Details

analyze13.0ms (0.3%)

Algorithm

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 7 to 7 computations (0% saved)

sample212.0ms (4.1%)

Algorithm

1×

intervals

Results

201.0ms

256×

body

128

valid

Compiler

Compiled 13 to 14 computations (-7.7% saved)

simplify271.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

461×	`unswap-sqr_binary64`
436×	`cube-prod_binary64`
402×	`distribute-rgt-out_binary64`
374×	`distribute-rgt-in_binary64`
364×	`associate-/l*_binary64`
342×	`cube-div_binary64`
264×	`distribute-lft-in_binary64`
212×	`*-commutative_binary64`
187×	`associate-/r/_binary64`
171×	`associate-/l/_binary64`
158×	`swap-sqr_binary64`
157×	`associate-/r*_binary64`
155×	`sqr-pow_binary64`
150×	`associate-l_binary64`
103×	`associate-r_binary64`
85×	`*-lft-identity_binary64`
77×	`*-rgt-identity_binary64`
72×	`distribute-lft-out_binary64`
71×	`unpow3_binary64`
70×	`cube-mult_binary64` `pow-sqr_binary64`
66×	`times-frac_binary64`
54×	`associate-*l/_binary64`
43×	`associate-*r/_binary64`
36×	`pow-plus_binary64`
29×	`exp-prod_binary64`
27×	`associate-+l+_binary64`
26×	`remove-double-div_binary64`
25×	`associate-+r+_binary64`
21×	`distribute-rgt1-in_binary64`
18×	`/-rgt-identity_binary64`
16×	`div-exp_binary64` `prod-exp_binary64`
11×	`distribute-lft1-in_binary64`
9×	`cube-unmult_binary64`
8×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`pow-base-1_binary64` `rec-exp_binary64` `distribute-rgt-out--_binary64`
3×	`neg-mul-1_binary64` `neg-sub0_binary64`
2×	`exp-sum_binary64` `+-inverses_binary64` `cancel-sign-sub-inv_binary64` `distribute-lft-neg-in_binary64` `count-2_binary64`
1×	`unpow2_binary64` `unpow1_binary64` `exp-lft-sqr_binary64` `exp-sqrt_binary64` `1-exp_binary64` `--rgt-identity_binary64` `*-inverses_binary64` `rgt-mult-inverse_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` `unpow1/2_binary64` `exp-to-pow_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `exp-diff_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-1-e_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-sqrt-square_binary64` `rem-square-sqrt_binary64` `div-sub_binary64` `unsub-neg_binary64` `mul-1-neg_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `lft-mult-inverse_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-neg-out_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-out--_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	6	9
1	11	9
2	25	9
3	42	9
4	144	9
5	528	9
6	1716	9
7	4157	9

prune4.0ms (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

30.1b

Counts

2 → 1

Compiler

Compiled 12 to 11 computations (8.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 2 (pow.f64 x 2))
28.9b	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

rewrite64.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

30.0b

Rules

11×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
7×	`add-exp-log_binary64`
5×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
4×	`add-cbrt-cube_binary64` `unpow-prod-down_binary64` `unswap-sqr_binary64`
3×	`pow1_binary64` `prod-exp_binary64` `associate-l_binary64`
2×	`add-log-exp_binary64` `unpow2_binary64` `sqr-pow_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `sqrt-prod_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `cbrt-unprod_binary64` `*-commutative_binary64`

Counts

2 → 37

Calls

2 calls:

6.0ms	(*.f64 2 (pow.f64 x 2))
5.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Compiler

Compiled 437 to 371 computations (15.1% saved)

series99.0ms (1.9%)

Error

0.2b

Counts

2 → 6

Calls

2 calls:

52.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
41.0ms	(*.f64 2 (pow.f64 x 2))

Compiler

Compiled 96 to 91 computations (5.2% saved)

simplify572.0ms (11.2%)

Algorithm

1×	egg-herbie

Rules

361×	`exp-prod_binary64`
358×	`log-prod_binary64`
351×	`associate-l_binary64`
338×	`associate-/r*_binary64`
310×	`cube-prod_binary64`
284×	`associate-r_binary64`
247×	`sqr-pow_binary64`
202×	`log-div_binary64`
197×	`cube-div_binary64`
186×	`associate-/r/_binary64`
116×	`pow-sqr_binary64`
96×	`associate-/l/_binary64`
82×	`swap-sqr_binary64`
78×	`distribute-rgt-out_binary64`
68×	`pow-plus_binary64`
64×	`log-pow_binary64`
62×	`associate-*l/_binary64`
61×	`sub-neg_binary64`
50×	`unpow3_binary64`
48×	`unswap-sqr_binary64`
46×	`/-rgt-identity_binary64`
45×	`div-sub_binary64`
44×	`cube-mult_binary64`
43×	`exp-sqrt_binary64` `*-commutative_binary64`
38×	`exp-to-pow_binary64` `times-frac_binary64` `distribute-lft-neg-in_binary64`
37×	`exp-sum_binary64`
35×	`neg-mul-1_binary64`
34×	`distribute-rgt-neg-in_binary64`
33×	`neg-sub0_binary64`
32×	`distribute-rgt-in_binary64`
29×	`exp-lft-sqr_binary64`
27×	`cancel-sign-sub-inv_binary64` `associate-*r/_binary64`
25×	`*-lft-identity_binary64` `distribute-rgt-out--_binary64`
22×	`rem-sqrt-square_binary64`
21×	`*-rgt-identity_binary64` `distribute-lft-in_binary64`
18×	`associate-+l+_binary64`
14×	`pow-base-1_binary64` `cube-unmult_binary64` `associate-+r+_binary64`
12×	`prod-exp_binary64` `exp-diff_binary64`
11×	`distribute-lft-out_binary64` `associate-/l*_binary64`
9×	`associate-+l-_binary64`
8×	`unsub-neg_binary64` `sub0-neg_binary64`
7×	`log-rec_binary64`
6×	`associate--l-_binary64` `associate--l+_binary64` `+-commutative_binary64`
5×	`unpow2_binary64` `+-inverses_binary64` `distribute-rgt1-in_binary64`
4×	`unpow1_binary64` `div-exp_binary64` `distribute-lft1-in_binary64`
3×	`+-lft-identity_binary64` `associate-+r-_binary64`
2×	`rec-exp_binary64` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `mul0-lft_binary64` `distribute-neg-frac_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `count-2_binary64`
1×	`1-exp_binary64` `exp-1-e_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `*-inverses_binary64` `distribute-neg-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` `pow-base-0_binary64` `unpow1/3_binary64` `unpow1/2_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `cube-neg_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `remove-double-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `mul0-rgt_binary64` `div0_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-in_binary64` `associate--r-_binary64` `associate--r+_binary64`

Counts

43 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	62	439
1	115	382
2	335	377
3	1355	377
4	3227	377

prune97.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	5	97

Error

0.2b

Counts

97 → 5

Compiler

Compiled 1270 to 905 computations (28.7% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

8×	`add-sqr-sqrt_binary64`
6×	`associate-l_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-r_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 (sqrt.f64 2) (fabs.f64 x))

Compiler

Compiled 240 to 167 computations (30.4% saved)

series50.0ms (1%)

Error

0.2b

Counts

1 → 3

Calls

1 calls:

48.0ms

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

Compiler

Compiled 45 to 41 computations (8.9% saved)

simplify365.0ms (7.1%)

Algorithm

1×	egg-herbie

Rules

470×	`distribute-lft-out--_binary64`
329×	`associate-/l/_binary64`
317×	`log-prod_binary64`
291×	`log-div_binary64`
253×	`associate-/r*_binary64`
248×	`distribute-rgt-out_binary64`
220×	`distribute-rgt-out--_binary64`
208×	`*-commutative_binary64`
207×	`associate-l_binary64`
206×	`times-frac_binary64`
201×	`unswap-sqr_binary64`
169×	`associate-/r/_binary64`
137×	`cube-div_binary64`
133×	`cancel-sign-sub-inv_binary64`
119×	`exp-prod_binary64`
112×	`cube-prod_binary64`
108×	`sqr-pow_binary64` `associate-r_binary64`
81×	`swap-sqr_binary64`
73×	`log-pow_binary64`
69×	`pow-sqr_binary64`
67×	`distribute-rgt-in_binary64`
59×	`associate-/l*_binary64`
53×	`distribute-rgt-neg-in_binary64`
52×	`pow-plus_binary64` `distribute-lft-in_binary64`
41×	`distribute-lft-neg-in_binary64`
38×	`associate-*l/_binary64`
32×	`unpow3_binary64`
31×	`log-rec_binary64`
28×	`exp-to-pow_binary64` `*-lft-identity_binary64`
27×	`*-rgt-identity_binary64`
23×	`distribute-neg-frac_binary64` `distribute-rgt1-in_binary64`
20×	`associate--l+_binary64`
16×	`exp-sqrt_binary64` `/-rgt-identity_binary64`
15×	`associate-*r/_binary64` `associate--r+_binary64` `associate-+l+_binary64`
14×	`sub-neg_binary64`
13×	`exp-lft-sqr_binary64`
11×	`associate-+r+_binary64`
8×	`cube-unmult_binary64` `cube-mult_binary64` `neg-mul-1_binary64` `remove-double-div_binary64` `distribute-neg-in_binary64` `distribute-lft1-in_binary64` `associate--r-_binary64` `associate--l-_binary64`
7×	`+-commutative_binary64`
6×	`exp-sum_binary64` `associate-+r-_binary64`
5×	`prod-exp_binary64` `associate-+l-_binary64`
4×	`pow-base-1_binary64` `neg-sub0_binary64` `+-inverses_binary64`
3×	`div-sub_binary64` `difference-of-squares_binary64` `distribute-lft-out_binary64` `count-2_binary64`
2×	`exp-diff_binary64` `rem-log-exp_binary64` `rem-sqrt-square_binary64`
1×	`log-E_binary64` `div-exp_binary64` `rec-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `sqr-abs_binary64` `rem-square-sqrt_binary64` `sub0-neg_binary64` `div0_binary64` `*-inverses_binary64` `rgt-mult-inverse_binary64` `distribute-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` `pow-base-0_binary64` `unpow1/3_binary64` `unpow2_binary64` `unpow1/2_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_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-neg_binary64` `unsub-neg_binary64` `mul-1-neg_binary64` `remove-double-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `lft-mult-inverse_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64`

Counts

25 → 12

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	282
1	67	270
2	178	270
3	310	270
4	489	270
5	790	270
6	1726	270
7	4557	270

prune20.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	9	3	12
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	11	6	17

Error

0.0b

Counts

17 → 6

Compiler

Compiled 177 to 133 computations (24.9% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.2b	(*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2))))

rewrite96.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

2 → 48

Calls

2 calls:

11.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2))))
6.0ms	(*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2)))

Compiler

Compiled 1021 to 860 computations (15.8% saved)

series205.0ms (4%)

Error

0.0b

Counts

2 → 6

Calls

2 calls:

151.0ms	(*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2)))
49.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2))))

Compiler

Compiled 180 to 170 computations (5.6% saved)

simplify344.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

529×	`distribute-rgt-in_binary64`
511×	`associate-/r*_binary64`
488×	`distribute-lft-in_binary64`
444×	`unswap-sqr_binary64`
251×	`associate-/l*_binary64`
206×	`*-commutative_binary64`
176×	`sqr-pow_binary64`
148×	`associate-/l/_binary64`
121×	`associate-l_binary64`
105×	`associate-r_binary64`
95×	`pow-sqr_binary64`
88×	`log-prod_binary64`
87×	`distribute-rgt-out_binary64`
86×	`exp-prod_binary64`
85×	`associate-*r/_binary64`
80×	`distribute-lft-out_binary64`
73×	`associate-+l+_binary64`
61×	`cube-prod_binary64`
60×	`associate-*l/_binary64`
54×	`times-frac_binary64`
53×	`associate-+r+_binary64`
43×	`swap-sqr_binary64`
31×	`rem-sqrt-square_binary64`
30×	`*-rgt-identity_binary64`
29×	`pow-plus_binary64`
27×	`*-lft-identity_binary64`
18×	`log-pow_binary64`
17×	`/-rgt-identity_binary64` `distribute-rgt1-in_binary64`
14×	`cube-unmult_binary64`
9×	`log-div_binary64` `unpow3_binary64` `count-2_binary64` `+-commutative_binary64`
8×	`cube-div_binary64`
7×	`distribute-lft1-in_binary64` `associate-/r/_binary64`
5×	`cube-mult_binary64`
4×	`*-inverses_binary64`
3×	`+-rgt-identity_binary64` `+-lft-identity_binary64`
2×	`rem-cbrt-cube_binary64` `rgt-mult-inverse_binary64`
1×	`log-rec_binary64` `unpow1/3_binary64` `pow-base-1_binary64` `prod-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-log-exp_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `sqr-abs_binary64` `rem-square-sqrt_binary64` `lft-mult-inverse_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` `unpow2_binary64` `unpow1/2_binary64` `exp-to-pow_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-cube-cbrt_binary64` `sqr-neg_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` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `+-inverses_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

54 → 67

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	77	1158
1	157	640
2	496	622
3	992	622
4	3290	612

prune105.0ms (2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	67	6	73

Error

0.0b

Counts

73 → 6

Compiler

Compiled 1360 to 1143 computations (16% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.2b	(*.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 2))))

rewrite79.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

2 → 50

Calls

2 calls:

9.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 2))))
7.0ms	(*.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 2)))

Compiler

Compiled 858 to 704 computations (17.9% saved)

series113.0ms (2.2%)

Error

0.0b

Counts

2 → 6

Calls

2 calls:

65.0ms	(*.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 2)))
44.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 2))))

Compiler

Compiled 135 to 125 computations (7.4% saved)

simplify207.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

347×	`associate-/r/_binary64`
316×	`log-prod_binary64`
314×	`unswap-sqr_binary64`
311×	`associate-l_binary64`
296×	`cube-prod_binary64`
230×	`distribute-rgt-out_binary64`
216×	`sqr-pow_binary64`
213×	`exp-prod_binary64`
207×	`times-frac_binary64`
200×	`associate-r_binary64`
165×	`swap-sqr_binary64`
145×	`*-commutative_binary64`
135×	`pow-sqr_binary64`
134×	`distribute-lft-out_binary64`
111×	`log-div_binary64`
107×	`cube-div_binary64`
95×	`associate-/r*_binary64`
93×	`*-rgt-identity_binary64`
91×	`*-lft-identity_binary64` `distribute-lft-out--_binary64`
74×	`associate-/l*_binary64`
73×	`distribute-rgt-out--_binary64`
32×	`distribute-rgt-in_binary64`
31×	`unpow3_binary64`
28×	`cube-mult_binary64`
27×	`pow-plus_binary64`
26×	`log-pow_binary64`
23×	`distribute-rgt1-in_binary64` `associate-/l/_binary64`
22×	`associate-*l/_binary64`
20×	`cancel-sign-sub-inv_binary64`
17×	`exp-lft-sqr_binary64`
15×	`exp-to-pow_binary64` `rem-sqrt-square_binary64` `sub-neg_binary64`
14×	`distribute-rgt-neg-in_binary64`
13×	`associate-*r/_binary64`
11×	`log-rec_binary64`
10×	`distribute-lft1-in_binary64`
8×	`exp-sqrt_binary64` `cube-unmult_binary64` `/-rgt-identity_binary64` `distribute-lft-neg-in_binary64`
6×	`exp-sum_binary64` `remove-double-div_binary64` `associate-+l+_binary64`
5×	`associate-+r+_binary64`
4×	`pow-base-1_binary64` `prod-exp_binary64` `+-commutative_binary64`
3×	`div-sub_binary64` `count-2_binary64`
2×	`rem-log-exp_binary64` `rem-square-sqrt_binary64` `neg-mul-1_binary64` `mul0-lft_binary64` `*-inverses_binary64` `rgt-mult-inverse_binary64`
1×	`exp-lft-cube_binary64` `exp-diff_binary64` `1-exp_binary64` `exp-1-e_binary64` `sqr-abs_binary64` `unsub-neg_binary64` `div0_binary64` `lft-mult-inverse_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` `unpow2_binary64` `unpow1/2_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-cbrt_binary64` `div-exp_binary64` `rec-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_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-neg_binary64` `neg-sub0_binary64` `mul-1-neg_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `+-inverses_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-neg-out_binary64` `distribute-lft-neg-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

56 → 63

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	68	860
1	133	697
2	360	697
3	691	697
4	861	697
5	1559	697
6	2526	697

prune73.0ms (1.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	2	1	3
Picked	0	1	1
Done	0	2	2
Total	64	5	69

Error

0.0b

Counts

69 → 5

Compiler

Compiled 971 to 769 computations (20.8% saved)

regimes467.0ms (9.1%)

Accuracy

Total 0.4b remaining (99.7%)

Threshold costs 0.4b (99.7%)

Compiler

Compiled 4113 to 3656 computations (11.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

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	9	24
1	11	24

Proof

(=> (* f64 (* f64 (* f64 (cbrt f64 (sqrt f64 2)) (cbrt f64 (sqrt f64 2))) (fabs f64 h0)) (cbrt f64 (sqrt f64 2))))
*-commutative_binary64 =>
(* f64 (cbrt f64 (sqrt f64 2)) (* f64 (* f64 (cbrt f64 (sqrt f64 2)) (cbrt f64 (sqrt f64 2))) (fabs f64 h0)))

end0.0ms (0%)

sample1.6s (31.3%)

Algorithm

1×

intervals

Results

265.0ms	8000×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 954 to 847 computations (11.2% saved)

Details

analyze13.0ms (0.3%)

sample212.0ms (4.1%)

simplify271.0ms (5.3%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

rewrite64.0ms (1.3%)

series99.0ms (1.9%)

simplify572.0ms (11.2%)

prune97.0ms (1.9%)

localize6.0ms (0.1%)

rewrite27.0ms (0.5%)

series50.0ms (1%)

simplify365.0ms (7.1%)

prune20.0ms (0.4%)

localize7.0ms (0.1%)

rewrite96.0ms (1.9%)

series205.0ms (4%)

simplify344.0ms (6.7%)

prune105.0ms (2%)

localize6.0ms (0.1%)

rewrite79.0ms (1.6%)

series113.0ms (2.2%)

simplify207.0ms (4.1%)

prune73.0ms (1.4%)

regimes467.0ms (9.1%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.6s (31.3%)

Profiling