Details

analyze22.0ms (1.1%)

Algorithm

1×	search
2×	egg-herbie

Rules

2×	`count-2_binary64` `associate-r_binary64` `*-commutative_binary64`
1×	`distribute-rgt-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` `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-lft-out_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64` `associate-l/_binary64` `associate-*r/_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+l-_binary64` `associate-+r-_binary64` `associate-+l+_binary64` `associate-+r+_binary64` `+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	9
1	9	9
2	12	9
3	13	9
4	13	9
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 9 to 5 computations (44.4% saved)

sample12.0ms (0.6%)

Algorithm

1×

intervals

Results

6.0ms

256×

body

128

valid

Compiler

Compiled 17 to 10 computations (41.2% saved)

simplify8.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

2×	`count-2_binary64` `associate-r_binary64` `*-commutative_binary64`
1×	`distribute-rgt-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` `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-lft-out_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64` `associate-l/_binary64` `associate-*r/_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+l-_binary64` `associate-+r-_binary64` `associate-+l+_binary64` `associate-+r+_binary64` `+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	9
1	9	9
2	12	9
3	13	9
4	13	9

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

27.9b

Counts

2 → 1

Compiler

Compiled 12 to 8 computations (33.3% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

26.9b

(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite22.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

13.7b

Rules

4×	`pow1_binary64`
2×	`sqrt-pow1_binary64` `associate-*r/_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `flip-+_binary64` `sqrt-prod_binary64` `*-un-lft-identity_binary64`

Counts

1 → 13

Calls

1 calls:

5.0ms

(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 152 to 46 computations (69.7% saved)

series11.0ms (0.6%)

Error

0.2b

Counts

1 → 3

Calls

1 calls:

8.0ms

(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 38 to 37 computations (2.6% saved)

simplify76.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

594×	`distribute-rgt-neg-in_binary64`
533×	`unsub-neg_binary64`
481×	`distribute-lft-neg-in_binary64`
403×	`neg-sub0_binary64`
401×	`neg-mul-1_binary64`
312×	`sub-neg_binary64`
293×	`distribute-lft-out_binary64`
274×	`distribute-rgt-out_binary64`
246×	`distribute-lft-neg-out_binary64`
240×	`cancel-sign-sub-inv_binary64`
237×	`distribute-neg-in_binary64`
235×	`*-commutative_binary64`
213×	`associate-l_binary64`
188×	`distribute-rgt-neg-out_binary64`
184×	`associate-r_binary64`
150×	`distribute-rgt-in_binary64`
130×	`associate--r+_binary64`
123×	`distribute-lft-out--_binary64`
106×	`unswap-sqr_binary64`
103×	`distribute-lft-in_binary64`
92×	`associate--l+_binary64`
84×	`swap-sqr_binary64`
78×	`associate-+r-_binary64`
68×	`distribute-rgt-out--_binary64`
66×	`+-commutative_binary64`
65×	`associate-+l-_binary64`
61×	`associate--r-_binary64`
52×	`distribute-neg-out_binary64`
40×	`associate--l-_binary64`
34×	`distribute-rgt1-in_binary64`
31×	`remove-double-neg_binary64`
27×	`sqr-pow_binary64`
24×	`count-2_binary64`
21×	`associate-+l+_binary64`
20×	`difference-of-squares_binary64`
17×	`associate-+r+_binary64`
15×	`cube-prod_binary64`
12×	`mul0-lft_binary64`
11×	`pow-plus_binary64` `sub0-neg_binary64` `mul0-rgt_binary64` `+-inverses_binary64`
9×	`cube-unmult_binary64` `rem-sqrt-square_binary64` `+-rgt-identity_binary64`
8×	`distribute-lft1-in_binary64`
7×	`--rgt-identity_binary64`
6×	`*-lft-identity_binary64`
5×	`sqr-neg_binary64`
4×	`log-prod_binary64` `exp-prod_binary64`
3×	`unpow3_binary64`
2×	`unpow2_binary64` `exp-diff_binary64` `exp-sum_binary64` `*-rgt-identity_binary64`
1×	`unpow1/2_binary64` `unpow1_binary64` `1-exp_binary64` `exp-1-e_binary64` `cube-mult_binary64` `cube-neg_binary64` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `pow-sqr_binary64` `cancel-sign-sub_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-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-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-div_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `times-frac_binary64` `div-sub_binary64` `/-rgt-identity_binary64` `+-lft-identity_binary64` `div0_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` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64` `associate-l/_binary64` `associate-*r/_binary64`

Counts

16 → 6

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	35	155
1	67	143
2	126	140
3	336	140
4	1155	140
5	2396	140
6	4359	140
7	5009	140

prune7.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	3	3	6
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	3	4	7

Error

14.3b

Counts

7 → 4

Compiler

Compiled 58 to 45 computations (22.4% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.4b	(*.f64 x (sqrt.f64 2))

rewrite24.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

14.2b

Rules

8×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`
4×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64` `sqrt-prod_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
2×	`unswap-sqr_binary64`
1×	`pow-prod-down_binary64` `prod-exp_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `*-commutative_binary64`

Counts

1 → 22

Calls

1 calls:

5.0ms

(*.f64 x (sqrt.f64 2))

Compiler

Compiled 190 to 157 computations (17.4% saved)

series9.0ms (0.4%)

Error

14.3b

Counts

1 → 3

Calls

1 calls:

8.0ms

(*.f64 x (sqrt.f64 2))

Compiler

Compiled 35 to 35 computations (0% saved)

simplify53.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

860×	`unswap-sqr_binary64`
330×	`associate-l_binary64`
278×	`associate-*l/_binary64`
249×	`*-commutative_binary64`
228×	`cube-div_binary64`
224×	`log-div_binary64`
222×	`associate-r_binary64`
213×	`associate-*r/_binary64`
192×	`associate-+l+_binary64`
173×	`associate-/l/_binary64`
154×	`associate-/l*_binary64`
133×	`sqr-pow_binary64`
131×	`cube-prod_binary64`
122×	`log-prod_binary64`
102×	`associate-/r/_binary64`
72×	`associate-+r+_binary64`
66×	`associate-/r*_binary64`
64×	`exp-prod_binary64`
45×	`pow-sqr_binary64`
29×	`unsub-neg_binary64`
28×	`cube-unmult_binary64` `*-lft-identity_binary64`
23×	`distribute-lft-out_binary64`
22×	`pow-plus_binary64`
21×	`times-frac_binary64` `*-rgt-identity_binary64` `distribute-rgt-out_binary64`
18×	`unpow3_binary64` `cube-mult_binary64`
17×	`log-rec_binary64`
16×	`rem-sqrt-square_binary64`
12×	`exp-sqrt_binary64`
11×	`swap-sqr_binary64` `+-commutative_binary64`
8×	`sub-neg_binary64`
7×	`exp-lft-sqr_binary64` `distribute-rgt1-in_binary64`
5×	`distribute-lft1-in_binary64`
3×	`log-pow_binary64` `unpow1/2_binary64`
2×	`prod-exp_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `/-rgt-identity_binary64` `remove-double-div_binary64` `distribute-rgt-in_binary64` `count-2_binary64`
1×	`unpow2_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-square-sqrt_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `div-exp_binary64` `rec-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `div-sub_binary64` `mul-1-neg_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_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-rgt-out--_binary64` `distribute-lft-out--_binary64` `distribute-lft-in_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+l-_binary64` `associate-+r-_binary64`

Counts

25 → 8

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	223
1	68	211
2	166	211
3	210	211
4	310	211
5	542	211
6	1169	211
7	2780	211
8	5010	211

prune8.0ms (0.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	6	2	8
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	6	6	12

Error

14.3b

Counts

12 → 6

Compiler

Compiled 90 to 70 computations (22.2% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.5b	(cbrt.f64 x)
0.5b	(cbrt.f64 x)
0.5b	(cbrt.f64 x)

rewrite62.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

14.2b

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
11×	`pow1_binary64`
9×	`pow1/3_binary64`
6×	`add-exp-log_binary64` `swap-sqr_binary64` `associate-l_binary64` `associate-r_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`pow2_binary64` `pow-plus_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `*-commutative_binary64`

Counts

4 → 73

Calls

4 calls:

6.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

Compiler

Compiled 1147 to 491 computations (57.2% saved)

series79.0ms (3.9%)

Error

14.3b

Counts

4 → 12

Calls

4 calls:

19.0ms	(cbrt.f64 x)
19.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
16.0ms	(cbrt.f64 x)
16.0ms	(cbrt.f64 x)

Compiler

Compiled 468 to 373 computations (20.3% saved)

simplify100.0ms (5%)

Algorithm

1×	egg-herbie

Rules

586×	`log-prod_binary64`
416×	`sqr-pow_binary64`
335×	`associate-l_binary64`
309×	`*-commutative_binary64`
277×	`distribute-rgt-neg-in_binary64`
257×	`distribute-lft-neg-in_binary64`
227×	`associate-r_binary64`
188×	`exp-prod_binary64`
161×	`log-pow_binary64`
149×	`cube-prod_binary64`
128×	`pow-sqr_binary64`
124×	`unswap-sqr_binary64`
111×	`swap-sqr_binary64`
104×	`associate-/l*_binary64`
81×	`cancel-sign-sub-inv_binary64`
75×	`associate-+l+_binary64`
69×	`associate-+r+_binary64`
61×	`distribute-rgt-in_binary64`
60×	`distribute-lft-out_binary64`
57×	`distribute-lft-in_binary64`
54×	`neg-sub0_binary64`
53×	`neg-mul-1_binary64`
48×	`distribute-rgt-out_binary64`
45×	`+-commutative_binary64`
43×	`pow-plus_binary64` `rem-sqrt-square_binary64`
41×	`times-frac_binary64` `sub-neg_binary64`
37×	`associate-/r/_binary64`
35×	`associate-*r/_binary64`
32×	`unpow3_binary64`
31×	`-rgt-identity_binary64` `-lft-identity_binary64` `associate-/l/_binary64`
29×	`count-2_binary64`
27×	`cube-mult_binary64`
24×	`associate-/r*_binary64`
17×	`log-div_binary64` `cube-div_binary64` `distribute-neg-frac_binary64`
13×	`cube-unmult_binary64` `distribute-rgt1-in_binary64`
11×	`distribute-rgt-neg-out_binary64`
10×	`unpow1/2_binary64`
9×	`distribute-lft-neg-out_binary64` `distribute-lft1-in_binary64`
8×	`unpow2_binary64` `associate-*l/_binary64`
5×	`unpow1_binary64`
3×	`unpow1/3_binary64`
2×	`exp-sqrt_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `mul-1-neg_binary64`
1×	`exp-lft-sqr_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-3cbrt-rft_binary64` `rem-square-sqrt_binary64` `sub0-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` `pow-base-0_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `div-sub_binary64` `unsub-neg_binary64` `/-rgt-identity_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-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+r-_binary64`

Counts

85 → 50

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	56	718
1	97	666
2	308	646
3	1135	632
4	2034	548
5	3257	548
6	4939	548
7	4873	548

prune26.0ms (1.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	46	4	50
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	47	9	56

Error

14.3b

Counts

56 → 9

Compiler

Compiled 474 to 295 computations (37.8% saved)

localize14.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 x)
0.6b	(cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
0.6b	(cbrt.f64 (cbrt.f64 x))
0.9b	(pow.f64 (cbrt.f64 (cbrt.f64 x)) 4)

rewrite58.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

14.2b

Rules

22×	`cbrt-prod_binary64`
11×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
9×	`unpow-prod-down_binary64`
5×	`pow1_binary64` `add-exp-log_binary64`
4×	`pow1/3_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`pow-unpow_binary64`
2×	`pow-pow_binary64`
1×	`pow-to-exp_binary64` `pow-exp_binary64` `sqr-pow_binary64`

Counts

4 → 58

Calls

4 calls:

4.0ms	(cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
4.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 x)) 4)
1.0ms	(cbrt.f64 (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

Compiler

Compiled 1379 to 609 computations (55.8% saved)

series101.0ms (5.1%)

Error

14.3b

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 x)) 4)
25.0ms	(cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
23.0ms	(cbrt.f64 (cbrt.f64 x))
17.0ms	(cbrt.f64 x)

Compiler

Compiled 686 to 515 computations (24.9% saved)

simplify132.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

496×	`swap-sqr_binary64`
454×	`log-prod_binary64`
375×	`associate-l_binary64`
339×	`distribute-rgt-neg-in_binary64`
335×	`distribute-lft-neg-in_binary64`
328×	`cube-prod_binary64`
325×	`associate-r_binary64`
317×	`sqr-pow_binary64`
170×	`unpow3_binary64`
159×	`log-pow_binary64`
103×	`pow-plus_binary64`
95×	`neg-mul-1_binary64` `neg-sub0_binary64` `unswap-sqr_binary64`
89×	`pow-sqr_binary64`
84×	`exp-prod_binary64`
78×	`cancel-sign-sub-inv_binary64`
77×	`distribute-rgt-out_binary64`
61×	`distribute-rgt-in_binary64`
53×	`distribute-lft-in_binary64`
51×	`cube-mult_binary64`
48×	`*-commutative_binary64`
37×	`cube-unmult_binary64`
26×	`rem-sqrt-square_binary64`
18×	`distribute-rgt-neg-out_binary64` `associate-/l*_binary64`
17×	`unpow2_binary64` `associate-+l+_binary64` `associate-+r+_binary64`
16×	`sub-neg_binary64`
14×	`*-rgt-identity_binary64` `distribute-lft-neg-out_binary64`
12×	`unpow1/2_binary64` `unpow1_binary64`
10×	`*-lft-identity_binary64`
8×	`rem-3cbrt-rft_binary64`
7×	`associate-/l/_binary64`
6×	`count-2_binary64`
5×	`unpow1/3_binary64` `distribute-lft-out_binary64`
4×	`mul-1-neg_binary64` `associate-*r/_binary64`
3×	`rem-3cbrt-lft_binary64` `distribute-rgt1-in_binary64`
2×	`distribute-lft1-in_binary64` `associate-/r/_binary64` `associate-*l/_binary64`
1×	`1-exp_binary64` `rem-cbrt-cube_binary64` `times-frac_binary64` `/-rgt-identity_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-rec_binary64` `log-div_binary64` `pow-base-0_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-div_binary64` `cube-neg_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-square-sqrt_binary64` `div-sub_binary64` `unsub-neg_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `associate-/r_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+l-_binary64` `associate-+r-_binary64`

Counts

70 → 38

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	85	744
1	162	675
2	379	666
3	1699	637
4	3123	626
5	4652	626
6	4977	626
7	4832	626

prune20.0ms (1%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	37	10	47

Error

14.3b

Counts

47 → 10

Compiler

Compiled 585 to 325 computations (44.4% saved)

regimes478.0ms (24%)

Accuracy

Total -14.4b remaining (-3666.4%)

Threshold costs -14.4b (-3666.4%)

Compiler

Compiled 3811 to 2524 computations (33.8% saved)

bsearch16.0ms (0.8%)

Steps

Iters	Range		Point
10	-5.152681537499351e-300	4.271833802488331e-307	3.34772934547096e-310

Compiler

Compiled 1 to 1 computations (0% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
5×	`neg-mul-1_binary64` `neg-sub0_binary64` `sub-neg_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64` `+-commutative_binary64`
1×	`cancel-sign-sub-inv_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` `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` `distribute-lft-neg-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	36
1	25	36
2	39	36
3	50	36
4	56	36
5	58	36
6	58	36

end1.0ms (0.1%)

Compiler: Compiled 22 to 20 computations (9.1% saved)

sample627.0ms (31.5%)

Algorithm

1×

intervals

Results

192.0ms	8000×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 157 to 124 computations (21% saved)

Details

analyze22.0ms (1.1%)

sample12.0ms (0.6%)

simplify8.0ms (0.4%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

rewrite22.0ms (1.1%)

series11.0ms (0.6%)

simplify76.0ms (3.8%)

prune7.0ms (0.4%)

localize4.0ms (0.2%)

rewrite24.0ms (1.2%)

series9.0ms (0.4%)

simplify53.0ms (2.7%)

prune8.0ms (0.4%)

localize8.0ms (0.4%)

rewrite62.0ms (3.1%)

series79.0ms (3.9%)

simplify100.0ms (5%)

prune26.0ms (1.3%)

localize14.0ms (0.7%)

rewrite58.0ms (2.9%)

series101.0ms (5.1%)

simplify132.0ms (6.6%)

prune20.0ms (1%)

regimes478.0ms (24%)

bsearch16.0ms (0.8%)

simplify5.0ms (0.2%)

end1.0ms (0.1%)

sample627.0ms (31.5%)

Profiling