Details

analyze25.0ms (0.9%)

Algorithm

1×	search
2×	egg-herbie

Rules

1× 1-exp_binary64 sub-neg_binary64 +-commutative_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 unpow2_binary64 unpow1/2_binary64 pow-plus_binary64 exp-to-pow_binary64 pow-base-1_binary64 unpow0_binary64 unpow1_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 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 neg-mul-1_binary64 neg-sub0_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 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 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_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 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 distribute-rgt-in_binary64 distribute-lft-in_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 associate-*r*_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64 *-commutative_binary64

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	10	6
2	11	6
3	9	6
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	74.6%	25.4%	0
0%	74.6%	25.4%	1
37.3%	37.3%	25.4%	2
37.3%	18.7%	44%	3
46.7%	9.3%	44%	4
46.7%	4.7%	48.7%	5
49%	2.3%	48.7%	6
49%	1.2%	49.8%	7
49.6%	0.6%	49.8%	8
49.9%	0.3%	49.8%	9
49.9%	0.1%	50%	10
49.9%	0.1%	50.1%	11
49.9%	0%	50.1%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample36.0ms (1.3%)

Algorithm

1×

intervals

Results

16.0ms	132×	body	1024	valid
4.0ms	58×	body	512	valid
3.0ms	256×	pre	128	true
2.0ms	41×	body	256	valid
1.0ms	12×	body	2048	valid
0.0ms	13×	body	128	valid

Compiler

Compiled 11 to 11 computations (0% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1× 1-exp_binary64 sub-neg_binary64 +-commutative_binary64

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	10	6
2	11	6
3	9	6

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

58.4b

Counts

1 → 1

Compiler

Compiled 4 to 4 computations (0% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

5.1b	(-.f64 (exp.f64 x) 1)

rewrite30.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

58.3b

Rules

6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
3×	`add-log-exp_binary64` `cancel-sign-sub-inv_binary64`
2×	`add-cube-cbrt_binary64` `difference-of-squares_binary64`
1×	`diff-log_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`

Counts

1 → 18

Calls

1 calls:

5.0ms

(-.f64 (exp.f64 x) 1)

Compiler

Compiled 168 to 110 computations (34.5% saved)

series14.0ms (0.5%)

Error

0.1b

Counts

1 → 6

Calls

1 calls:

7.0ms

(-.f64 (exp.f64 x) 1)

Compiler

Compiled 100 to 84 computations (16% saved)

simplify105.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

737×	`unsub-neg_binary64`
502×	`distribute-lft-out_binary64`
411×	`sub-neg_binary64`
337×	`distribute-rgt-out_binary64`
294×	`*-commutative_binary64`
188×	`unswap-sqr_binary64`
187×	`associate-l_binary64`
179×	`associate--l+_binary64`
178×	`neg-sub0_binary64` `distribute-rgt-in_binary64`
168×	`neg-mul-1_binary64`
163×	`associate--r+_binary64`
149×	`distribute-lft-in_binary64`
147×	`+-commutative_binary64`
139×	`associate-r_binary64` `associate-+l+_binary64`
137×	`associate-+l-_binary64`
112×	`associate-+r+_binary64`
109×	`cancel-sign-sub-inv_binary64`
104×	`exp-prod_binary64`
93×	`associate-+r-_binary64`
92×	`sqr-pow_binary64`
82×	`cube-prod_binary64`
76×	`distribute-neg-out_binary64`
64×	`unpow3_binary64`
60×	`div-sub_binary64` `pow-sqr_binary64`
58×	`distribute-neg-in_binary64`
48×	`distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64`
47×	`associate--r-_binary64`
39×	`associate-/l*_binary64`
36×	`exp-sum_binary64`
35×	`distribute-rgt1-in_binary64`
32×	`pow-plus_binary64` `cube-mult_binary64`
31×	`remove-double-neg_binary64`
26×	`fabs-mul_binary64` `*-rgt-identity_binary64`
25×	`cube-div_binary64`
24×	`distribute-rgt-neg-in_binary64`
22×	`sub0-neg_binary64`
20×	`difference-of-squares_binary64` `distribute-lft1-in_binary64` `associate-/l/_binary64` `associate--l-_binary64`
19×	`distribute-lft-neg-in_binary64` `associate-/r*_binary64`
18×	`exp-diff_binary64`
17×	`+-rgt-identity_binary64` `distribute-rgt-out--_binary64`
16×	`associate-/r/_binary64`
15×	`cube-unmult_binary64` `rem-sqrt-square_binary64`
14×	`log-prod_binary64` `*-lft-identity_binary64`
13×	`times-frac_binary64` `associate-*r/_binary64`
12×	`mul-1-neg_binary64`
11×	`fabs-sqr_binary64` `--rgt-identity_binary64`
10×	`difference-of-sqr--1_binary64`
9×	`difference-of-sqr-1_binary64`
8×	`cube-neg_binary64`
6×	`cancel-sign-sub_binary64` `count-2_binary64`
5×	`sqr-neg_binary64`
4×	`unpow2_binary64` `unpow1/2_binary64` `exp-lft-sqr_binary64` `exp-sqrt_binary64` `prod-exp_binary64` `fabs-div_binary64`
3×	`unpow1_binary64` `swap-sqr_binary64` `distribute-lft-out--_binary64`
2×	`exp-neg_binary64` `fabs-sub_binary64` `mul0-rgt_binary64` `associate-*l/_binary64`
1×	`exp-lft-cube_binary64` `div-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-3cbrt-lft_binary64` `/-rgt-identity_binary64` `mul0-lft_binary64` `distribute-frac-neg_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` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-cbrt_binary64` `rec-exp_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `fabs-neg_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `rem-square-sqrt_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`

Counts

24 → 14

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	254
1	107	241
2	222	235
3	423	232
4	985	232
5	2215	232
6	3810	232
7	4450	232
8	4970	232
9	4855	232

prune11.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	11	3	14
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	11	4	15

Error

0.1b

Counts

15 → 4

Compiler

Compiled 130 to 88 computations (32.3% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 x (.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 x 1/24))))))
0.0b	(+.f64 1/6 (*.f64 x 1/24))
0.3b	(*.f64 x 1/24)
0.3b	(.f64 x (+.f64 1/6 (.f64 x 1/24)))

rewrite93.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

13×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64` `-un-lft-identity_binary64` `associate-l*_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64` `associate-*r/_binary64`
5×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64`
3×	`flip3-+_binary64` `flip-+_binary64` `*-commutative_binary64`
2×	`unswap-sqr_binary64`
1×	`sum-log_binary64` `+-commutative_binary64`

Counts

4 → 75

Calls

4 calls:

6.0ms	(.f64 x (.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 x 1/24))))))
6.0ms	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
4.0ms	(*.f64 x 1/24)
3.0ms	(+.f64 1/6 (*.f64 x 1/24))

Compiler

Compiled 1569 to 1091 computations (30.5% saved)

series53.0ms (2%)

Error

0.1b

Counts

4 → 20

Calls

4 calls:

13.0ms	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
11.0ms	(.f64 x (.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 x 1/24))))))
9.0ms	(+.f64 1/6 (*.f64 x 1/24))
6.0ms	(*.f64 x 1/24)

Compiler

Compiled 595 to 446 computations (25% saved)

simplify105.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

367×	`*-commutative_binary64` `+-commutative_binary64`
340×	`sqr-pow_binary64`
255×	`sub-neg_binary64`
230×	`unswap-sqr_binary64`
216×	`associate-l_binary64`
204×	`associate-+l+_binary64`
195×	`distribute-rgt-neg-in_binary64`
188×	`associate-r_binary64`
185×	`associate-+r+_binary64`
171×	`distribute-lft-neg-in_binary64`
149×	`cancel-sign-sub-inv_binary64`
139×	`exp-prod_binary64`
127×	`pow-sqr_binary64`
108×	`distribute-rgt-in_binary64`
105×	`neg-mul-1_binary64`
101×	`distribute-lft-in_binary64`
99×	`neg-sub0_binary64`
84×	`associate--r+_binary64`
78×	`distribute-rgt-out_binary64`
72×	`associate-+l-_binary64`
70×	`exp-sum_binary64`
65×	`distribute-neg-in_binary64`
55×	`associate-/l*_binary64`
42×	`sub0-neg_binary64`
40×	`log-prod_binary64` `cube-prod_binary64` `unsub-neg_binary64`
39×	`rem-sqrt-square_binary64`
38×	`associate-+r-_binary64`
35×	`swap-sqr_binary64`
26×	`associate-/l/_binary64`
23×	`+-rgt-identity_binary64` `associate-*r/_binary64`
22×	`times-frac_binary64`
21×	`*-rgt-identity_binary64`
20×	`*-lft-identity_binary64`
18×	`associate-/r/_binary64`
17×	`distribute-lft-neg-out_binary64` `distribute-lft-out_binary64`
16×	`unpow1/2_binary64` `associate--l+_binary64`
14×	`--rgt-identity_binary64` `associate-/r*_binary64`
12×	`distribute-rgt-out--_binary64`
11×	`unpow3_binary64` `distribute-rgt-neg-out_binary64`
10×	`fabs-mul_binary64`
8×	`pow-plus_binary64` `cube-unmult_binary64` `div-sub_binary64`
7×	`remove-double-neg_binary64`
6×	`cube-mult_binary64` `count-2_binary64`
5×	`log-pow_binary64` `log-div_binary64` `exp-diff_binary64` `cube-div_binary64`
4×	`prod-exp_binary64`
3×	`fabs-sqr_binary64` `distribute-rgt1-in_binary64`
2×	`unpow2_binary64` `distribute-lft1-in_binary64` `associate--r-_binary64` `associate--l-_binary64`
1×	`unpow1_binary64` `exp-sqrt_binary64` `1-exp_binary64` `exp-1-e_binary64` `+-lft-identity_binary64` `distribute-lft-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` `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` `exp-neg_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` `fabs-div_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `/-rgt-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-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64`

Counts

95 → 57

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	140	1332
1	343	1164
2	1248	1158
3	1880	1156
4	3149	1156
5	4232	1156
6	4880	1156

prune39.0ms (1.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	57	4	61

Error

0.1b

Counts

61 → 4

Compiler

Compiled 731 to 502 computations (31.3% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1/6 (*.f64 x 1/24))
0.3b	(*.f64 x 1/24)
0.3b	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
2.3b	(log.f64 (pow.f64 (exp.f64 x) (.f64 x (+.f64 (.f64 x (+.f64 1/6 (*.f64 x 1/24))) 1/2))))

rewrite120.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

14×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
9×	`log-prod_binary64` `add-exp-log_binary64`
8×	`pow1_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64` `associate-r_binary64`
3×	`unpow-prod-down_binary64` `rem-log-exp_binary64`
2×	`distribute-rgt-in_binary64` `unpow-prod-up_binary64` `distribute-lft-in_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `flip3-+_binary64` `associate-r/_binary64` `flip-+_binary64` `-commutative_binary64`
1×	`log-pow_binary64` `sqr-pow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

4 → 71

Calls

4 calls:

8.0ms	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
4.0ms	(*.f64 x 1/24)
3.0ms	(+.f64 1/6 (*.f64 x 1/24))
3.0ms	(log.f64 (pow.f64 (exp.f64 x) (.f64 x (+.f64 (.f64 x (+.f64 1/6 (*.f64 x 1/24))) 1/2))))

Compiler

Compiled 1692 to 1157 computations (31.6% saved)

series92.0ms (3.4%)

Error

0.1b

Counts

4 → 20

Calls

4 calls:

48.0ms	(log.f64 (pow.f64 (exp.f64 x) (.f64 x (+.f64 (.f64 x (+.f64 1/6 (*.f64 x 1/24))) 1/2))))
14.0ms	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
10.0ms	(+.f64 1/6 (*.f64 x 1/24))
7.0ms	(*.f64 x 1/24)

Compiler

Compiled 715 to 546 computations (23.6% saved)

simplify143.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

378×	`distribute-rgt-in_binary64`
362×	`distribute-lft-in_binary64`
344×	`associate-+l+_binary64`
322×	`associate-+r+_binary64`
229×	`*-commutative_binary64`
224×	`log-pow_binary64`
208×	`log-prod_binary64`
164×	`exp-prod_binary64`
153×	`associate-*l/_binary64`
132×	`associate-/l*_binary64`
129×	`associate-l_binary64`
111×	`sqr-pow_binary64`
99×	`associate-r_binary64`
97×	`+-commutative_binary64`
89×	`distribute-rgt-out_binary64`
86×	`exp-sum_binary64` `associate-/l/_binary64`
84×	`associate-*r/_binary64`
71×	`unswap-sqr_binary64`
70×	`log-div_binary64`
61×	`associate-/r/_binary64`
49×	`distribute-rgt-neg-in_binary64`
48×	`exp-to-pow_binary64`
39×	`swap-sqr_binary64`
38×	`associate-/r*_binary64`
36×	`distribute-lft-neg-in_binary64`
34×	`-rgt-identity_binary64` `-lft-identity_binary64` `cancel-sign-sub-inv_binary64`
33×	`pow-sqr_binary64`
31×	`cube-prod_binary64`
28×	`times-frac_binary64`
27×	`count-2_binary64`
25×	`sub-neg_binary64`
19×	`exp-sqrt_binary64`
17×	`distribute-lft-out_binary64`
11×	`unpow3_binary64` `neg-mul-1_binary64` `neg-sub0_binary64`
9×	`unpow1/2_binary64` `associate-+l-_binary64`
8×	`log-rec_binary64` `distribute-rgt-out--_binary64`
6×	`rem-sqrt-square_binary64`
5×	`pow-plus_binary64` `pow-base-1_binary64` `exp-lft-sqr_binary64` `cube-unmult_binary64` `cube-mult_binary64` `fabs-mul_binary64` `distribute-lft-neg-out_binary64` `associate-+r-_binary64`
4×	`distribute-rgt1-in_binary64`
3×	`/-rgt-identity_binary64` `sub0-neg_binary64` `associate--r+_binary64`
2×	`rem-log-exp_binary64` `fabs-sqr_binary64` `unsub-neg_binary64` `+-rgt-identity_binary64`
1×	`log-E_binary64` `unpow2_binary64` `unpow1_binary64` `prod-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-exp-log_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-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` `pow-base-0_binary64` `unpow1/3_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `div-exp_binary64` `rec-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `cube-div_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `fabs-div_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-square-sqrt_binary64` `div-sub_binary64` `mul-1-neg_binary64` `remove-double-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` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-lft1-in_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

91 → 56

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	145	1365
1	300	1247
2	892	1207
3	2247	1189
4	4472	1189
5	4981	1189
6	4997	1189
7	4916	1189

prune40.0ms (1.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	56	4	60

Error

0.1b

Counts

60 → 4

Compiler

Compiled 772 to 516 computations (33.2% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (exp.f64 x))
0.0b	(sqrt.f64 (exp.f64 x))
0.0b	(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
5.1b	(+.f64 -1 (sqrt.f64 (exp.f64 x)))

rewrite67.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

17×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
8×	`pow1_binary64` `sqrt-pow1_binary64`
7×	`flip3-+_binary64` `flip-+_binary64` `sqrt-prod_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `exp-prod_binary64`
5×	`associate-l_binary64`
4×	`distribute-lft-out_binary64` `frac-times_binary64` `associate-r_binary64`
2×	`associate-l/_binary64` `associate-r/_binary64` `pow1/2_binary64` `rem-sqrt-square_binary64`
1×	`sum-log_binary64` `+-commutative_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `*-commutative_binary64`

Counts

4 → 75

Calls

4 calls:

12.0ms	(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
4.0ms	(+.f64 -1 (sqrt.f64 (exp.f64 x)))
2.0ms	(sqrt.f64 (exp.f64 x))
2.0ms	(sqrt.f64 (exp.f64 x))

Compiler

Compiled 1351 to 674 computations (50.1% saved)

series54.0ms (2%)

Error

0.1b

Counts

4 → 24

Calls

4 calls:

12.0ms	(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (+.f64 -1 (sqrt.f64 (exp.f64 x))))
9.0ms	(+.f64 -1 (sqrt.f64 (exp.f64 x)))
8.0ms	(sqrt.f64 (exp.f64 x))
8.0ms	(sqrt.f64 (exp.f64 x))

Compiler

Compiled 697 to 538 computations (22.8% saved)

simplify105.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

619×	`unsub-neg_binary64`
618×	`distribute-rgt-in_binary64`
600×	`neg-mul-1_binary64`
569×	`distribute-lft-in_binary64`
405×	`distribute-rgt-neg-out_binary64`
262×	`distribute-neg-out_binary64`
190×	`associate-+l+_binary64`
188×	`*-commutative_binary64`
165×	`distribute-neg-in_binary64`
150×	`associate-+r+_binary64`
128×	`times-frac_binary64`
110×	`sub-neg_binary64`
102×	`cancel-sign-sub-inv_binary64`
98×	`exp-sum_binary64` `neg-sub0_binary64`
89×	`exp-prod_binary64`
87×	`associate-l_binary64`
75×	`associate-r_binary64`
72×	`exp-diff_binary64`
58×	`distribute-lft-neg-out_binary64`
50×	`sqr-pow_binary64` `+-commutative_binary64`
46×	`associate-+l-_binary64`
44×	`*-rgt-identity_binary64`
43×	`cube-prod_binary64`
41×	`div-sub_binary64`
40×	`*-lft-identity_binary64`
39×	`log-prod_binary64`
38×	`unswap-sqr_binary64`
37×	`associate-+r-_binary64`
36×	`distribute-rgt-out_binary64`
23×	`mul-1-neg_binary64`
22×	`sqr-neg_binary64`
21×	`exp-neg_binary64` `distribute-lft-out_binary64`
14×	`cube-neg_binary64` `swap-sqr_binary64`
11×	`sub0-neg_binary64`
10×	`rem-sqrt-square_binary64`
9×	`unpow3_binary64` `pow-plus_binary64` `cube-unmult_binary64` `remove-double-neg_binary64`
8×	`pow-sqr_binary64` `associate--r+_binary64`
6×	`unpow1/2_binary64` `+-rgt-identity_binary64` `distribute-rgt-out--_binary64` `associate--r-_binary64`
5×	`cube-mult_binary64` `fabs-mul_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt1-in_binary64`
4×	`prod-exp_binary64` `--rgt-identity_binary64` `associate--l-_binary64`
2×	`unpow2_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `sqr-abs_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `distribute-frac-neg_binary64` `distribute-lft1-in_binary64`
1×	`unpow1_binary64` `unpow-1_binary64` `1-exp_binary64` `exp-1-e_binary64` `fabs-sqr_binary64` `rem-square-sqrt_binary64` `+-inverses_binary64` `distribute-lft-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-pow_binary64` `log-rec_binary64` `log-div_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `exp-lft-cube_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` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `fabs-div_binary64` `fabs-fabs_binary64` `/-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `count-2_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/r_binary64` `associate-l/_binary64` `associate-r/_binary64` `associate--l+_binary64`

Counts

99 → 57

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	1454
1	315	1363
2	926	1336
3	2763	1128
4	4380	1128
5	5355	1128

prune31.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	0	0	0
Picked	1	0	1
Done	1	2	3
Total	57	4	61

Error

0.1b

Counts

61 → 4

Compiler

Compiled 823 to 461 computations (44% saved)

regimes181.0ms (6.8%)

Accuracy

Total 0.3b remaining (94.7%)

Threshold costs 0.3b (94.7%)

Compiler

Compiled 2333 to 1787 computations (23.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`+-commutative_binary64`
1×	`1-exp_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` `fabs-div_binary64` `fabs-mul_binary64` `fabs-sqr_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `unsub-neg_binary64` `sub-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	41
1	35	41
2	34	41

end1.0ms (0%)

Compiler: Compiled 27 to 23 computations (14.8% saved)

sample1.3s (48%)

Algorithm

1×

intervals

Results

526.0ms	4131×	body	1024	valid
125.0ms	1902×	body	512	valid
89.0ms	8001×	pre	128	true
56.0ms	421×	body	2048	valid
38.0ms	971×	body	256	valid
16.0ms	575×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 117 to 92 computations (21.4% saved)

Details

analyze25.0ms (0.9%)

sample36.0ms (1.3%)

simplify8.0ms (0.3%)

prune1.0ms (0%)

localize3.0ms (0.1%)

rewrite30.0ms (1.1%)

series14.0ms (0.5%)

simplify105.0ms (3.9%)

prune11.0ms (0.4%)

localize11.0ms (0.4%)

rewrite93.0ms (3.5%)

series53.0ms (2%)

simplify105.0ms (3.9%)

prune39.0ms (1.5%)

localize12.0ms (0.4%)

rewrite120.0ms (4.5%)

series92.0ms (3.4%)

simplify143.0ms (5.4%)

prune40.0ms (1.5%)

localize7.0ms (0.2%)

rewrite67.0ms (2.5%)

series54.0ms (2%)

simplify105.0ms (3.9%)

prune31.0ms (1.2%)

regimes181.0ms (6.8%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.3s (48%)

Profiling