Details

analyze93.0ms (5.3%)

Algorithm

1×	search
2×	egg-herbie

Rules

11×	`+-commutative_binary64`
6×	`associate-+l+_binary64` `associate-+r+_binary64`
4×	`*-commutative_binary64`
2×	`distribute-rgt-out_binary64` `distribute-lft-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` `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` `1-exp_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-unmult_binary64` `cube-mult_binary64` `cube-div_binary64` `cube-prod_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `times-frac_binary64` `div-sub_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` `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-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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	26	26
2	40	26
3	40	26
4	40	26
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%	62.4%	12.6%	6
25%	40.6%	34.4%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample15.0ms (0.9%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 23 to 19 computations (17.4% saved)

simplify9.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
3×	`associate-+l+_binary64` `associate-+r+_binary64`
2×	`*-commutative_binary64`
1×	`distribute-rgt-out_binary64` `distribute-lft-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` `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` `1-exp_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-unmult_binary64` `cube-mult_binary64` `cube-div_binary64` `cube-prod_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `times-frac_binary64` `div-sub_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` `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-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`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	16	13
2	24	13
3	24	13
4	24	13

prune3.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 2

Compiler

Compiled 29 to 22 computations (24.1% saved)

localize11.0ms (0.6%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
0.0b	(+.f64 (.f64 x 2) (.f64 x x))

rewrite31.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

9×	`add-log-exp_binary64`
4×	`sum-log_binary64`
2×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `flip3-+_binary64` `*-un-lft-identity_binary64` `flip-+_binary64` `+-commutative_binary64`
1×	`distribute-lft-out_binary64` `associate-+l+_binary64`

Counts

2 → 25

Calls

2 calls:

6.0ms	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
4.0ms	(+.f64 (.f64 x 2) (.f64 x x))

Compiler

Compiled 519 to 236 computations (54.5% saved)

series52.0ms (3%)

Error

0.0b

Counts

2 → 21

Calls

2 calls:

32.0ms	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
12.0ms	(+.f64 (.f64 x 2) (.f64 x x))

Compiler

Compiled 318 to 277 computations (12.9% saved)

simplify92.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

465×	`cancel-sign-sub-inv_binary64`
410×	`distribute-rgt-out_binary64`
328×	`associate-l_binary64`
285×	`distribute-rgt-in_binary64`
284×	`distribute-lft-out_binary64`
280×	`associate-r_binary64`
257×	`distribute-lft-in_binary64`
234×	`unswap-sqr_binary64`
169×	`sub-neg_binary64`
142×	`distribute-rgt-neg-in_binary64`
127×	`neg-mul-1_binary64`
123×	`neg-sub0_binary64`
121×	`distribute-lft-neg-in_binary64`
107×	`unsub-neg_binary64`
103×	`exp-prod_binary64`
100×	`*-commutative_binary64`
89×	`associate-+l+_binary64`
71×	`distribute-rgt-out--_binary64`
65×	`associate-+r+_binary64`
55×	`sqr-pow_binary64`
48×	`distribute-neg-in_binary64` `+-commutative_binary64`
47×	`unpow3_binary64`
46×	`distribute-lft-neg-out_binary64`
45×	`cube-prod_binary64`
43×	`distribute-lft-out--_binary64`
42×	`prod-exp_binary64`
37×	`pow-plus_binary64`
34×	`difference-of-squares_binary64`
30×	`pow-sqr_binary64`
25×	`exp-sum_binary64`
23×	`log-prod_binary64` `distribute-rgt-neg-out_binary64`
19×	`cube-unmult_binary64` `associate-+r-_binary64`
16×	`associate--r+_binary64`
15×	`associate-+l-_binary64`
14×	`associate--l+_binary64`
13×	`+-rgt-identity_binary64`
10×	`cube-mult_binary64`
8×	`sub0-neg_binary64` `swap-sqr_binary64`
6×	`remove-double-neg_binary64`
4×	`log-pow_binary64` `rem-sqrt-square_binary64`
3×	`unpow1/2_binary64` `unpow1_binary64` `+-lft-identity_binary64`
2×	`unpow2_binary64` `exp-lft-sqr_binary64` `exp-diff_binary64` `-lft-identity_binary64` `associate-/l_binary64`
1×	`1-exp_binary64` `sqr-neg_binary64` `cancel-sign-sub_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_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` `div-exp_binary64` `rec-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` `cube-neg_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` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_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` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/r_binary64` `associate-l/_binary64` `associate-*r/_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

46 → 38

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	58	601
1	195	550
2	615	541
3	2298	541
4	4422	541
5	4903	541
6	4963	541

prune19.0ms (1.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	37	3	40

Error

Counts

40 → 3

Compiler

Compiled 326 to 186 computations (42.9% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
0.0b	(*.f64 x (+.f64 x 2))

rewrite44.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

6×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `associate-r_binary64`
3×	`associate-l_binary64`
2×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64` `flip3-+_binary64` `associate-*r/_binary64` `flip-+_binary64` `associate-+l+_binary64`
1×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `distribute-lft-out_binary64` `*-commutative_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

2 → 36

Calls

2 calls:

6.0ms	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
6.0ms	(*.f64 x (+.f64 x 2))

Compiler

Compiled 550 to 295 computations (46.4% saved)

series46.0ms (2.6%)

Error

Counts

2 → 21

Calls

2 calls:

31.0ms	(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
10.0ms	(*.f64 x (+.f64 x 2))

Compiler

Compiled 318 to 277 computations (12.9% saved)

simplify79.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

475×	`distribute-rgt-in_binary64`
464×	`distribute-lft-in_binary64`
397×	`associate-l_binary64`
361×	`cancel-sign-sub-inv_binary64`
322×	`associate-r_binary64`
311×	`sub-neg_binary64`
238×	`unswap-sqr_binary64`
203×	`+-commutative_binary64`
201×	`distribute-rgt-out_binary64`
140×	`distribute-rgt-neg-in_binary64`
111×	`sqr-pow_binary64` `distribute-lft-neg-in_binary64`
104×	`neg-mul-1_binary64`
102×	`neg-sub0_binary64`
101×	`associate--r+_binary64`
98×	`*-commutative_binary64`
96×	`difference-of-squares_binary64`
86×	`distribute-lft-out_binary64`
80×	`unsub-neg_binary64`
70×	`associate-+l+_binary64`
64×	`exp-prod_binary64`
63×	`distribute-neg-in_binary64`
59×	`associate-+r+_binary64`
57×	`associate--l+_binary64`
48×	`associate-+l-_binary64`
41×	`distribute-rgt-out--_binary64`
31×	`cube-prod_binary64` `pow-sqr_binary64` `distribute-lft-neg-out_binary64` `associate-+r-_binary64`
28×	`-rgt-identity_binary64` `-lft-identity_binary64`
22×	`sub0-neg_binary64`
21×	`exp-sum_binary64`
20×	`log-prod_binary64`
16×	`distribute-rgt-neg-out_binary64`
15×	`pow-plus_binary64` `+-rgt-identity_binary64`
14×	`unpow3_binary64` `distribute-lft-out--_binary64`
13×	`cube-unmult_binary64`
10×	`prod-exp_binary64` `swap-sqr_binary64`
6×	`unpow1/2_binary64` `associate--r-_binary64`
5×	`rem-sqrt-square_binary64` `associate-/l*_binary64`
4×	`cube-mult_binary64`
3×	`log-pow_binary64` `associate-/l/_binary64` `associate-*r/_binary64`
2×	`unpow2_binary64` `unpow1_binary64` `exp-lft-sqr_binary64` `count-2_binary64`
1×	`1-exp_binary64` `exp-1-e_binary64` `times-frac_binary64` `remove-double-neg_binary64` `distribute-rgt1-in_binary64` `associate-/r/_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-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `exp-diff_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` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-square-sqrt_binary64` `div-sub_binary64` `mul-1-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-l/_binary64` `associate--l-_binary64`

Counts

57 → 48

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	73	656
1	205	620
2	650	611
3	2434	611
4	4128	611
5	5006	611

prune21.0ms (1.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	48	3	51

Error

Counts

51 → 3

Compiler

Compiled 447 to 245 computations (45.2% saved)

localize11.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 (.f64 x (+.f64 2 x)) (.f64 y y)))
0.0b	(*.f64 x (+.f64 2 x))
0.0b	(*.f64 x (+.f64 2 x))
0.1b	(.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))) (sqrt.f64 (+.f64 (.f64 x (+.f64 2 x)) (*.f64 y y))))

rewrite158.0ms (9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

36×	`add-sqr-sqrt_binary64`
24×	`pow1_binary64`
21×	`*-un-lft-identity_binary64` `sqrt-prod_binary64`
17×	`add-cube-cbrt_binary64`
14×	`sqrt-div_binary64` `associate-r_binary64`
12×	`associate-l_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64`
8×	`swap-sqr_binary64`
6×	`unswap-sqr_binary64` `associate-*r/_binary64`
5×	`pow-prod-down_binary64` `pow-prod-up_binary64`
4×	`add-log-exp_binary64` `frac-times_binary64`
3×	`prod-exp_binary64` `cbrt-unprod_binary64` `rem-sqrt-square_binary64` `pow-sqr_binary64` `*-commutative_binary64`
2×	`associate-*l/_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `distribute-lft-out_binary64`
1×	`pow2_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `sqr-abs_binary64` `rem-square-sqrt_binary64`

Counts

4 → 119

Calls

4 calls:

19.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))) (sqrt.f64 (+.f64 (.f64 x (+.f64 2 x)) (*.f64 y y))))
6.0ms	(*.f64 x (+.f64 2 x))
6.0ms	(*.f64 x (+.f64 2 x))
6.0ms	(sqrt.f64 (+.f64 (.f64 x (+.f64 2 x)) (.f64 y y)))

Compiler

Compiled 3194 to 1782 computations (44.2% saved)

series121.0ms (6.9%)

Error

Counts

4 → 44

Calls

4 calls:

41.0ms	(sqrt.f64 (+.f64 (.f64 x (+.f64 2 x)) (.f64 y y)))
31.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))) (sqrt.f64 (+.f64 (.f64 x (+.f64 2 x)) (*.f64 y y))))
13.0ms	(*.f64 x (+.f64 2 x))
12.0ms	(*.f64 x (+.f64 2 x))

Compiler

Compiled 1791 to 1302 computations (27.3% saved)

simplify156.0ms (8.9%)

Algorithm

1×	egg-herbie

Rules

568×	`distribute-rgt-in_binary64`
540×	`distribute-lft-in_binary64`
309×	`times-frac_binary64`
213×	`associate-/l*_binary64`
157×	`cancel-sign-sub-inv_binary64`
142×	`associate-/r*_binary64`
119×	`associate-l_binary64`
109×	`associate-r_binary64`
102×	`sub-neg_binary64`
89×	`neg-sub0_binary64`
87×	`neg-mul-1_binary64`
76×	`unswap-sqr_binary64`
75×	`distribute-rgt-neg-in_binary64`
72×	`*-commutative_binary64`
63×	`distribute-lft-neg-in_binary64` `associate-*l/_binary64`
57×	`associate-*r/_binary64`
54×	`+-commutative_binary64`
50×	`exp-prod_binary64` `distribute-neg-in_binary64`
47×	`log-prod_binary64`
39×	`sqr-pow_binary64`
38×	`distribute-neg-frac_binary64`
33×	`associate--l+_binary64`
32×	`associate--r+_binary64`
31×	`cube-prod_binary64`
29×	`associate-+l+_binary64`
26×	`exp-sum_binary64` `associate-+r+_binary64`
24×	`unsub-neg_binary64` `distribute-rgt-out_binary64`
21×	`associate-/r/_binary64`
19×	`unpow3_binary64`
18×	`-rgt-identity_binary64` `-lft-identity_binary64`
17×	`div-sub_binary64` `distribute-rgt-out--_binary64`
15×	`pow-plus_binary64`
14×	`rem-sqrt-square_binary64` `distribute-lft-out_binary64`
11×	`log-pow_binary64`
10×	`cube-unmult_binary64` `distribute-lft-neg-out_binary64`
9×	`swap-sqr_binary64`
8×	`rem-square-sqrt_binary64`
6×	`pow-sqr_binary64` `associate-/l/_binary64`
5×	`cube-mult_binary64`
4×	`unpow1/2_binary64` `cube-div_binary64` `distribute-lft-out--_binary64`
3×	`/-rgt-identity_binary64` `difference-of-squares_binary64`
2×	`unpow2_binary64` `unpow1_binary64` `mul-1-neg_binary64` `distribute-rgt-neg-out_binary64` `count-2_binary64` `associate-+r-_binary64`
1×	`exp-lft-sqr_binary64` `prod-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `+-rgt-identity_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_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-diff_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-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-frac-neg_binary64` `distribute-neg-out_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

163 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	172	2887
1	424	2639
2	1466	2516
3	4776	2491
4	4980	2491
5	4943	2491

prune67.0ms (3.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	122	3	125

Error

Counts

125 → 3

Compiler

Compiled 1785 to 994 computations (44.3% saved)

regimes169.0ms (9.6%)

Accuracy

Total 0.0b remaining (62.4%)

Threshold costs 0.0b (62.4%)

Compiler

Compiled 1326 to 1097 computations (17.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-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` `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` `1-exp_binary64` `exp-1-e_binary64` `exp-0_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	9	16
1	12	16
2	12	16

end1.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

sample550.0ms (31.3%)

Algorithm

1×

intervals

Results

234.0ms	8000×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 78 to 65 computations (16.7% saved)

Details

analyze93.0ms (5.3%)

sample15.0ms (0.9%)

simplify9.0ms (0.5%)

prune3.0ms (0.2%)

localize11.0ms (0.6%)

rewrite31.0ms (1.8%)

series52.0ms (3%)

simplify92.0ms (5.2%)

prune19.0ms (1.1%)

localize6.0ms (0.3%)

rewrite44.0ms (2.5%)

series46.0ms (2.6%)

simplify79.0ms (4.5%)

prune21.0ms (1.2%)

localize11.0ms (0.6%)

rewrite158.0ms (9%)

series121.0ms (6.9%)

simplify156.0ms (8.9%)

prune67.0ms (3.8%)

regimes169.0ms (9.6%)

bsearch0.0ms (0%)

simplify3.0ms (0.2%)

end1.0ms (0%)

sample550.0ms (31.3%)

Profiling