×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64`
8×	`/-rgt-identity_binary64` `associate-+r-_binary64`
7×	`cancel-sign-sub-inv_binary64`
5×	`unpow1/2_binary64` `pow-plus_binary64` `exp-sqrt_binary64`
4×	`unpow2_binary64` `unpow1_binary64` `mul-1-neg_binary64` `distribute-neg-frac_binary64` `associate--l+_binary64` `associate--r+_binary64`
3×	`unsub-neg_binary64` `pow-sqr_binary64` `associate-+r+_binary64`
2×	`rem-square-sqrt_binary64` `div-sub_binary64` `distribute-neg-in_binary64`
1×	`1-exp_binary64` `exp-1-e_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `associate-+l-_binary64`
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` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-rec_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-mult_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-rgt-out_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64` `count-2_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

151 → 92

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	260	2654
1	530	2419
2	2125	2413
3	4756	2413
4	5039	2413

prune116.0ms (0.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	74	18	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	18	93

Error

14.9b

Counts

93 → 18

Compiler

Compiled 2053 to 1136 computations (44.7% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.6b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
5.3b	(/.f64 (.f64 M D) (.f64 d 2))
9.7b	(sqrt.f64 (/.f64 d l))
15.6b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite363.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

11.9b

Rules

93×	`add-exp-log_binary64`
48×	`prod-exp_binary64`
37×	`add-cbrt-cube_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`div-exp_binary64` `times-frac_binary64`
19×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
16×	`pow1_binary64` `cbrt-unprod_binary64` `associate-r_binary64`
13×	`sqrt-div_binary64` `sqrt-prod_binary64`
12×	`associate-*r/_binary64`
10×	`pow-exp_binary64`
9×	`frac-times_binary64`
7×	`pow-prod-down_binary64`
6×	`cbrt-undiv_binary64` `associate-*l/_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
3×	`div-inv_binary64`
2×	`pow-to-exp_binary64` `associate-l_binary64` `*-commutative_binary64` `rem-sqrt-square_binary64` `sub-neg_binary64` `distribute-rgt-in_binary64` `cancel-sign-sub-inv_binary64` `distribute-lft-in_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `frac-2neg_binary64` `clear-num_binary64` `associate-/l_binary64` `associate-/r_binary64`

Counts

4 → 126

Calls

4 calls:

19.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
11.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
5.0ms	(/.f64 (.f64 M D) (.f64 d 2))
5.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 5947 to 2215 computations (62.8% saved)

series616.0ms (3.5%)

Error

13.9b

Counts

4 → 51

Calls

4 calls:

390.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (sqrt.f64 (/.f64 d l))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))
138.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
42.0ms	(/.f64 (.f64 M D) (.f64 d 2))
22.0ms	(sqrt.f64 (/.f64 d l))

Compiler

Compiled 4504 to 3652 computations (18.9% saved)

simplify250.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

655×	`associate-l_binary64`
521×	`associate-r_binary64`
298×	`*-commutative_binary64`
213×	`log-prod_binary64`
210×	`times-frac_binary64`
176×	`associate-/l*_binary64`
141×	`associate-*r/_binary64`
122×	`log-div_binary64`
117×	`associate-*l/_binary64`
101×	`associate-/r*_binary64`
96×	`cube-prod_binary64`
95×	`exp-prod_binary64` `sqr-pow_binary64`
59×	`distribute-rgt-in_binary64`
58×	`distribute-lft-in_binary64`
51×	`sub-neg_binary64`
49×	`neg-sub0_binary64`
42×	`*-lft-identity_binary64`
41×	`neg-mul-1_binary64`
40×	`+-commutative_binary64`
39×	`*-rgt-identity_binary64`
36×	`cube-div_binary64`
28×	`distribute-rgt-neg-in_binary64`
27×	`associate-+l+_binary64`
24×	`cancel-sign-sub-inv_binary64`
23×	`swap-sqr_binary64` `distribute-lft-neg-in_binary64`
21×	`associate-/r/_binary64`
20×	`associate-/l/_binary64`
16×	`log-pow_binary64`
13×	`cube-unmult_binary64`
10×	`associate-+r+_binary64`
9×	`mul-1-neg_binary64` `/-rgt-identity_binary64`
8×	`exp-sum_binary64` `associate-+r-_binary64`
7×	`rem-sqrt-square_binary64` `div-sub_binary64`
6×	`unpow3_binary64` `pow-plus_binary64` `unsub-neg_binary64` `pow-sqr_binary64` `unswap-sqr_binary64` `distribute-neg-frac_binary64` `distribute-lft-neg-out_binary64`
5×	`unpow1/2_binary64` `exp-sqrt_binary64`
4×	`unpow1/3_binary64` `unpow2_binary64` `unpow1_binary64` `exp-diff_binary64` `cube-mult_binary64` `associate--l+_binary64` `associate--r+_binary64`
3×	`distribute-rgt-neg-out_binary64` `distribute-rgt-out_binary64`
2×	`rem-square-sqrt_binary64` `distribute-neg-in_binary64` `distribute-rgt1-in_binary64` `distribute-lft-out_binary64` `associate-+l-_binary64`
1×	`log-rec_binary64` `exp-neg_binary64` `1-exp_binary64` `exp-1-e_binary64` `sqr-abs_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `associate--r-_binary64` `associate--l-_binary64`
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` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `pow-base-0_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-neg_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `count-2_binary64`

Counts

177 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	392	6191
1	982	5748
2	4141	5747
3	4849	5747
4	4997	5747
5	4947	5747

prune163.0ms (0.9%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	124	12	136
Fresh	4	13	17
Picked	1	0	1
Done	0	0	0
Total	129	25	154

Error

12.4b

Counts

154 → 25

Compiler

Compiled 4038 to 1919 computations (52.5% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 h)
4.6b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
5.3b	(/.f64 (.f64 M D) (.f64 d 2))
15.6b	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))

rewrite283.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

9.2b

Rules

102×	`add-exp-log_binary64`
55×	`prod-exp_binary64`
46×	`add-cbrt-cube_binary64`
24×	`pow1_binary64`
23×	`cbrt-unprod_binary64`
20×	`div-exp_binary64`
18×	`associate-*r/_binary64`
16×	`associate-r_binary64`
14×	`pow-prod-down_binary64`
13×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
12×	`sqrt-div_binary64`
10×	`pow-exp_binary64` `times-frac_binary64`
9×	`frac-times_binary64`
6×	`cbrt-undiv_binary64` `associate-*l/_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
3×	`cbrt-prod_binary64`
2×	`pow-to-exp_binary64` `associate-l_binary64` `div-inv_binary64` `*-commutative_binary64` `sub-neg_binary64` `distribute-rgt-in_binary64` `cancel-sign-sub-inv_binary64` `distribute-lft-in_binary64`
1×	`frac-2neg_binary64` `clear-num_binary64` `associate-/l_binary64` `associate-/r_binary64` `pow1/3_binary64`

Counts

4 → 118

Calls

4 calls:

26.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
12.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
5.0ms	(/.f64 (.f64 M D) (.f64 d 2))
1.0ms	(cbrt.f64 h)

Compiler

Compiled 6839 to 2143 computations (68.7% saved)

series780.0ms (4.4%)

Error

11.4b

Counts

4 → 51

Calls

4 calls:

539.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))))
142.0ms	(.f64 (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 d 2)) 2)) (/.f64 h l))
42.0ms	(/.f64 (.f64 M D) (.f64 d 2))
20.0ms	(cbrt.f64 h)

Compiler

Compiled 5721 to 4254 computations (25.6% saved)

simplify227.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

431×	`*-commutative_binary64`
211×	`times-frac_binary64`
184×	`associate-/l*_binary64`
163×	`log-prod_binary64`
160×	`distribute-rgt-neg-in_binary64`
147×	`associate-*r/_binary64`
138×	`log-div_binary64`
117×	`unswap-sqr_binary64`
116×	`associate-/r_binary64` `associate-l/_binary64`
115×	`sqr-pow_binary64`
113×	`distribute-neg-frac_binary64`
98×	`cancel-sign-sub-inv_binary64`
88×	`associate-r_binary64`
87×	`associate-l_binary64`
83×	`exp-prod_binary64` `swap-sqr_binary64`
70×	`sub-neg_binary64`
67×	`distribute-rgt-in_binary64`
66×	`distribute-lft-in_binary64`
65×	`cube-prod_binary64`
56×	`neg-sub0_binary64`
54×	`neg-mul-1_binary64`
47×	`distribute-lft-neg-out_binary64` `+-commutative_binary64`
42×	`distribute-rgt-neg-out_binary64`
41×	`cube-div_binary64`
37×	`associate-+l+_binary64`
29×	`distribute-lft-neg-in_binary64`
28×	`*-rgt-identity_binary64`
25×	`div-sub_binary64`
22×	`*-lft-identity_binary64`
20×	`cube-unmult_binary64`
19×	`exp-diff_binary64` `associate-/r/_binary64`
18×	`exp-sum_binary64`
16×	`log-pow_binary64` `unsub-neg_binary64` `associate-+r+_binary64`
15×	`associate-/l/_binary64` `associate-+r-_binary64`
12×	`pow-sqr_binary64`
10×	`distribute-neg-out_binary64`
9×	`unpow1/3_binary64`
8×	`rem-sqrt-square_binary64`
7×	`associate-+l-_binary64`
6×	`exp-neg_binary64` `/-rgt-identity_binary64` `distribute-frac-neg_binary64`
5×	`unpow3_binary64` `unpow1/2_binary64` `exp-sqrt_binary64`
4×	`log-rec_binary64` `unpow2_binary64` `pow-plus_binary64` `exp-to-pow_binary64` `unpow1_binary64` `distribute-neg-in_binary64` `associate--l+_binary64` `associate--r+_binary64`
3×	`cube-mult_binary64` `distribute-rgt-out_binary64`
2×	`sqr-abs_binary64` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `distribute-rgt1-in_binary64` `distribute-lft-out_binary64` `associate--l-_binary64`
1×	`1-exp_binary64` `exp-1-e_binary64` `rem-3cbrt-lft_binary64`
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` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `pow-base-0_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-neg_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `count-2_binary64` `associate--r-_binary64`

Counts

169 → 141

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	426	7854
1	1122	7098
2	3172	7097
3	4858	7097
4	4966	7097

prune139.0ms (0.8%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	134	7	141
Fresh	2	22	24
Picked	1	0	1
Done	0	0	0
Total	137	29	166

Error

10.9b

Counts

166 → 29

Compiler

Compiled 4843 to 2086 computations (56.9% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.6b	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)))
5.3b	(/.f64 (.f64 M D) (.f64 2 d))
7.2b	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
9.2b	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)

rewrite278.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

9.4b

Rules

104×	`add-exp-log_binary64`
55×	`prod-exp_binary64`
48×	`add-cbrt-cube_binary64`
24×	`pow1_binary64`
23×	`cbrt-unprod_binary64`
21×	`div-exp_binary64`
17×	`associate-*r/_binary64`
15×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
14×	`pow-prod-down_binary64` `cancel-sign-sub-inv_binary64`
12×	`add-cube-cbrt_binary64` `sqrt-div_binary64`
10×	`pow-exp_binary64` `times-frac_binary64`
9×	`frac-times_binary64`
8×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64`
7×	`cbrt-undiv_binary64` `associate-r_binary64`
6×	`associate-*l/_binary64`
4×	`add-log-exp_binary64` `div-inv_binary64` `associate-/r_binary64` `associate-l*_binary64` `flip3--_binary64` `flip--_binary64`
2×	`pow-to-exp_binary64` `frac-2neg_binary64` `clear-num_binary64` `associate-/l_binary64` `-commutative_binary64` `sub-neg_binary64` `difference-of-squares_binary64`
1×	`distribute-lft-out--_binary64`

Counts

4 → 130

Calls

4 calls:

33.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)))
9.0ms	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)
7.0ms	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
5.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 7829 to 2531 computations (67.7% saved)

series804.0ms (4.6%)

Error

10.9b

Counts

4 → 60

Calls

4 calls:

493.0ms	(.f64 (.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 h)))) (.f64 (fabs.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))) (sqrt.f64 (/.f64 (cbrt.f64 d) (cbrt.f64 l))))) (-.f64 1 (/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)))
141.0ms	(/.f64 (.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2))) l)
98.0ms	(.f64 h (.f64 1/2 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))
44.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 6513 to 4790 computations (26.5% saved)

simplify282.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

451×	`*-commutative_binary64`
227×	`times-frac_binary64`
213×	`associate-/l*_binary64`
160×	`log-prod_binary64`
148×	`log-div_binary64`
147×	`associate-*r/_binary64`
138×	`associate-*l/_binary64`
135×	`distribute-neg-frac_binary64`
128×	`associate-/r*_binary64`
104×	`sqr-pow_binary64`
102×	`associate-r_binary64`
94×	`unpow3_binary64`
88×	`distribute-rgt-neg-out_binary64`
87×	`sub-neg_binary64` `swap-sqr_binary64`
83×	`associate-l_binary64`
82×	`neg-mul-1_binary64` `neg-sub0_binary64` `cancel-sign-sub-inv_binary64`
71×	`distribute-rgt-in_binary64`
70×	`distribute-lft-in_binary64`
67×	`exp-prod_binary64`
66×	`cube-prod_binary64`
55×	`cube-div_binary64` `unswap-sqr_binary64`
48×	`+-commutative_binary64`
45×	`associate-/r/_binary64`
36×	`div-sub_binary64`
33×	`*-rgt-identity_binary64`
31×	`distribute-lft-neg-out_binary64`
30×	`distribute-rgt-neg-in_binary64`
25×	`associate-+l+_binary64`
23×	`*-lft-identity_binary64`
22×	`unsub-neg_binary64` `distribute-lft-neg-in_binary64` `associate-/l/_binary64`
20×	`associate-+r+_binary64`
18×	`exp-sum_binary64`
17×	`exp-diff_binary64` `cube-unmult_binary64`
15×	`associate--l+_binary64`
14×	`distribute-frac-neg_binary64`
12×	`log-pow_binary64`
10×	`distribute-neg-out_binary64`
9×	`pow-sqr_binary64`
7×	`unpow1/3_binary64` `associate-+r-_binary64`
6×	`exp-neg_binary64` `associate-+l-_binary64`
5×	`log-rec_binary64` `rem-sqrt-square_binary64`
4×	`unpow2_binary64` `unpow1/2_binary64` `pow-plus_binary64` `exp-to-pow_binary64` `unpow1_binary64` `cube-mult_binary64` `/-rgt-identity_binary64` `associate--r+_binary64`
3×	`exp-sqrt_binary64` `rem-square-sqrt_binary64` `div0_binary64`
2×	`sqr-abs_binary64` `distribute-neg-in_binary64` `distribute-rgt1-in_binary64` `associate--l-_binary64`
1×	`1-exp_binary64` `exp-1-e_binary64` `rem-3cbrt-lft_binary64` `mul-1-neg_binary64` `distribute-rgt-out_binary64`
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` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `pow-base-0_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-neg_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64` `count-2_binary64` `associate--r-_binary64`

Counts

190 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	437	9932
1	1182	9027
2	3395	9026
3	4741	9026
4	4963	9026

prune76.0ms (0.4%)

Pruning

33 alts after pruning (32 fresh and 1 done)

	Pruned	Kept	Total
New	133	5	138
Fresh	1	27	28
Picked	0	1	1
Done	0	0	0
Total	134	33	167

Error

10.0b

Counts

167 → 33

Compiler

Compiled 2627 to 915 computations (65.2% saved)

regimes5.2s (29.4%)

Accuracy

Total 3.2b remaining (26.3%)

Threshold costs 0b (0%)

Compiler

Compiled 88933 to 64675 computations (27.3% saved)

bsearch21.0ms (0.1%)

Compiler: Compiled 35 to 31 computations (11.4% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

23×	`*-commutative_binary64`
12×	`+-commutative_binary64`
11×	`sub-neg_binary64`
7×	`neg-mul-1_binary64` `neg-sub0_binary64`
4×	`distribute-rgt-neg-in_binary64`
3×	`cancel-sign-sub-inv_binary64` `distribute-lft-neg-in_binary64`
1×	`1-exp_binary64` `distribute-neg-frac_binary64` `distribute-lft-neg-out_binary64`
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` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `unpow1_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `unsub-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	326
1	87	326
2	109	326
3	123	326
4	133	326
5	137	326
6	138	326
7	135	326

end17.0ms (0.1%)

Remove: (sort M D)
Compiler: Compiled 612 to 294 computations (52% saved)

sample5.1s (29.2%)

Algorithm

1×

intervals

Results

1.2s	8000×	body	128	valid
1.1s	8539×	body	128	nan
699.0ms	4865×	body	128	invalid

Compiler

Compiled 1763 to 1201 computations (31.9% saved)

Details

analyze1.9s (11%)

sample161.0ms (0.9%)

simplify39.0ms (0.2%)

prune4.0ms (0%)

localize19.0ms (0.1%)

rewrite288.0ms (1.6%)

series217.0ms (1.2%)

simplify116.0ms (0.7%)

prune116.0ms (0.7%)

localize26.0ms (0.1%)

rewrite363.0ms (2.1%)

series616.0ms (3.5%)

simplify250.0ms (1.4%)

prune163.0ms (0.9%)

localize34.0ms (0.2%)

rewrite283.0ms (1.6%)

series780.0ms (4.4%)

simplify227.0ms (1.3%)

prune139.0ms (0.8%)

localize31.0ms (0.2%)

rewrite278.0ms (1.6%)

series804.0ms (4.6%)

simplify282.0ms (1.6%)

prune76.0ms (0.4%)

regimes5.2s (29.4%)

bsearch21.0ms (0.1%)

simplify15.0ms (0.1%)

end17.0ms (0.1%)

sample5.1s (29.2%)

Profiling