Details

analyze92.0ms (3.9%)

Algorithm

1×	search
2×	egg-herbie

Rules

806×	`sub-neg_binary64`
743×	`div-sub_binary64`
502×	`associate-/l*_binary64`
427×	`unsub-neg_binary64`
423×	`distribute-rgt-in_binary64`
347×	`distribute-lft-in_binary64`
288×	`neg-mul-1_binary64`
276×	`*-commutative_binary64`
246×	`associate-/r*_binary64`
237×	`neg-sub0_binary64`
227×	`distribute-rgt-neg-out_binary64`
217×	`associate-/r/_binary64`
214×	`associate-l_binary64`
200×	`distribute-lft-neg-out_binary64`
188×	`associate-r_binary64`
186×	`cancel-sign-sub-inv_binary64`
159×	`distribute-rgt-neg-in_binary64`
154×	`associate--r+_binary64`
153×	`associate--r-_binary64`
116×	`distribute-lft-neg-in_binary64`
112×	`distribute-neg-in_binary64`
108×	`associate-*l/_binary64`
101×	`cancel-sign-sub_binary64` `associate-*r/_binary64`
100×	`distribute-rgt-out--_binary64`
95×	`distribute-neg-frac_binary64` `associate-/l/_binary64`
93×	`associate--l-_binary64`
76×	`distribute-frac-neg_binary64`
58×	`associate--l+_binary64`
55×	`mul0-rgt_binary64`
54×	`mul0-lft_binary64`
52×	`+-lft-identity_binary64` `associate-+l-_binary64`
48×	`+-commutative_binary64`
44×	`sub0-neg_binary64`
34×	`div0_binary64`
29×	`*-rgt-identity_binary64`
28×	`*-lft-identity_binary64`
24×	`--rgt-identity_binary64` `distribute-rgt-out_binary64` `associate-+r-_binary64`
19×	`associate-+r+_binary64`
13×	`remove-double-neg_binary64`
12×	`/-rgt-identity_binary64`
11×	`distribute-lft-out--_binary64` `associate-+l+_binary64`
9×	`distribute-neg-out_binary64`
8×	`+-rgt-identity_binary64`
5×	`mul-1-neg_binary64` `distribute-lft1-in_binary64`
2×	`distribute-rgt1-in_binary64` `distribute-lft-out_binary64`
1×	`1-exp_binary64` `sqr-neg_binary64` `difference-of-sqr-1_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` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `times-frac_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-squares_binary64` `unswap-sqr_binary64` `swap-sqr_binary64` `count-2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	37	29
2	82	29
3	187	29
4	471	29
5	845	29
6	1231	29
7	2569	29
8	2876	29
9	4256	29
10	5039	29
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

Compiler

Compiled 20 to 16 computations (20% saved)

sample19.0ms (0.8%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 39 to 32 computations (17.9% saved)

simplify82.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

806×	`sub-neg_binary64`
743×	`div-sub_binary64`
502×	`associate-/l*_binary64`
427×	`unsub-neg_binary64`
423×	`distribute-rgt-in_binary64`
347×	`distribute-lft-in_binary64`
288×	`neg-mul-1_binary64`
276×	`*-commutative_binary64`
246×	`associate-/r*_binary64`
237×	`neg-sub0_binary64`
227×	`distribute-rgt-neg-out_binary64`
217×	`associate-/r/_binary64`
214×	`associate-l_binary64`
200×	`distribute-lft-neg-out_binary64`
188×	`associate-r_binary64`
186×	`cancel-sign-sub-inv_binary64`
159×	`distribute-rgt-neg-in_binary64`
154×	`associate--r+_binary64`
153×	`associate--r-_binary64`
116×	`distribute-lft-neg-in_binary64`
112×	`distribute-neg-in_binary64`
108×	`associate-*l/_binary64`
101×	`cancel-sign-sub_binary64` `associate-*r/_binary64`
100×	`distribute-rgt-out--_binary64`
95×	`distribute-neg-frac_binary64` `associate-/l/_binary64`
93×	`associate--l-_binary64`
76×	`distribute-frac-neg_binary64`
58×	`associate--l+_binary64`
55×	`mul0-rgt_binary64`
54×	`mul0-lft_binary64`
52×	`+-lft-identity_binary64` `associate-+l-_binary64`
48×	`+-commutative_binary64`
44×	`sub0-neg_binary64`
34×	`div0_binary64`
29×	`*-rgt-identity_binary64`
28×	`*-lft-identity_binary64`
24×	`--rgt-identity_binary64` `distribute-rgt-out_binary64` `associate-+r-_binary64`
19×	`associate-+r+_binary64`
13×	`remove-double-neg_binary64`
12×	`/-rgt-identity_binary64`
11×	`distribute-lft-out--_binary64` `associate-+l+_binary64`
9×	`distribute-neg-out_binary64`
8×	`+-rgt-identity_binary64`
5×	`mul-1-neg_binary64` `distribute-lft1-in_binary64`
2×	`distribute-rgt1-in_binary64` `distribute-lft-out_binary64`
1×	`1-exp_binary64` `sqr-neg_binary64` `difference-of-sqr-1_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` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `times-frac_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-squares_binary64` `unswap-sqr_binary64` `swap-sqr_binary64` `count-2_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	37	29
2	82	29
3	187	29
4	471	29
5	845	29
6	1231	29
7	2569	29
8	2876	29
9	4256	29
10	5039	29

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

1 → 1

Compiler

Compiled 19 to 15 computations (21.1% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))
0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
0.0b	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
0.2b	(.f64 3 (.f64 v v))

rewrite226.0ms (9.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

41×	`add-sqr-sqrt_binary64`
26×	`associate-l_binary64`
23×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64` `times-frac_binary64`
20×	`sqrt-prod_binary64`
18×	`sqrt-div_binary64` `frac-times_binary64`
17×	`pow1_binary64`
15×	`flip3--_binary64` `flip--_binary64`
12×	`associate-r_binary64`
10×	`prod-exp_binary64` `cbrt-unprod_binary64` `associate-*r/_binary64`
9×	`associate-*l/_binary64`
7×	`pow-prod-down_binary64` `unswap-sqr_binary64`
4×	`add-log-exp_binary64`
3×	`*-commutative_binary64`
2×	`div-exp_binary64` `cbrt-undiv_binary64` `sub-neg_binary64` `distribute-rgt-in_binary64` `cancel-sign-sub-inv_binary64` `distribute-lft-in_binary64` `difference-of-squares_binary64`
1×	`div-inv_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 129

Calls

4 calls:

14.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
12.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
6.0ms	(.f64 3 (.f64 v v))
3.0ms	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))

Compiler

Compiled 3696 to 2603 computations (29.6% saved)

series75.0ms (3.2%)

Error

0.0b

Counts

4 → 21

Calls

4 calls:

18.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
14.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
10.0ms	(sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))
8.0ms	(.f64 3 (.f64 v v))

Compiler

Compiled 959 to 839 computations (12.5% saved)

simplify167.0ms (7.1%)

Algorithm

1×	egg-herbie

Rules

550×	`distribute-rgt-in_binary64`
499×	`distribute-lft-in_binary64`
361×	`associate-l_binary64`
340×	`associate-r_binary64`
310×	`cancel-sign-sub-inv_binary64`
241×	`distribute-rgt-neg-in_binary64`
221×	`*-commutative_binary64`
212×	`distribute-lft-neg-in_binary64`
134×	`exp-prod_binary64`
73×	`sub-neg_binary64`
71×	`associate-*l/_binary64`
68×	`distribute-rgt-out_binary64`
57×	`log-prod_binary64` `distribute-lft-neg-out_binary64`
51×	`neg-sub0_binary64` `*-lft-identity_binary64`
49×	`neg-mul-1_binary64`
48×	`+-commutative_binary64`
45×	`distribute-rgt-neg-out_binary64`
39×	`associate-*r/_binary64`
37×	`sqr-pow_binary64`
31×	`*-rgt-identity_binary64`
30×	`distribute-lft-out_binary64`
29×	`associate-/l*_binary64`
26×	`exp-sum_binary64`
25×	`swap-sqr_binary64`
24×	`cube-prod_binary64` `distribute-neg-in_binary64`
22×	`unswap-sqr_binary64` `distribute-lft-out--_binary64`
17×	`associate--r+_binary64` `associate-+l+_binary64`
16×	`unpow3_binary64` `unsub-neg_binary64`
12×	`associate-+r+_binary64`
11×	`distribute-rgt1-in_binary64`
10×	`log-div_binary64` `exp-neg_binary64`
8×	`exp-diff_binary64`
7×	`pow-plus_binary64` `cube-div_binary64` `distribute-neg-frac_binary64`
6×	`cube-unmult_binary64` `distribute-rgt-out--_binary64` `associate--l+_binary64`
5×	`cube-mult_binary64`
4×	`unpow1/2_binary64`
3×	`log-pow_binary64` `pow-sqr_binary64` `distribute-lft1-in_binary64` `associate-+l-_binary64`
2×	`unpow-1_binary64` `exp-lft-cube_binary64` `prod-exp_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `associate-+r-_binary64`
1×	`unpow2_binary64` `unpow1_binary64` `1-exp_binary64` `exp-1-e_binary64` `div-sub_binary64` `mul-1-neg_binary64` `count-2_binary64` `associate-/r/_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` `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-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` `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` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `associate-/l/_binary64` `associate-/r_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

150 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	267	3914
1	706	3618
2	2379	3598
3	4939	3598
4	4879	3598
5	4922	3598

prune91.0ms (3.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	94	3	97

Error

Counts

97 → 3

Compiler

Compiled 1987 to 1500 computations (24.5% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 1/4 (.f64 (pow.f64 v 4) 3/32)) (.f64 (*.f64 v v) 5/8))
0.0b	(.f64 (sqrt.f64 2) (-.f64 (+.f64 1/4 (.f64 (pow.f64 v 4) 3/32)) (.f64 (.f64 v v) 5/8)))
0.1b	(*.f64 (pow.f64 v 4) 3/32)
0.1b	(.f64 (.f64 v v) 5/8)

rewrite136.0ms (5.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

21×	`add-sqr-sqrt_binary64`
16×	`add-exp-log_binary64`
14×	`associate-l_binary64`
13×	`add-cbrt-cube_binary64`
11×	`pow1_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
9×	`add-log-exp_binary64` `associate-r_binary64`
7×	`prod-exp_binary64`
6×	`unswap-sqr_binary64`
5×	`cbrt-unprod_binary64`
4×	`pow-prod-down_binary64` `unpow-prod-down_binary64` `sqrt-prod_binary64`
3×	`*-commutative_binary64` `sub-neg_binary64` `distribute-rgt-in_binary64` `cancel-sign-sub-inv_binary64` `associate--l+_binary64` `distribute-lft-in_binary64`
2×	`sqr-pow_binary64` `flip3--_binary64` `associate-*r/_binary64` `flip--_binary64` `diff-log_binary64`
1×	`pow-to-exp_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 88

Calls

4 calls:

10.0ms	(.f64 (sqrt.f64 2) (-.f64 (+.f64 1/4 (.f64 (pow.f64 v 4) 3/32)) (.f64 (.f64 v v) 5/8)))
8.0ms	(*.f64 (pow.f64 v 4) 3/32)
6.0ms	(-.f64 (+.f64 1/4 (.f64 (pow.f64 v 4) 3/32)) (.f64 (*.f64 v v) 5/8))
6.0ms	(.f64 (.f64 v v) 5/8)

Compiler

Compiled 2021 to 1549 computations (23.4% saved)

series54.0ms (2.3%)

Error

Counts

4 → 16

Calls

4 calls:

16.0ms	(.f64 (sqrt.f64 2) (-.f64 (+.f64 1/4 (.f64 (pow.f64 v 4) 3/32)) (.f64 (.f64 v v) 5/8)))
10.0ms	(-.f64 (+.f64 1/4 (.f64 (pow.f64 v 4) 3/32)) (.f64 (*.f64 v v) 5/8))
9.0ms	(*.f64 (pow.f64 v 4) 3/32)
9.0ms	(.f64 (.f64 v v) 5/8)

Compiler

Compiled 510 to 474 computations (7.1% saved)

simplify117.0ms (5%)

Algorithm

1×	egg-herbie

Rules

523×	`distribute-rgt-in_binary64`
515×	`distribute-lft-in_binary64`
401×	`*-commutative_binary64`
267×	`exp-prod_binary64`
263×	`cancel-sign-sub-inv_binary64`
245×	`distribute-rgt-neg-in_binary64`
214×	`associate-l_binary64`
164×	`associate-r_binary64`
131×	`unswap-sqr_binary64`
117×	`sqr-pow_binary64`
113×	`distribute-lft-neg-out_binary64`
110×	`unsub-neg_binary64`
101×	`distribute-rgt-neg-out_binary64`
86×	`associate-+l+_binary64`
82×	`distribute-lft-neg-in_binary64`
76×	`log-prod_binary64`
70×	`neg-mul-1_binary64` `neg-sub0_binary64`
65×	`associate-+r+_binary64`
59×	`exp-sum_binary64`
56×	`sub-neg_binary64`
48×	`*-rgt-identity_binary64`
45×	`swap-sqr_binary64`
44×	`cube-prod_binary64` `*-lft-identity_binary64`
41×	`+-commutative_binary64`
26×	`times-frac_binary64`
25×	`distribute-rgt-out_binary64`
21×	`exp-diff_binary64`
19×	`pow-sqr_binary64`
17×	`associate--l+_binary64`
16×	`pow-plus_binary64`
14×	`distribute-lft-out_binary64`
13×	`log-pow_binary64` `unpow3_binary64`
12×	`unpow1/2_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `distribute-neg-in_binary64`
10×	`associate-+l-_binary64`
9×	`fabs-mul_binary64` `distribute-rgt-out--_binary64`
8×	`+-rgt-identity_binary64` `associate-+r-_binary64`
7×	`cube-mult_binary64` `sub0-neg_binary64` `difference-of-squares_binary64`
6×	`div-sub_binary64`
5×	`div-exp_binary64` `cube-unmult_binary64` `associate-/l*_binary64`
4×	`unpow2_binary64`
3×	`unpow1_binary64` `distribute-lft-out--_binary64` `associate-/r*_binary64`
2×	`rem-sqrt-square_binary64` `rem-square-sqrt_binary64`
1×	`prod-exp_binary64` `exp-neg_binary64` `1-exp_binary64` `exp-1-e_binary64` `fabs-sqr_binary64` `sqr-neg_binary64` `count-2_binary64` `associate-/r/_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-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_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-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` `mul-1-neg_binary64` `/-rgt-identity_binary64` `remove-double-neg_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` `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-rgt1-in_binary64` `distribute-lft1-in_binary64` `associate-/l/_binary64` `associate-l/_binary64` `associate-*r/_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--r+_binary64`

Counts

104 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	1977
1	348	1817
2	1241	1772
3	3369	1766
4	4881	1766
5	4870	1766

prune68.0ms (2.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	80	3	83

Error

Counts

83 → 3

Compiler

Compiled 1297 to 1004 computations (22.6% saved)

localize12.0ms (0.5%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 3/32 (pow.f64 v 4))
0.1b	(.f64 5/8 (.f64 v v))
1.0b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (+.f64 (.f64 3/32 (pow.f64 v 4)) (-.f64 1/4 (.f64 5/8 (*.f64 v v)))) (sqrt.f64 (sqrt.f64 2))))

rewrite97.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

18×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cbrt-cube_binary64` `associate-l_binary64`
13×	`pow1_binary64`
10×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
9×	`prod-exp_binary64` `sqrt-prod_binary64` `associate-r_binary64`
7×	`cbrt-unprod_binary64`
6×	`pow-prod-down_binary64`
4×	`unswap-sqr_binary64` `unpow-prod-down_binary64`
3×	`add-log-exp_binary64` `*-commutative_binary64`
2×	`associate-l/_binary64` `associate-r/_binary64` `sqr-pow_binary64`
1×	`flip3-+_binary64` `flip-+_binary64` `pow-to-exp_binary64` `pow-exp_binary64`

Counts

3 → 70

Calls

3 calls:

14.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (+.f64 (.f64 3/32 (pow.f64 v 4)) (-.f64 1/4 (.f64 5/8 (*.f64 v v)))) (sqrt.f64 (sqrt.f64 2))))
5.0ms	(.f64 5/8 (.f64 v v))
5.0ms	(*.f64 3/32 (pow.f64 v 4))

Compiler

Compiled 1842 to 1500 computations (18.6% saved)

series40.0ms (1.7%)

Error

Counts

3 → 11

Calls

3 calls:

15.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (+.f64 (.f64 3/32 (pow.f64 v 4)) (-.f64 1/4 (.f64 5/8 (*.f64 v v)))) (sqrt.f64 (sqrt.f64 2))))
10.0ms	(*.f64 3/32 (pow.f64 v 4))
9.0ms	(.f64 5/8 (.f64 v v))

Compiler

Compiled 452 to 423 computations (6.4% saved)

simplify126.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

490×	`associate-+l+_binary64`
441×	`distribute-rgt-in_binary64`
437×	`distribute-lft-in_binary64`
422×	`*-commutative_binary64`
297×	`exp-prod_binary64`
163×	`associate-l_binary64`
160×	`associate-r_binary64`
123×	`cancel-sign-sub-inv_binary64`
120×	`unswap-sqr_binary64`
118×	`log-prod_binary64`
95×	`distribute-rgt-neg-out_binary64`
89×	`sqr-pow_binary64`
88×	`distribute-lft-neg-out_binary64`
84×	`distribute-rgt-neg-in_binary64`
69×	`distribute-lft-neg-in_binary64`
52×	`swap-sqr_binary64`
50×	`unsub-neg_binary64`
44×	`sub-neg_binary64`
41×	`neg-mul-1_binary64` `neg-sub0_binary64`
39×	`cube-prod_binary64`
35×	`associate-+r+_binary64`
30×	`associate--r+_binary64`
29×	`exp-sum_binary64`
27×	`distribute-rgt-out_binary64`
23×	`distribute-neg-in_binary64` `+-commutative_binary64`
19×	`log-pow_binary64`
18×	`associate-+l-_binary64`
17×	`unpow3_binary64`
16×	`pow-plus_binary64` `distribute-rgt-out--_binary64`
15×	`pow-sqr_binary64`
13×	`associate-/l*_binary64`
11×	`exp-diff_binary64`
9×	`associate-/l/_binary64` `associate-*r/_binary64` `associate-+r-_binary64`
7×	`cube-unmult_binary64` `cube-mult_binary64` `associate--r-_binary64`
6×	`remove-double-neg_binary64` `+-rgt-identity_binary64` `associate-/r/_binary64`
5×	`unpow2_binary64` `fabs-mul_binary64` `distribute-neg-out_binary64` `associate-/r*_binary64` `associate--l+_binary64`
4×	`sub0-neg_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64`
3×	`unpow1/2_binary64` `unpow1_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `div-sub_binary64`
2×	`unpow-1_binary64` `difference-of-squares_binary64` `count-2_binary64`
1×	`1-exp_binary64` `cube-neg_binary64` `fabs-sqr_binary64` `sqr-neg_binary64` `--rgt-identity_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` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-neg_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` `fabs-div_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `times-frac_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-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` `associate-l/_binary64`

Counts

81 → 52

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	143	1637
1	327	1311
2	1018	1254
3	2767	1245
4	4741	1245
5	4967	1245
6	4992	1245

prune38.0ms (1.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	52	3	55

Error

Counts

55 → 3

Compiler

Compiled 820 to 657 computations (19.9% saved)

regimes190.0ms (8.1%)

Accuracy

Total 0.0b remaining (63.2%)

Threshold costs 0.0b (63.2%)

Compiler

Compiled 3269 to 2721 computations (16.8% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
5×	`sub-neg_binary64` `+-commutative_binary64`
3×	`neg-mul-1_binary64` `neg-sub0_binary64` `cancel-sign-sub-inv_binary64` `distribute-rgt-neg-in_binary64`
2×	`distribute-lft-neg-in_binary64`
1×	`1-exp_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` `fabs-div_binary64` `fabs-mul_binary64` `fabs-sqr_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_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-neg-frac_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	15	29
1	31	29
2	42	29
3	48	29
4	51	29
5	49	29

end1.0ms (0%)

Compiler: Compiled 19 to 15 computations (21.1% saved)

sample683.0ms (29.2%)

Algorithm

1×

intervals

Results

400.0ms	8000×	body	128	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 95 to 80 computations (15.8% saved)

Details

analyze92.0ms (3.9%)

sample19.0ms (0.8%)

simplify82.0ms (3.5%)

prune2.0ms (0.1%)

localize11.0ms (0.5%)

rewrite226.0ms (9.7%)

series75.0ms (3.2%)

simplify167.0ms (7.1%)

prune91.0ms (3.9%)

localize10.0ms (0.4%)

rewrite136.0ms (5.8%)

series54.0ms (2.3%)

simplify117.0ms (5%)

prune68.0ms (2.9%)

localize12.0ms (0.5%)

rewrite97.0ms (4.2%)

series40.0ms (1.7%)

simplify126.0ms (5.4%)

prune38.0ms (1.6%)

regimes190.0ms (8.1%)

bsearch0.0ms (0%)

simplify4.0ms (0.2%)

end1.0ms (0%)

sample683.0ms (29.2%)

Profiling