Details

analyze22.0ms (1.6%)

Algorithm

1×	search
2×	egg-herbie

Rules

2×	`associate-l_binary64` `*-commutative_binary64`
1×	`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	5	7
1	7	7
2	10	7
3	10	7
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
50%	25%	25%	4
62.5%	12.5%	25%	5
68.7%	6.2%	25%	6
71.8%	3.1%	25%	7
73.4%	1.6%	25%	8
74.2%	0.8%	25%	9
74.6%	0.4%	25%	10
74.8%	0.2%	25%	11
74.9%	0.1%	25%	12
74.9%	0%	25.1%	13
74.9%	0%	25.1%	14

Compiler

Compiled 6 to 5 computations (16.7% saved)

sample10.0ms (0.7%)

Algorithm

1×

intervals

Results

4.0ms

256×

body

128

valid

Compiler

Compiled 11 to 10 computations (9.1% saved)

simplify8.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

2×	`associate-l_binary64` `*-commutative_binary64`
1×	`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	7	7
2	10	7
3	10	7

prune7.0ms (0.5%)

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 3) x)

rewrite20.0ms (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` `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 3) x)

Compiler

Compiled 170 to 109 computations (35.9% saved)

series8.0ms (0.6%)

Error

0.1b

Counts

1 → 3

Calls

1 calls:

7.0ms

(*.f64 (*.f64 x 3) x)

Compiler

Compiled 35 to 35 computations (0% saved)

simplify68.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

496×	`associate-/r*_binary64`
445×	`times-frac_binary64`
318×	`associate-l_binary64`
300×	`log-div_binary64`
265×	`log-prod_binary64`
257×	`sqr-pow_binary64`
211×	`*-commutative_binary64`
184×	`associate-r_binary64`
165×	`associate-/l*_binary64`
142×	`unswap-sqr_binary64`
140×	`associate-+l+_binary64`
126×	`pow-sqr_binary64`
118×	`distribute-rgt-in_binary64`
117×	`cube-prod_binary64`
112×	`associate-/l/_binary64`
108×	`exp-prod_binary64` `distribute-lft-in_binary64` `associate-/r/_binary64`
101×	`+-commutative_binary64`
95×	`distribute-rgt-out_binary64`
91×	`associate-+r+_binary64`
66×	`distribute-lft-out_binary64`
60×	`associate-*r/_binary64`
46×	`swap-sqr_binary64`
32×	`unpow3_binary64` `rem-sqrt-square_binary64` `*-lft-identity_binary64`
28×	`log-pow_binary64` `cube-div_binary64` `*-rgt-identity_binary64`
27×	`cube-mult_binary64`
25×	`count-2_binary64`
24×	`associate-*l/_binary64`
20×	`pow-plus_binary64`
17×	`distribute-rgt1-in_binary64`
10×	`log-rec_binary64`
9×	`unpow1/2_binary64`
8×	`prod-exp_binary64`
7×	`distribute-lft1-in_binary64`
6×	`exp-lft-cube_binary64`
5×	`cube-unmult_binary64`
3×	`unpow2_binary64`
2×	`exp-lft-sqr_binary64` `exp-sqrt_binary64` `/-rgt-identity_binary64` `remove-double-div_binary64`
1×	`unpow1_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-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` `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` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+l-_binary64` `associate-+r-_binary64`

Counts

21 → 17

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	215
1	87	179
2	278	170
3	551	168
4	796	168
5	1471	168
6	2549	168
7	4446	168
8	4931	168

prune15.0ms (1.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	12	5	17
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	6	18

Error

0.0b

Counts

18 → 6

Compiler

Compiled 134 to 87 computations (35.1% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.2b	(.f64 3 (.f64 x x))

rewrite20.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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:

6.0ms

(*.f64 3 (*.f64 x x))

Compiler

Compiled 172 to 101 computations (41.3% saved)

series8.0ms (0.6%)

Error

0.0b

Counts

1 → 3

Calls

1 calls:

7.0ms

(*.f64 3 (*.f64 x x))

Compiler

Compiled 35 to 35 computations (0% saved)

simplify69.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

701×	`associate-/l/_binary64`
568×	`associate-/r/_binary64`
384×	`distribute-rgt-in_binary64`
347×	`distribute-lft-in_binary64`
212×	`*-commutative_binary64`
196×	`sqr-pow_binary64`
171×	`times-frac_binary64`
165×	`associate-l_binary64`
124×	`unswap-sqr_binary64`
122×	`associate-r_binary64`
120×	`associate-/l*_binary64`
116×	`associate-+l+_binary64`
95×	`pow-sqr_binary64`
88×	`distribute-rgt-out_binary64`
73×	`associate-+r+_binary64`
69×	`exp-prod_binary64`
61×	`log-prod_binary64`
59×	`cube-prod_binary64`
48×	`distribute-lft-out_binary64` `associate-/r*_binary64`
42×	`log-div_binary64`
39×	`associate-*r/_binary64`
30×	`count-2_binary64`
27×	`log-pow_binary64`
26×	`unpow3_binary64`
21×	`cube-mult_binary64`
19×	`associate-*l/_binary64`
18×	`swap-sqr_binary64`
17×	`pow-plus_binary64` `*-lft-identity_binary64`
16×	`+-commutative_binary64`
13×	`distribute-rgt1-in_binary64`
10×	`*-rgt-identity_binary64`
9×	`distribute-lft1-in_binary64`
7×	`prod-exp_binary64` `cube-unmult_binary64`
4×	`/-rgt-identity_binary64`
3×	`unpow2_binary64` `exp-lft-cube_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-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-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

22 → 11

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	225
1	74	189
2	172	180
3	415	180
4	626	180
5	1022	180
6	1992	180
7	4963	180
8	4886	180

prune11.0ms (0.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	10	1	11
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	10	7	17

Error

0.0b

Counts

17 → 7

Compiler

Compiled 96 to 73 computations (24% saved)

localize6.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 3 (.f64 x x))
0.3b	(.f64 (sqrt.f64 (.f64 3 (.f64 x x))) (sqrt.f64 (.f64 3 (*.f64 x x))))
21.8b	(sqrt.f64 (.f64 3 (.f64 x x)))
21.8b	(sqrt.f64 (.f64 3 (.f64 x x)))

rewrite115.0ms (8.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

148×	`pow1_binary64`
80×	`pow-prod-down_binary64`
66×	`sqrt-pow1_binary64`
17×	`pow-prod-up_binary64`
14×	`pow1/2_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `pow-sqr_binary64`
9×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
7×	`associate-l_binary64`
6×	`sqrt-prod_binary64`
5×	`associate-r_binary64`
4×	`add-log-exp_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `swap-sqr_binary64`
2×	`unswap-sqr_binary64` `*-commutative_binary64`
1×	`pow2_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `rem-square-sqrt_binary64`

Counts

4 → 109

Calls

4 calls:

14.0ms	(.f64 (sqrt.f64 (.f64 3 (.f64 x x))) (sqrt.f64 (.f64 3 (*.f64 x x))))
5.0ms	(.f64 3 (.f64 x x))
4.0ms	(sqrt.f64 (.f64 3 (.f64 x x)))
4.0ms	(sqrt.f64 (.f64 3 (.f64 x x)))

Compiler

Compiled 1308 to 782 computations (40.2% saved)

series44.0ms (3.1%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

11.0ms	(.f64 (sqrt.f64 (.f64 3 (.f64 x x))) (sqrt.f64 (.f64 3 (*.f64 x x))))
8.0ms	(sqrt.f64 (.f64 3 (.f64 x x)))
8.0ms	(sqrt.f64 (.f64 3 (.f64 x x)))
8.0ms	(.f64 3 (.f64 x x))

Compiler

Compiled 335 to 280 computations (16.4% saved)

simplify116.0ms (8.2%)

Algorithm

1×	egg-herbie

Rules

545×	`associate-r_binary64`
378×	`unswap-sqr_binary64`
317×	`sqr-pow_binary64`
282×	`associate-/l*_binary64`
225×	`associate-/l/_binary64`
197×	`associate-/r/_binary64`
196×	`log-prod_binary64`
134×	`distribute-rgt-in_binary64` `*-commutative_binary64`
123×	`exp-prod_binary64`
115×	`pow-sqr_binary64`
108×	`distribute-lft-in_binary64`
93×	`swap-sqr_binary64`
92×	`cube-prod_binary64`
90×	`+-commutative_binary64`
86×	`associate-l_binary64`
68×	`distribute-lft-out_binary64`
59×	`log-div_binary64`
55×	`associate-+l+_binary64`
52×	`associate-+r+_binary64`
42×	`distribute-rgt-out_binary64`
39×	`times-frac_binary64`
37×	`pow-plus_binary64`
36×	`associate-*r/_binary64`
35×	`log-pow_binary64` `rem-sqrt-square_binary64`
32×	`unpow3_binary64`
29×	`*-lft-identity_binary64` `distribute-rgt-neg-in_binary64`
27×	`cube-mult_binary64`
23×	`distribute-lft-neg-in_binary64` `count-2_binary64`
18×	`associate-/r*_binary64`
17×	`neg-sub0_binary64`
15×	`neg-mul-1_binary64`
13×	`sub-neg_binary64` `*-rgt-identity_binary64`
9×	`unpow1/2_binary64` `cube-unmult_binary64`
7×	`unpow2_binary64` `prod-exp_binary64`
6×	`cube-div_binary64` `cancel-sign-sub-inv_binary64`
5×	`unpow1_binary64` `distribute-rgt1-in_binary64`
4×	`exp-lft-cube_binary64` `rem-square-sqrt_binary64` `unsub-neg_binary64`
2×	`log-rec_binary64` `mul-1-neg_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `distribute-lft-neg-out_binary64` `distribute-lft1-in_binary64`
1×	`exp-sqrt_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `/-rgt-identity_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` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-sqr_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-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-neg-out_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `associate-l/_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+r-_binary64`

Counts

121 → 91

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	78	1061
1	134	907
2	402	884
3	1226	871
4	2319	772
5	3072	772
6	4889	772
7	4997	772

prune41.0ms (2.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	91	7	98

Error

0.0b

Counts

98 → 7

Compiler

Compiled 527 to 345 computations (34.5% saved)

localize9.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 x 3) x)
0.3b	(.f64 (sqrt.f64 (.f64 3 (.f64 x x))) (sqrt.f64 (.f64 (*.f64 x 3) x)))
21.8b	(sqrt.f64 (.f64 (.f64 x 3) x))
21.8b	(sqrt.f64 (.f64 3 (.f64 x x)))

rewrite96.0ms (6.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

59×	`pow1_binary64`
38×	`pow-prod-down_binary64`
24×	`sqrt-pow1_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64` `-un-lft-identity_binary64` `associate-r*_binary64`
5×	`associate-l_binary64`
4×	`pow1/2_binary64` `add-log-exp_binary64` `sqrt-prod_binary64` `prod-exp_binary64` `cbrt-unprod_binary64`
2×	`*-commutative_binary64`
1×	`sqrt-unprod_binary64` `unswap-sqr_binary64`

Counts

4 → 73

Calls

4 calls:

13.0ms	(.f64 (sqrt.f64 (.f64 3 (.f64 x x))) (sqrt.f64 (.f64 (*.f64 x 3) x)))
6.0ms	(.f64 (.f64 x 3) x)
4.0ms	(sqrt.f64 (.f64 3 (.f64 x x)))
3.0ms	(sqrt.f64 (.f64 (.f64 x 3) x))

Compiler

Compiled 1130 to 733 computations (35.1% saved)

series43.0ms (3%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

12.0ms	(.f64 (sqrt.f64 (.f64 3 (.f64 x x))) (sqrt.f64 (.f64 (*.f64 x 3) x)))
8.0ms	(sqrt.f64 (.f64 3 (.f64 x x)))
8.0ms	(sqrt.f64 (.f64 (.f64 x 3) x))
8.0ms	(.f64 (.f64 x 3) x)

Compiler

Compiled 335 to 282 computations (15.8% saved)

simplify105.0ms (7.4%)

Algorithm

1×	egg-herbie

Rules

898×	`unswap-sqr_binary64`
412×	`associate-+l+_binary64`
281×	`associate-+r+_binary64`
279×	`*-commutative_binary64`
217×	`associate-*r/_binary64`
215×	`distribute-rgt-in_binary64`
207×	`sqr-pow_binary64` `associate-/l*_binary64`
191×	`distribute-lft-in_binary64`
174×	`associate-*l/_binary64`
167×	`associate-/l/_binary64`
138×	`associate-l_binary64`
129×	`associate-/r/_binary64`
106×	`log-div_binary64`
101×	`associate-r_binary64`
92×	`pow-sqr_binary64`
72×	`exp-prod_binary64` `associate-/r*_binary64`
69×	`log-prod_binary64`
61×	`cube-prod_binary64`
49×	`swap-sqr_binary64`
47×	`distribute-rgt-out_binary64` `distribute-lft-out_binary64`
33×	`times-frac_binary64`
30×	`rem-sqrt-square_binary64` `+-commutative_binary64`
23×	`distribute-rgt-neg-in_binary64`
21×	`distribute-lft-neg-in_binary64`
18×	`unpow3_binary64`
17×	`*-lft-identity_binary64` `distribute-rgt1-in_binary64` `count-2_binary64`
16×	`pow-plus_binary64` `*-rgt-identity_binary64`
12×	`cube-unmult_binary64`
11×	`log-pow_binary64` `neg-sub0_binary64`
10×	`sub-neg_binary64`
9×	`neg-mul-1_binary64` `distribute-lft1-in_binary64`
8×	`unpow1/2_binary64` `cube-mult_binary64`
6×	`log-rec_binary64` `prod-exp_binary64`
4×	`rem-square-sqrt_binary64` `unsub-neg_binary64`
3×	`unpow2_binary64` `unpow1_binary64` `exp-lft-cube_binary64` `cube-div_binary64` `cancel-sign-sub-inv_binary64`
2×	`mul-1-neg_binary64` `mul0-rgt_binary64` `mul0-lft_binary64`
1×	`exp-lft-sqr_binary64` `exp-sqrt_binary64` `1-exp_binary64` `exp-1-e_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` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_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` `/-rgt-identity_binary64` `remove-double-neg_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `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-out--_binary64` `distribute-lft-out--_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+r-_binary64`

Counts

85 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	975
1	142	853
2	443	724
3	696	722
4	1324	722
5	2816	722
6	4953	722
7	5029	722

prune44.0ms (3.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	67	7	74

Error

0.0b

Counts

74 → 7

Compiler

Compiled 620 to 441 computations (28.9% saved)

regimes94.0ms (6.6%)

Accuracy

Total 0.2b remaining (91.9%)

Threshold costs 0.2b (91.9%)

Compiler

Compiled 855 to 672 computations (21.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1× *-commutative_binary64

0× not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 unpow1_binary64 e-exp-1_binary64 1-exp_binary64 exp-1-e_binary64 exp-0_binary64 sqr-abs_binary64 sqr-neg_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64 +-commutative_binary64

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	7	7
2	7	7

end1.0ms (0%)

Compiler: Compiled 5 to 5 computations (0% saved)

sample429.0ms (30.2%)

Algorithm

1×

intervals

Results

130.0ms

8000×

body

128

valid

Compiler

Compiled 72 to 63 computations (12.5% saved)

Details

analyze22.0ms (1.6%)

sample10.0ms (0.7%)

simplify8.0ms (0.6%)

prune7.0ms (0.5%)

localize3.0ms (0.2%)

rewrite20.0ms (1.4%)

series8.0ms (0.6%)

simplify68.0ms (4.8%)

prune15.0ms (1.1%)

localize3.0ms (0.2%)

rewrite20.0ms (1.4%)

series8.0ms (0.6%)

simplify69.0ms (4.9%)

prune11.0ms (0.8%)

localize6.0ms (0.4%)

rewrite115.0ms (8.1%)

series44.0ms (3.1%)

simplify116.0ms (8.2%)

prune41.0ms (2.9%)

localize9.0ms (0.6%)

rewrite96.0ms (6.8%)

series43.0ms (3%)

simplify105.0ms (7.4%)

prune44.0ms (3.1%)

regimes94.0ms (6.6%)

bsearch0.0ms (0%)

simplify3.0ms (0.2%)

end1.0ms (0%)

sample429.0ms (30.2%)

Profiling