Details

analyze80.0ms (5.1%)

Algorithm

1×	search
2×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-l_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-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-rgt-out_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `count-2_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64` `associate-l/_binary64` `associate-*r/_binary64` `associate--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	7	14
1	13	14
2	15	14
3	15	14
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
37.5%	62.4%	0.1%	6
50%	37.5%	12.6%	7
56.2%	31.2%	12.6%	8
62.4%	18.7%	18.8%	9
65.6%	15.6%	18.8%	10
68.7%	9.4%	22%	11
70.2%	7.8%	22%	12
71.8%	4.7%	23.5%	13
72.6%	3.9%	23.5%	14

Compiler

Compiled 6 to 5 computations (16.7% saved)

sample13.0ms (0.8%)

Algorithm

1×

intervals

Results

5.0ms	256×	body	128	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 11 to 11 computations (0% saved)

simplify9.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`associate-l_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-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-rgt-out_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `count-2_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64` `associate-l/_binary64` `associate-*r/_binary64` `associate--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	7
1	9	7
2	10	7
3	10	7

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.2b

Counts

2 → 1

Compiler

Compiled 10 to 8 computations (20% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.2b	(.f64 (.f64 x y) y)

rewrite24.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

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

Counts

1 → 18

Calls

1 calls:

5.0ms

(*.f64 (*.f64 x y) y)

Compiler

Compiled 170 to 51 computations (70% saved)

series17.0ms (1.1%)

Error

0.1b

Counts

1 → 6

Calls

1 calls:

15.0ms

(*.f64 (*.f64 x y) y)

Compiler

Compiled 65 to 65 computations (0% saved)

simplify68.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

373×	`associate-l_binary64`
319×	`unswap-sqr_binary64`
312×	`associate-*r/_binary64`
263×	`associate-*l/_binary64`
242×	`associate-/l*_binary64`
210×	`associate-/l/_binary64`
193×	`log-div_binary64` `cube-div_binary64`
187×	`associate-/r/_binary64`
172×	`associate-r_binary64`
164×	`sqr-pow_binary64`
157×	`distribute-rgt-in_binary64`
152×	`log-prod_binary64`
144×	`exp-prod_binary64` `*-commutative_binary64`
143×	`distribute-lft-in_binary64`
103×	`associate-/r*_binary64`
83×	`associate-+l+_binary64`
62×	`pow-sqr_binary64` `associate-+r+_binary64`
61×	`times-frac_binary64`
50×	`cube-prod_binary64`
45×	`+-commutative_binary64`
27×	`unpow3_binary64` `exp-sqrt_binary64`
24×	`cube-mult_binary64`
23×	`rem-sqrt-square_binary64`
19×	`log-pow_binary64` `pow-plus_binary64`
18×	`swap-sqr_binary64` `distribute-lft-out_binary64`
17×	`*-rgt-identity_binary64` `distribute-rgt-out_binary64`
16×	`*-lft-identity_binary64`
10×	`unpow1/2_binary64`
9×	`count-2_binary64`
6×	`exp-lft-sqr_binary64` `cube-unmult_binary64`
4×	`distribute-rgt1-in_binary64`
3×	`unpow2_binary64` `distribute-lft1-in_binary64`
2×	`log-rec_binary64`
1×	`unpow1_binary64` `prod-exp_binary64` `1-exp_binary64` `exp-1-e_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` `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` `rem-square-sqrt_binary64` `div-sub_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `unsub-neg_binary64` `sub-neg_binary64` `mul-1-neg_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-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` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+l-_binary64` `associate-+r-_binary64`

Counts

24 → 19

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	245
1	93	200
2	298	200
3	590	198
4	875	198
5	1700	198
6	4160	198
7	5057	198

prune10.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	14	5	19
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	14	6	20

Error

0.1b

Counts

20 → 6

Compiler

Compiled 136 to 58 computations (57.4% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

11.4b

(*.f64 x (*.f64 y y))

rewrite22.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

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

Counts

1 → 19

Calls

1 calls:

5.0ms

(*.f64 x (*.f64 y y))

Compiler

Compiled 204 to 82 computations (59.8% saved)

series17.0ms (1.1%)

Error

0.1b

Counts

1 → 6

Calls

1 calls:

16.0ms

(*.f64 x (*.f64 y y))

Compiler

Compiled 91 to 91 computations (0% saved)

simplify71.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

690×	`associate-/l/_binary64`
564×	`associate-/r/_binary64`
350×	`distribute-rgt-in_binary64`
330×	`unswap-sqr_binary64`
315×	`distribute-lft-in_binary64`
255×	`*-commutative_binary64`
209×	`log-prod_binary64`
204×	`associate-l_binary64`
192×	`sqr-pow_binary64`
152×	`times-frac_binary64`
138×	`associate-r_binary64`
117×	`associate-/l*_binary64`
116×	`associate-+l+_binary64`
87×	`pow-sqr_binary64`
73×	`associate-+r+_binary64`
58×	`distribute-rgt-out_binary64`
53×	`exp-prod_binary64`
48×	`associate-/r*_binary64`
43×	`log-div_binary64`
42×	`cube-prod_binary64`
40×	`associate-*r/_binary64`
27×	`log-pow_binary64`
26×	`distribute-lft-out_binary64`
20×	`associate-*l/_binary64`
19×	`count-2_binary64`
18×	`unpow3_binary64`
17×	`pow-plus_binary64` `*-lft-identity_binary64`
16×	`+-commutative_binary64`
14×	`cube-mult_binary64`
10×	`*-rgt-identity_binary64`
9×	`distribute-rgt1-in_binary64`
8×	`swap-sqr_binary64`
7×	`cube-unmult_binary64`
5×	`/-rgt-identity_binary64` `distribute-lft1-in_binary64`
3×	`unpow2_binary64`
1×	`unpow1/2_binary64` `unpow1_binary64` `1-exp_binary64` `rem-sqrt-square_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-rec_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `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-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` `neg-mul-1_binary64` `neg-sub0_binary64` `unsub-neg_binary64` `sub-neg_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` `remove-double-div_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` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+l-_binary64` `associate-+r-_binary64`

Counts

25 → 14

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	255
1	75	210
2	190	210
3	428	210
4	666	210
5	1218	210
6	2094	210
7	4843	210
8	5061	210

prune9.0ms (0.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	12	2	14
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	13	7	20

Error

0.1b

Counts

20 → 7

Compiler

Compiled 125 to 65 computations (48% saved)

localize10.0ms (0.6%)

Local error

Found 4 expressions with local error:

11.4b	(.f64 x (.f64 y y))
19.1b	(cbrt.f64 (.f64 x (.f64 y y)))
19.1b	(cbrt.f64 (.f64 x (.f64 y y)))
19.1b	(cbrt.f64 (.f64 x (.f64 y y)))

rewrite52.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

9×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`pow1/3_binary64` `cbrt-prod_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `associate-l_binary64`
1×	`unswap-sqr_binary64` `associate-r_binary64` `*-commutative_binary64`

Counts

4 → 46

Calls

4 calls:

5.0ms	(.f64 x (.f64 y y))
4.0ms	(cbrt.f64 (.f64 x (.f64 y y)))
4.0ms	(cbrt.f64 (.f64 x (.f64 y y)))
4.0ms	(cbrt.f64 (.f64 x (.f64 y y)))

Compiler

Compiled 1070 to 155 computations (85.5% saved)

series170.0ms (10.9%)

Error

0.1b

Counts

4 → 24

Calls

4 calls:

45.0ms	(cbrt.f64 (.f64 x (.f64 y y)))
44.0ms	(cbrt.f64 (.f64 x (.f64 y y)))
44.0ms	(cbrt.f64 (.f64 x (.f64 y y)))
20.0ms	(.f64 x (.f64 y y))

Compiler

Compiled 1655 to 943 computations (43% saved)

simplify120.0ms (7.7%)

Algorithm

1×	egg-herbie

Rules

445×	`exp-sum_binary64`
378×	`unsub-neg_binary64`
339×	`associate-l_binary64`
335×	`log-prod_binary64`
317×	`*-commutative_binary64`
298×	`div-sub_binary64`
263×	`associate-r_binary64`
229×	`exp-prod_binary64`
228×	`exp-diff_binary64`
181×	`unswap-sqr_binary64`
150×	`log-div_binary64`
131×	`log-pow_binary64` `distribute-rgt-in_binary64`
117×	`associate-+r+_binary64`
113×	`distribute-lft-in_binary64`
96×	`prod-exp_binary64`
89×	`associate--r+_binary64`
71×	`associate-+r-_binary64`
63×	`sqr-pow_binary64`
60×	`cube-prod_binary64`
56×	`neg-sub0_binary64`
55×	`associate--r-_binary64`
52×	`sub-neg_binary64`
50×	`neg-mul-1_binary64`
47×	`associate--l+_binary64`
45×	`associate-+l+_binary64`
40×	`log-rec_binary64`
38×	`exp-to-pow_binary64` `distribute-neg-out_binary64`
37×	`associate-+l-_binary64`
36×	`associate-*l/_binary64`
35×	`exp-neg_binary64`
34×	`associate-/l*_binary64`
33×	`+-commutative_binary64`
32×	`cancel-sign-sub-inv_binary64`
23×	`distribute-neg-in_binary64`
22×	`associate--l-_binary64`
21×	`distribute-rgt-neg-out_binary64`
20×	`pow-sqr_binary64`
19×	`distribute-lft-neg-out_binary64` `distribute-lft-out_binary64` `associate-*r/_binary64`
18×	`pow-plus_binary64`
16×	`unpow3_binary64`
14×	`swap-sqr_binary64` `distribute-rgt-neg-in_binary64`
13×	`cube-div_binary64`
12×	`unpow1/3_binary64` `cube-unmult_binary64`
11×	`rem-exp-log_binary64` `distribute-lft-neg-in_binary64`
10×	`cube-mult_binary64`
8×	`exp-lft-sqr_binary64` `distribute-frac-neg_binary64`
7×	`div-exp_binary64` `rem-sqrt-square_binary64` `associate-/r*_binary64`
5×	`count-2_binary64` `associate-/l/_binary64`
4×	`unpow2_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `distribute-lft-out--_binary64`
3×	`remove-double-neg_binary64` `sub0-neg_binary64` `distribute-rgt-out_binary64`
2×	`unpow1_binary64` `rem-cube-cbrt_binary64` `distribute-rgt-out--_binary64`
1×	`log-E_binary64` `unpow1/2_binary64` `rec-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-log-exp_binary64` `rem-3cbrt-lft_binary64` `cancel-sign-sub_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` `pow-base-0_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `e-exp-1_binary64` `exp-0_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-square-sqrt_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` `difference-of-squares_binary64` `distribute-neg-frac_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64`

Counts

70 → 58

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	827
1	156	718
2	377	696
3	1112	665
4	2845	665
5	4811	665
6	4784	665
7	5036	665

prune28.0ms (1.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	58	7	65

Error

0.1b

Counts

65 → 7

Compiler

Compiled 831 to 156 computations (81.2% saved)

localize6.0ms (0.4%)

Local error

Found 4 expressions with local error:

11.4b	(.f64 x (.f64 y y))
11.4b	(.f64 x (.f64 y y))
17.1b	(sqrt.f64 (.f64 x (.f64 y y)))
17.1b	(sqrt.f64 (.f64 x (.f64 y y)))

rewrite61.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

26×	`pow1_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`pow-prod-down_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64` `sqrt-pow1_binary64` `-un-lft-identity_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `associate-l*_binary64`
4×	`add-log-exp_binary64`
2×	`pow1/2_binary64` `sqrt-prod_binary64` `unswap-sqr_binary64` `associate-r_binary64` `*-commutative_binary64`

Counts

4 → 62

Calls

4 calls:

5.0ms	(.f64 x (.f64 y y))
5.0ms	(.f64 x (.f64 y y))
4.0ms	(sqrt.f64 (.f64 x (.f64 y y)))
4.0ms	(sqrt.f64 (.f64 x (.f64 y y)))

Compiler

Compiled 968 to 157 computations (83.8% saved)

series72.0ms (4.6%)

Error

0.1b

Counts

4 → 24

Calls

4 calls:

18.0ms	(sqrt.f64 (.f64 x (.f64 y y)))
17.0ms	(sqrt.f64 (.f64 x (.f64 y y)))
17.0ms	(.f64 x (.f64 y y))
16.0ms	(.f64 x (.f64 y y))

Compiler

Compiled 718 to 515 computations (28.3% saved)

simplify85.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

766×	`associate-/l/_binary64`
545×	`unswap-sqr_binary64`
379×	`distribute-rgt-in_binary64`
340×	`distribute-lft-in_binary64`
290×	`*-commutative_binary64`
272×	`associate-l_binary64`
221×	`sqr-pow_binary64`
190×	`associate-r_binary64`
120×	`associate-/l*_binary64`
117×	`times-frac_binary64`
116×	`associate-+l+_binary64`
99×	`pow-sqr_binary64`
73×	`associate-/r/_binary64` `associate-+r+_binary64`
63×	`distribute-rgt-out_binary64`
59×	`log-prod_binary64`
55×	`exp-prod_binary64`
48×	`associate-/r*_binary64`
43×	`cube-prod_binary64`
42×	`associate-*r/_binary64`
34×	`distribute-lft-out_binary64`
23×	`count-2_binary64`
21×	`unpow3_binary64` `associate-*l/_binary64`
20×	`pow-plus_binary64` `+-commutative_binary64`
19×	`log-pow_binary64`
18×	`*-lft-identity_binary64`
17×	`cube-mult_binary64`
13×	`sub-neg_binary64`
11×	`*-rgt-identity_binary64`
10×	`rem-sqrt-square_binary64` `distribute-rgt1-in_binary64`
9×	`distribute-rgt-neg-in_binary64`
8×	`cube-unmult_binary64` `neg-sub0_binary64` `unsub-neg_binary64` `swap-sqr_binary64` `distribute-lft-neg-in_binary64`
6×	`neg-mul-1_binary64` `/-rgt-identity_binary64` `distribute-lft1-in_binary64`
4×	`unpow2_binary64` `mul0-rgt_binary64` `mul0-lft_binary64`
3×	`sub0-neg_binary64` `--rgt-identity_binary64` `associate-+l-_binary64`
2×	`unpow1/2_binary64` `unpow1_binary64` `mul-1-neg_binary64` `cancel-sign-sub-inv_binary64`
1×	`1-exp_binary64` `rem-square-sqrt_binary64` `distribute-rgt-neg-out_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` `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` `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-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `div-sub_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` `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--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+r-_binary64`

Counts

86 → 46

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	52	804
1	104	702
2	258	702
3	632	702
4	989	702
5	1762	702
6	2819	702
7	4871	702

prune14.0ms (0.9%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	46	7	53

Error

0.1b

Counts

53 → 7

Compiler

Compiled 313 to 62 computations (80.2% saved)

regimes92.0ms (5.9%)

Accuracy

Total 0.1b remaining (71.6%)

Threshold costs 0.1b (71.6%)

Compiler

Compiled 806 to 499 computations (38.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2× *-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 +-commutative_binary64

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	7	7
2	7	7

end1.0ms (0%)

Compiler: Compiled 5 to 4 computations (20% saved)

sample497.0ms (31.9%)

Algorithm

1×

intervals

Results

160.0ms	8000×	body	128	valid
3.0ms	160×	body	128	invalid

Compiler

Compiled 89 to 65 computations (27% saved)

Details

analyze80.0ms (5.1%)

sample13.0ms (0.8%)

simplify9.0ms (0.6%)

prune2.0ms (0.1%)

localize3.0ms (0.2%)

rewrite24.0ms (1.5%)

series17.0ms (1.1%)

simplify68.0ms (4.4%)

prune10.0ms (0.7%)

localize5.0ms (0.3%)

rewrite22.0ms (1.4%)

series17.0ms (1.1%)

simplify71.0ms (4.5%)

prune9.0ms (0.6%)

localize10.0ms (0.6%)

rewrite52.0ms (3.4%)

series170.0ms (10.9%)

simplify120.0ms (7.7%)

prune28.0ms (1.8%)

localize6.0ms (0.4%)

rewrite61.0ms (3.9%)

series72.0ms (4.6%)

simplify85.0ms (5.5%)

prune14.0ms (0.9%)

regimes92.0ms (5.9%)

bsearch0.0ms (0%)

simplify3.0ms (0.2%)

end1.0ms (0%)

sample497.0ms (31.9%)

Profiling