Details

analyze232.0ms (5.6%)

Algorithm

1×	search
2×	egg-herbie

Rules

511×	`unsub-neg_binary64`
501×	`sub-neg_binary64`
352×	`associate--l+_binary64`
328×	`associate-+l+_binary64`
312×	`neg-mul-1_binary64`
308×	`neg-sub0_binary64`
296×	`associate-+r+_binary64`
251×	`associate-l_binary64`
245×	`distribute-rgt-neg-in_binary64`
243×	`distribute-rgt-in_binary64`
232×	`distribute-rgt-out_binary64`
217×	`associate-r_binary64`
205×	`distribute-neg-in_binary64`
185×	`distribute-lft-in_binary64`
179×	`*-commutative_binary64`
144×	`associate-+l-_binary64`
131×	`+-commutative_binary64`
101×	`distribute-lft-neg-out_binary64`
92×	`associate-+r-_binary64`
88×	`distribute-rgt-neg-out_binary64`
84×	`unswap-sqr_binary64`
81×	`cancel-sign-sub-inv_binary64`
58×	`associate--r+_binary64`
40×	`*-rgt-identity_binary64`
36×	`cancel-sign-sub_binary64`
28×	`distribute-lft-out_binary64`
27×	`*-lft-identity_binary64`
23×	`remove-double-neg_binary64`
22×	`associate--r-_binary64`
20×	`sub0-neg_binary64` `sqr-pow_binary64` `distribute-lft-neg-in_binary64`
16×	`+-rgt-identity_binary64`
10×	`pow-plus_binary64`
8×	`mul0-rgt_binary64` `mul0-lft_binary64` `difference-of-sqr--1_binary64`
6×	`cube-unmult_binary64` `difference-of-squares_binary64` `swap-sqr_binary64` `distribute-lft1-in_binary64`
5×	`unpow2_binary64` `rem-sqrt-square_binary64` `difference-of-sqr-1_binary64`
3×	`unpow3_binary64` `mul-1-neg_binary64`
2×	`cube-prod_binary64` `--rgt-identity_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64`
1×	`unpow1/2_binary64` `unpow1_binary64` `1-exp_binary64` `pow-sqr_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` `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-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` `times-frac_binary64` `div-sub_binary64` `/-rgt-identity_binary64` `+-lft-identity_binary64` `div0_binary64` `-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `count-2_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64` `associate-l/_binary64` `associate-*r/_binary64` `associate--l-_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	86
1	90	86
2	258	86
3	660	86
4	1912	86
5	3405	86
6	4573	86
7	4994	86
8	5000	86
9	4923	86
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 30 to 20 computations (33.3% saved)

sample25.0ms (0.6%)

Algorithm

1×

intervals

Results

15.0ms

256×

body

128

valid

Compiler

Compiled 59 to 41 computations (30.5% saved)

simplify82.0ms (2%)

Algorithm

1×	egg-herbie

Rules

705×	`unsub-neg_binary64`
556×	`cancel-sign-sub-inv_binary64`
344×	`+-commutative_binary64`
342×	`distribute-rgt-in_binary64`
317×	`sub-neg_binary64`
271×	`associate-l_binary64`
266×	`distribute-rgt-neg-in_binary64`
248×	`distribute-lft-in_binary64`
233×	`neg-sub0_binary64`
226×	`neg-mul-1_binary64`
213×	`associate-r_binary64`
206×	`distribute-lft-neg-in_binary64`
185×	`associate--l+_binary64`
173×	`associate-+l+_binary64`
162×	`unswap-sqr_binary64`
155×	`distribute-rgt-out_binary64`
153×	`distribute-neg-in_binary64`
151×	`associate-+r+_binary64`
102×	`*-commutative_binary64`
76×	`distribute-lft-out_binary64`
73×	`associate-+l-_binary64`
64×	`distribute-lft-neg-out_binary64`
48×	`associate-+r-_binary64`
45×	`difference-of-sqr--1_binary64`
44×	`remove-double-neg_binary64`
43×	`distribute-rgt-neg-out_binary64`
41×	`*-rgt-identity_binary64`
38×	`associate--r+_binary64`
31×	`sqr-pow_binary64`
29×	`*-lft-identity_binary64`
16×	`cube-prod_binary64`
13×	`pow-plus_binary64`
11×	`sub0-neg_binary64` `associate--r-_binary64`
9×	`mul-1-neg_binary64` `+-rgt-identity_binary64` `distribute-rgt-out--_binary64`
7×	`mul0-rgt_binary64` `mul0-lft_binary64` `distribute-lft1-in_binary64`
6×	`unpow3_binary64` `cube-unmult_binary64` `swap-sqr_binary64` `distribute-rgt1-in_binary64`
5×	`unpow2_binary64` `sqr-neg_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`
4×	`difference-of-squares_binary64`
3×	`unpow1_binary64` `cube-neg_binary64` `rem-sqrt-square_binary64` `pow-sqr_binary64`
2×	`cube-mult_binary64`
1×	`unpow1/2_binary64` `1-exp_binary64` `--rgt-identity_binary64` `cancel-sign-sub_binary64` `distribute-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` `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` `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-div_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `rem-square-sqrt_binary64` `times-frac_binary64` `div-sub_binary64` `/-rgt-identity_binary64` `+-lft-identity_binary64` `div0_binary64` `-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `count-2_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64` `associate-l/_binary64` `associate-*r/_binary64` `associate--l-_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	43
1	55	43
2	150	43
3	389	43
4	1083	43
5	2231	43
6	4328	43
7	4714	43
8	4915	43

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

2 → 1

Compiler

Compiled 58 to 38 computations (34.5% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
0.0b	(.f64 (.f64 a a) (-.f64 1 a))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.7b	(.f64 (.f64 b b) (+.f64 3 a))

rewrite191.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

15×	`pow1_binary64` `add-exp-log_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
14×	`add-cbrt-cube_binary64`
10×	`add-cube-cbrt_binary64` `associate-r_binary64`
6×	`pow-prod-down_binary64` `prod-exp_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `cancel-sign-sub-inv_binary64`
4×	`associate-*r/_binary64`
3×	`unpow-prod-down_binary64` `pow-unpow_binary64`
2×	`unswap-sqr_binary64` `flip3-+_binary64` `flip-+_binary64` `associate-l_binary64` `*-commutative_binary64` `sub-neg_binary64` `difference-of-squares_binary64` `associate-+r+_binary64`
1×	`distribute-lft-out_binary64` `pow-pow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `unpow2_binary64` `sqr-pow_binary64` `flip3--_binary64` `flip--_binary64` `distribute-lft-out--_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

4 → 87

Calls

4 calls:

11.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
9.0ms	(.f64 (.f64 a a) (-.f64 1 a))
8.0ms	(.f64 (.f64 b b) (+.f64 3 a))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

Compiler

Compiled 3139 to 1575 computations (49.8% saved)

series224.0ms (5.4%)

Error

Counts

4 → 54

Calls

4 calls:

88.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
51.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
24.0ms	(.f64 (.f64 b b) (+.f64 3 a))
14.0ms	(.f64 (.f64 a a) (-.f64 1 a))

Compiler

Compiled 2893 to 2229 computations (23% saved)

simplify145.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

534×	`associate-+l+_binary64`
345×	`associate-+r+_binary64`
267×	`associate-l_binary64`
224×	`exp-prod_binary64`
217×	`associate-r_binary64` `+-commutative_binary64`
212×	`cancel-sign-sub-inv_binary64`
148×	`associate--l+_binary64`
139×	`neg-mul-1_binary64`
138×	`neg-sub0_binary64`
136×	`*-commutative_binary64`
117×	`distribute-rgt-out_binary64`
107×	`distribute-rgt-in_binary64`
106×	`exp-sum_binary64`
101×	`distribute-lft-in_binary64`
99×	`log-prod_binary64`
97×	`unswap-sqr_binary64`
69×	`distribute-rgt-neg-in_binary64`
67×	`distribute-lft-out_binary64`
66×	`sqr-pow_binary64`
59×	`cube-prod_binary64`
58×	`distribute-lft-neg-in_binary64`
51×	`associate--r+_binary64`
45×	`distribute-lft-neg-out_binary64`
43×	`sub-neg_binary64` `distribute-rgt-neg-out_binary64`
39×	`distribute-neg-in_binary64`
29×	`log-pow_binary64`
28×	`associate-+r-_binary64`
27×	`*-lft-identity_binary64`
26×	`associate-+l-_binary64`
22×	`exp-diff_binary64` `*-rgt-identity_binary64`
20×	`swap-sqr_binary64` `distribute-rgt-out--_binary64`
18×	`cube-unmult_binary64`
17×	`pow-plus_binary64`
16×	`unsub-neg_binary64`
15×	`unpow3_binary64` `rem-sqrt-square_binary64`
13×	`exp-neg_binary64`
12×	`pow-sqr_binary64`
10×	`cube-mult_binary64`
8×	`unpow1/2_binary64`
7×	`unpow2_binary64` `div-sub_binary64` `distribute-lft-out--_binary64`
6×	`unpow1_binary64`
4×	`difference-of-squares_binary64`
3×	`associate-/l/_binary64` `associate-*r/_binary64`
2×	`exp-lft-cube_binary64` `rem-square-sqrt_binary64` `count-2_binary64`
1×	`prod-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `mul-1-neg_binary64` `distribute-rgt1-in_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` `log-rec_binary64` `log-div_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-div_binary64` `cube-neg_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `times-frac_binary64` `/-rgt-identity_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` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-lft1-in_binary64` `associate-/r_binary64` `associate-*l/_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

141 → 116

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	215	2929
1	585	2618
2	1868	2522
3	4253	2518
4	4980	2518
5	4962	2518

prune109.0ms (2.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	114	3	117

Error

Counts

117 → 3

Compiler

Compiled 2343 to 1235 computations (47.3% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 a (+.f64 4 (.f64 2 a)))
0.0b	(-.f64 (*.f64 a a) (pow.f64 a 3))
0.0b	(.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3)))
0.9b	(.f64 (.f64 b b) (+.f64 12 (.f64 a (+.f64 4 (.f64 2 a)))))

rewrite245.0ms (5.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

36×	`cancel-sign-sub-inv_binary64`
29×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
15×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64` `associate-r_binary64`
13×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`unpow-prod-down_binary64` `cube-prod_binary64`
8×	`difference-of-squares_binary64`
7×	`associate-l_binary64`
6×	`add-log-exp_binary64` `associate-*r/_binary64`
5×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unpow3_binary64` `cube-mult_binary64` `sqr-pow_binary64`
3×	`unswap-sqr_binary64` `*-commutative_binary64` `sub-neg_binary64`
2×	`flip3-+_binary64` `flip-+_binary64` `flip3--_binary64` `flip--_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64`
1×	`diff-log_binary64`

Counts

4 → 126

Calls

4 calls:

11.0ms	(.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3)))
8.0ms	(.f64 (.f64 b b) (+.f64 12 (.f64 a (+.f64 4 (.f64 2 a)))))
7.0ms	(-.f64 (*.f64 a a) (pow.f64 a 3))
5.0ms	(.f64 a (+.f64 4 (.f64 2 a)))

Compiler

Compiled 4500 to 3046 computations (32.3% saved)

series133.0ms (3.2%)

Error

Counts

4 → 28

Calls

4 calls:

44.0ms	(.f64 (.f64 b b) (+.f64 12 (.f64 a (+.f64 4 (.f64 2 a)))))
19.0ms	(.f64 4 (-.f64 (.f64 a a) (pow.f64 a 3)))
16.0ms	(-.f64 (*.f64 a a) (pow.f64 a 3))
16.0ms	(.f64 a (+.f64 4 (.f64 2 a)))

Compiler

Compiled 1880 to 1502 computations (20.1% saved)

simplify227.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

651×	`unswap-sqr_binary64`
375×	`associate-l_binary64`
347×	`associate-r_binary64`
275×	`cancel-sign-sub-inv_binary64`
254×	`exp-prod_binary64`
159×	`*-commutative_binary64`
143×	`log-prod_binary64`
134×	`distribute-lft-in_binary64`
133×	`distribute-rgt-in_binary64`
102×	`difference-of-squares_binary64`
91×	`cube-prod_binary64`
69×	`sqr-pow_binary64`
43×	`swap-sqr_binary64`
40×	`sub-neg_binary64`
38×	`neg-sub0_binary64`
36×	`neg-mul-1_binary64`
35×	`distribute-rgt-neg-in_binary64` `+-commutative_binary64`
31×	`distribute-lft-neg-in_binary64`
29×	`exp-sum_binary64`
20×	`*-lft-identity_binary64` `distribute-neg-in_binary64`
19×	`*-rgt-identity_binary64`
17×	`distribute-rgt-out_binary64`
16×	`distribute-lft-neg-out_binary64`
15×	`pow-sqr_binary64`
14×	`unsub-neg_binary64`
13×	`unpow3_binary64`
12×	`pow-plus_binary64`
10×	`log-pow_binary64` `cube-unmult_binary64`
9×	`distribute-rgt-neg-out_binary64`
8×	`cube-mult_binary64` `rem-sqrt-square_binary64` `associate-+r+_binary64`
7×	`associate-+l+_binary64`
6×	`distribute-rgt-out--_binary64`
5×	`exp-diff_binary64` `distribute-rgt1-in_binary64` `associate-+r-_binary64`
3×	`exp-lft-sqr_binary64`
2×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `exp-neg_binary64` `rem-square-sqrt_binary64` `div-sub_binary64` `+-rgt-identity_binary64` `distribute-lft-out_binary64`
1×	`div-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `distribute-lft-out--_binary64` `count-2_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` `log-div_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `rec-exp_binary64` `prod-exp_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-div_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `times-frac_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `remove-double-neg_binary64` `sub0-neg_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` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-lft1-in_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64` `associate-l/_binary64` `associate-*r/_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+l-_binary64`

Counts

154 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	220	2390
1	536	2156
2	2292	2153
3	4870	2153
4	4992	2153

prune218.0ms (5.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	124	3	127

Error

Counts

127 → 3

Compiler

Compiled 2230 to 1532 computations (31.3% saved)

localize27.0ms (0.6%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 (pow.f64 a 3) (+.f64 a -4)) (.f64 (.f64 a a) (+.f64 (.f64 2 (*.f64 b b)) 4)))
0.1b	(*.f64 (pow.f64 a 3) (+.f64 a -4))
0.5b	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) 4))

rewrite298.0ms (7.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

16×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64` `associate-l_binary64`
12×	`associate-*r/_binary64`
10×	`add-cbrt-cube_binary64` `*-un-lft-identity_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64`
7×	`flip3-+_binary64` `flip-+_binary64` `associate-r_binary64`
6×	`prod-exp_binary64`
5×	`add-log-exp_binary64` `unswap-sqr_binary64`
4×	`cbrt-unprod_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `frac-add_binary64`
3×	`pow-prod-down_binary64`
2×	`*-commutative_binary64` `sqr-pow_binary64` `associate-+l+_binary64` `associate-+r+_binary64`
1×	`pow-to-exp_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64` `distribute-lft-out_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

3 → 78

Calls

3 calls:

20.0ms	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) 4))
18.0ms	(+.f64 (.f64 (pow.f64 a 3) (+.f64 a -4)) (.f64 (.f64 a a) (+.f64 (.f64 2 (*.f64 b b)) 4)))
15.0ms	(*.f64 (pow.f64 a 3) (+.f64 a -4))

Compiler

Compiled 2356 to 1506 computations (36.1% saved)

series166.0ms (4%)

Error

Counts

3 → 30

Calls

3 calls:

66.0ms	(+.f64 (.f64 (pow.f64 a 3) (+.f64 a -4)) (.f64 (.f64 a a) (+.f64 (.f64 2 (*.f64 b b)) 4)))
65.0ms	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) 4))
15.0ms	(*.f64 (pow.f64 a 3) (+.f64 a -4))

Compiler

Compiled 1197 to 1039 computations (13.2% saved)

simplify113.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

483×	`exp-prod_binary64`
428×	`associate-l_binary64`
385×	`cancel-sign-sub-inv_binary64`
370×	`unswap-sqr_binary64`
332×	`associate-r_binary64`
202×	`distribute-rgt-neg-in_binary64`
188×	`distribute-rgt-in_binary64`
182×	`log-prod_binary64`
174×	`distribute-lft-neg-in_binary64` `distribute-lft-in_binary64`
164×	`distribute-rgt-out_binary64`
151×	`*-commutative_binary64`
79×	`distribute-rgt-out--_binary64`
72×	`cube-prod_binary64`
59×	`sqr-pow_binary64`
52×	`sub-neg_binary64`
46×	`unpow3_binary64`
44×	`+-commutative_binary64`
42×	`swap-sqr_binary64` `distribute-neg-in_binary64`
31×	`distribute-lft-neg-out_binary64`
30×	`neg-mul-1_binary64` `neg-sub0_binary64`
25×	`*-lft-identity_binary64`
24×	`*-rgt-identity_binary64`
21×	`distribute-rgt-neg-out_binary64`
19×	`pow-plus_binary64` `associate-+l+_binary64`
18×	`exp-sum_binary64`
15×	`log-pow_binary64`
12×	`associate-+r+_binary64`
10×	`associate--l+_binary64`
9×	`cube-mult_binary64` `pow-sqr_binary64`
7×	`unsub-neg_binary64`
6×	`associate-+l-_binary64`
5×	`exp-lft-sqr_binary64` `cube-unmult_binary64`
4×	`unpow1/2_binary64` `exp-diff_binary64` `rem-sqrt-square_binary64` `associate-+r-_binary64`
3×	`difference-of-squares_binary64` `distribute-lft-out_binary64` `associate--r+_binary64`
2×	`unpow2_binary64` `unpow1_binary64`
1×	`prod-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `rem-square-sqrt_binary64` `remove-double-neg_binary64` `distribute-neg-out_binary64` `count-2_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` `log-rec_binary64` `log-div_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-div_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `times-frac_binary64` `div-sub_binary64` `mul-1-neg_binary64` `/-rgt-identity_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` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-lft-out--_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64` `associate-l/_binary64` `associate-*r/_binary64`

Counts

108 → 76

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	174	2357
1	521	2222
2	2529	2135
3	4686	2117
4	5229	2117

prune71.0ms (1.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	76	3	79

Error

Counts

79 → 3

Compiler

Compiled 1289 to 832 computations (35.5% saved)

regimes735.0ms (17.7%)

Accuracy

Total 0.0b remaining (50.4%)

Threshold costs 0.0b (50.4%)

Compiler

Compiled 14173 to 10560 computations (25.5% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
5×	`*-commutative_binary64`
3×	`sub-neg_binary64`
1×	`1-exp_binary64` `neg-mul-1_binary64` `neg-sub0_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-inv_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	49
1	40	49
2	44	49
3	46	49
4	47	49
5	45	49

end1.0ms (0%)

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

sample876.0ms (21%)

Algorithm

1×

intervals

Results

501.0ms	8000×	body	128	valid
1.0ms	9×	body	128	invalid

Compiler

Compiled 149 to 119 computations (20.1% saved)

Details

analyze232.0ms (5.6%)

sample25.0ms (0.6%)

simplify82.0ms (2%)

prune3.0ms (0.1%)

localize15.0ms (0.4%)

rewrite191.0ms (4.6%)

series224.0ms (5.4%)

simplify145.0ms (3.5%)

prune109.0ms (2.6%)

localize22.0ms (0.5%)

rewrite245.0ms (5.9%)

series133.0ms (3.2%)

simplify227.0ms (5.5%)

prune218.0ms (5.2%)

localize27.0ms (0.6%)

rewrite298.0ms (7.2%)

series166.0ms (4%)

simplify113.0ms (2.7%)

prune71.0ms (1.7%)

regimes735.0ms (17.7%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample876.0ms (21%)

Profiling