Metrics for x / (x^2 + 1)

analyze24.0ms (1.1%)

Algorithm

1×	search
2×	egg-herbie

Rules

1× 1-exp_binary64 +-commutative_binary64

0× not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-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 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-*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	6	10
1	9	10
2	8	10
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
100%	0%	0%	2

Compiler

Compiled 8 to 6 computations (25% saved)

sample13.0ms (0.6%)

Algorithm

1×

intervals

Results

6.0ms

256×

body

128

valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify8.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1× 1-exp_binary64 +-commutative_binary64

0× not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same erfc-erf_binary64 erf-erfc_binary64 erf-odd_binary64 if-if-and-not_binary64 if-if-and_binary64 if-if-or-not_binary64 if-if-or_binary64 if-not_binary64 if-same_binary64 if-false_binary64 if-true_binary64 not-gte_binary64 not-lte_binary64 not-gt_binary64 not-lt_binary64 gte-same_binary64 lte-same_binary64 gt-same_binary64 lt-same_binary64 sinh---cosh_binary64 sinh-+-cosh_binary64 sinh-cosh_binary64 tanh-def-c_binary64 tanh-def-b_binary64 tanh-def-a_binary64 cosh-def_binary64 sinh-def_binary64 tan-neg_binary64 cos-neg_binary64 sin-neg_binary64 tan-0_binary64 cos-0_binary64 sin-0_binary64 hang-m-tan_binary64 hang-p-tan_binary64 hang-m0-tan_binary64 hang-p0-tan_binary64 hang-0m-tan_binary64 hang-0p-tan_binary64 tan-+PI/2_binary64 tan-+PI_binary64 tan-PI_binary64 tan-PI/3_binary64 tan-PI/4_binary64 tan-PI/6_binary64 cos-+PI/2_binary64 cos-+PI_binary64 cos-PI_binary64 cos-PI/2_binary64 cos-PI/3_binary64 cos-PI/4_binary64 cos-PI/6_binary64 sin-+PI/2_binary64 sin-+PI_binary64 sin-PI_binary64 sin-PI/2_binary64 sin-PI/3_binary64 sin-PI/4_binary64 sin-PI/6_binary64 sub-1-sin_binary64 sub-1-cos_binary64 -1-add-sin_binary64 -1-add-cos_binary64 1-sub-sin_binary64 1-sub-cos_binary64 cos-sin-sum_binary64 log-E_binary64 log-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 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-*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 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	9	10
2	8	10

prune1.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

15.5b

Counts

1 → 1

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

15.5b

(/.f64 x (+.f64 (*.f64 x x) 1))

rewrite39.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

15.4b

Rules

9×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `times-frac_binary64` `*-un-lft-identity_binary64`
3×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64` `associate-/r_binary64`
2×	`associate-/r/_binary64`
1×	`pow1_binary64` `div-exp_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64` `flip3-+_binary64` `flip-+_binary64`

Counts

1 → 29

Calls

1 calls:

6.0ms

(/.f64 x (+.f64 (*.f64 x x) 1))

Compiler

Compiled 460 to 236 computations (48.7% saved)

series15.0ms (0.7%)

Error

0b

Counts

1 → 6

Calls

1 calls:

10.0ms

(/.f64 x (+.f64 (*.f64 x x) 1))

Compiler

Compiled 87 to 73 computations (16.1% saved)

simplify108.0ms (5%)

Algorithm

1×	egg-herbie

Rules

577×	`distribute-rgt-in_binary64`
465×	`associate-+l+_binary64`
450×	`distribute-lft-in_binary64`
331×	`times-frac_binary64`
254×	`associate-/l*_binary64`
250×	`div-sub_binary64`
238×	`distribute-rgt-out_binary64`
201×	`associate-l_binary64`
154×	`associate-r_binary64`
136×	`associate-/r*_binary64`
131×	`associate-/l/_binary64`
119×	`unswap-sqr_binary64`
92×	`distribute-lft-out_binary64`
83×	`associate-*l/_binary64`
71×	`associate-/r/_binary64`
65×	`sub-neg_binary64`
58×	`associate-*r/_binary64`
57×	`associate-+r+_binary64`
56×	`*-commutative_binary64`
51×	`associate-+l-_binary64`
45×	`associate--l-_binary64`
41×	`associate--r+_binary64`
39×	`associate--l+_binary64`
37×	`cancel-sign-sub-inv_binary64`
33×	`-rgt-identity_binary64` `-lft-identity_binary64`
31×	`cube-prod_binary64` `distribute-neg-frac_binary64` `associate-+r-_binary64`
28×	`sqr-pow_binary64`
27×	`distribute-rgt-neg-in_binary64`
26×	`distribute-neg-in_binary64`
25×	`cube-div_binary64` `distribute-rgt1-in_binary64`
22×	`unpow3_binary64` `pow-plus_binary64` `neg-mul-1_binary64`
21×	`distribute-lft-neg-in_binary64` `distribute-lft1-in_binary64`
20×	`neg-sub0_binary64` `+-commutative_binary64`
19×	`associate--r-_binary64`
16×	`/-rgt-identity_binary64`
14×	`cube-mult_binary64`
12×	`log-div_binary64` `unsub-neg_binary64`
11×	`cube-unmult_binary64`
9×	`log-prod_binary64` `distribute-rgt-out--_binary64`
5×	`sub0-neg_binary64` `+-rgt-identity_binary64` `remove-double-div_binary64` `distribute-lft-neg-out_binary64`
4×	`log-rec_binary64` `--rgt-identity_binary64` `swap-sqr_binary64` `distribute-rgt-neg-out_binary64`
3×	`difference-of-sqr-1_binary64`
2×	`log-pow_binary64` `unpow2_binary64` `exp-prod_binary64` `mul-1-neg_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `pow-sqr_binary64`
1×	`unpow1/2_binary64` `unpow1_binary64` `exp-diff_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-sqrt-square_binary64` `remove-double-neg_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `count-2_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-neg_binary64` `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` `+-lft-identity_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `difference-of-sqr--1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-lft-out--_binary64`

Counts

35 → 27

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	64	585
1	137	535
2	332	535
3	733	535
4	2145	535
5	4565	535
6	4978	535
7	4980	535
8	4923	535

prune27.0ms (1.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	2	28

Error

15.4b

Counts

28 → 2

Compiler

Compiled 399 to 209 computations (47.6% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x))))
0.0b	(/.f64 (/.f64 x (sqrt.f64 (+.f64 1 (.f64 x x)))) (sqrt.f64 (+.f64 (.f64 x x) 1)))
15.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
15.5b	(sqrt.f64 (+.f64 1 (*.f64 x x)))

rewrite274.0ms (12.7%)

Algorithm

1×	rewrite-expression-head

Error

15.4b

Rules

288×	`times-frac_binary64`
164×	`add-sqr-sqrt_binary64`
162×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
156×	`sqrt-prod_binary64`
27×	`associate-/l*_binary64`
22×	`sqrt-div_binary64`
18×	`associate-/r/_binary64`
12×	`associate-/r*_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `flip3-+_binary64` `flip-+_binary64`
9×	`div-inv_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `div-exp_binary64` `cbrt-undiv_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `frac-2neg_binary64` `clear-num_binary64`
1×	`associate-/l/_binary64`

Counts

4 → 262

Calls

4 calls:

18.0ms	(/.f64 (/.f64 x (sqrt.f64 (+.f64 1 (.f64 x x)))) (sqrt.f64 (+.f64 (.f64 x x) 1)))
5.0ms	(/.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x))))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 x x)))

Compiler

Compiled 6679 to 3845 computations (42.4% saved)

series75.0ms (3.5%)

Error

15.4b

Counts

4 → 28

Calls

4 calls:

16.0ms	(sqrt.f64 (+.f64 1 (*.f64 x x)))
13.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
12.0ms	(/.f64 x (sqrt.f64 (+.f64 1 (*.f64 x x))))
10.0ms	(/.f64 (/.f64 x (sqrt.f64 (+.f64 1 (.f64 x x)))) (sqrt.f64 (+.f64 (.f64 x x) 1)))

Compiler

Compiled 983 to 746 computations (24.1% saved)

simplify333.0ms (15.4%)

Algorithm

1×	egg-herbie

Rules

804×	`times-frac_binary64`
491×	`associate-/l/_binary64`
435×	`associate-/l*_binary64`
358×	`associate-/r*_binary64`
229×	`associate-l_binary64`
207×	`unswap-sqr_binary64`
191×	`cancel-sign-sub-inv_binary64`
153×	`associate-r_binary64`
140×	`*-commutative_binary64`
131×	`associate-/r/_binary64`
129×	`associate-*l/_binary64`
123×	`distribute-rgt-neg-in_binary64`
108×	`cube-prod_binary64` `sub-neg_binary64`
103×	`log-prod_binary64` `div-sub_binary64`
100×	`log-div_binary64`
99×	`associate-*r/_binary64`
96×	`distribute-lft-neg-in_binary64`
88×	`cube-div_binary64`
75×	`distribute-neg-frac_binary64`
52×	`/-rgt-identity_binary64`
50×	`exp-prod_binary64`
48×	`*-rgt-identity_binary64`
47×	`distribute-rgt-in_binary64`
40×	`swap-sqr_binary64`
39×	`neg-mul-1_binary64` `neg-sub0_binary64`
38×	`distribute-lft-in_binary64`
36×	`distribute-rgt-out_binary64` `+-commutative_binary64`
34×	`*-lft-identity_binary64`
33×	`distribute-rgt-out--_binary64`
30×	`sqr-pow_binary64`
27×	`unpow3_binary64`
23×	`associate-+l-_binary64`
22×	`distribute-neg-in_binary64` `distribute-lft-out_binary64`
20×	`pow-plus_binary64` `cube-unmult_binary64`
19×	`log-rec_binary64`
18×	`associate-+r-_binary64`
16×	`cube-mult_binary64`
15×	`distribute-lft-neg-out_binary64`
13×	`unsub-neg_binary64` `difference-of-squares_binary64` `distribute-rgt1-in_binary64`
11×	`rem-sqrt-square_binary64` `sub0-neg_binary64` `+-rgt-identity_binary64`
10×	`distribute-rgt-neg-out_binary64`
9×	`associate-+l+_binary64`
7×	`log-pow_binary64`
6×	`distribute-lft-out--_binary64`
5×	`pow-sqr_binary64` `associate--l-_binary64` `associate--r+_binary64`
4×	`rem-square-sqrt_binary64` `remove-double-div_binary64` `associate--l+_binary64` `associate-+r+_binary64`
3×	`mul-1-neg_binary64` `remove-double-neg_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `distribute-lft1-in_binary64`
2×	`unpow2_binary64` `unpow1/2_binary64` `sqr-neg_binary64` `--rgt-identity_binary64` `div0_binary64` `associate--r-_binary64`
1×	`unpow1_binary64` `exp-diff_binary64` `exp-sum_binary64` `1-exp_binary64` `exp-1-e_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `sqr-abs_binary64` `distribute-neg-out_binary64` `count-2_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `+-lft-identity_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64`

Counts

290 → 238

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	299	10104
1	615	9217
2	1224	8705
3	3631	8537
4	4561	8524
5	4966	8524

prune118.0ms (5.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	238	2	240

Error

15.4b

Counts

240 → 2

Compiler

Compiled 3164 to 1842 computations (41.8% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.1b	(/.f64 1 (/.f64 (+.f64 1 (*.f64 x x)) x))
15.5b	(/.f64 (+.f64 1 (*.f64 x x)) x)

rewrite265.0ms (12.2%)

Algorithm

1×	rewrite-expression-head

Error

15.4b

Rules

84×	`times-frac_binary64`
52×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
16×	`associate-/r*_binary64`
15×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`div-exp_binary64`
6×	`div-inv_binary64` `associate-/l*_binary64`
4×	`cbrt-undiv_binary64`
3×	`pow1_binary64`
2×	`add-log-exp_binary64` `frac-2neg_binary64` `clear-num_binary64` `associate-/l/_binary64` `1-exp_binary64` `rec-exp_binary64`
1×	`flip3-+_binary64` `flip-+_binary64` `inv-pow_binary64` `pow-flip_binary64` `associate-/r/_binary64`

Counts

2 → 105

Calls

2 calls:

7.0ms	(/.f64 1 (/.f64 (+.f64 1 (*.f64 x x)) x))
5.0ms	(/.f64 (+.f64 1 (*.f64 x x)) x)

Compiler

Compiled 2076 to 1251 computations (39.7% saved)

series26.0ms (1.2%)

Error

0b

Counts

2 → 12

Calls

2 calls:

11.0ms	(/.f64 (+.f64 1 (*.f64 x x)) x)
9.0ms	(/.f64 1 (/.f64 (+.f64 1 (*.f64 x x)) x))

Compiler

Compiled 152 to 129 computations (15.1% saved)

simplify151.0ms (7%)

Algorithm

1×	egg-herbie

Rules

398×	`times-frac_binary64`
361×	`sub-neg_binary64`
343×	`div-sub_binary64`
290×	`distribute-rgt-in_binary64`
245×	`distribute-lft-in_binary64`
234×	`associate-/l*_binary64`
227×	`associate-/r/_binary64`
216×	`+-commutative_binary64`
211×	`associate-/r*_binary64`
200×	`associate-/l/_binary64`
180×	`associate-*l/_binary64`
175×	`associate-l_binary64`
163×	`distribute-rgt-out_binary64`
146×	`cancel-sign-sub-inv_binary64`
138×	`associate-+l-_binary64`
133×	`*-commutative_binary64`
132×	`associate-*r/_binary64`
131×	`associate-r_binary64` `associate-+r+_binary64`
116×	`unsub-neg_binary64`
115×	`associate--l+_binary64`
97×	`distribute-neg-in_binary64`
92×	`associate-+l+_binary64`
91×	`distribute-lft-out_binary64`
87×	`neg-mul-1_binary64`
73×	`neg-sub0_binary64`
70×	`distribute-rgt-neg-in_binary64`
64×	`associate--l-_binary64`
61×	`*-rgt-identity_binary64`
56×	`associate-+r-_binary64`
52×	`unswap-sqr_binary64`
49×	`sqr-pow_binary64`
46×	`associate--r+_binary64`
41×	`distribute-lft-neg-in_binary64`
34×	`*-lft-identity_binary64` `distribute-rgt1-in_binary64` `associate--r-_binary64`
33×	`distribute-neg-frac_binary64` `distribute-rgt-out--_binary64`
32×	`/-rgt-identity_binary64`
25×	`exp-prod_binary64`
22×	`distribute-lft-neg-out_binary64`
21×	`cube-prod_binary64` `distribute-lft1-in_binary64`
17×	`log-div_binary64`
16×	`exp-sum_binary64` `swap-sqr_binary64`
14×	`log-prod_binary64` `sub0-neg_binary64`
13×	`cube-div_binary64` `+-rgt-identity_binary64`
12×	`distribute-rgt-neg-out_binary64`
11×	`remove-double-div_binary64`
9×	`+-lft-identity_binary64`
8×	`rem-sqrt-square_binary64`
7×	`exp-diff_binary64` `cube-unmult_binary64` `--rgt-identity_binary64` `pow-sqr_binary64`
6×	`log-rec_binary64` `unpow3_binary64` `unpow1/2_binary64` `pow-plus_binary64` `difference-of-squares_binary64`
5×	`distribute-lft-out--_binary64`
3×	`cube-mult_binary64` `mul-1-neg_binary64` `mul0-rgt_binary64` `distribute-neg-out_binary64`
2×	`mul0-lft_binary64` `div0_binary64` `lft-mult-inverse_binary64` `difference-of-sqr-1_binary64` `distribute-frac-neg_binary64`
1×	`unpow2_binary64` `unpow1_binary64` `1-exp_binary64` `exp-1-e_binary64` `remove-double-neg_binary64` `+-inverses_binary64` `count-2_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-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` `*-inverses_binary64` `rgt-mult-inverse_binary64` `difference-of-sqr--1_binary64` `cancel-sign-sub_binary64`

Counts

117 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	134	2472
1	302	2244
2	874	2223
3	2207	2223
4	3352	2223
5	4206	2223
6	4956	2223

prune33.0ms (1.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	71	2	73

Error

15.4b

Counts

73 → 2

Compiler

Compiled 772 to 438 computations (43.3% saved)

regimes178.0ms (8.3%)

Accuracy

Total -14.8b remaining (-14768.2%)

Threshold costs -14.8b (-14768.2%)

Compiler

Compiled 1801 to 1266 computations (29.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1× 1-exp_binary64 +-commutative_binary64

0× not-true not-false not-not not-and not-or and-true-l and-true-r and-false-l and-false-r and-same or-true-l or-true-r or-false-l or-false-r or-same 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 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	10
1	9	10
2	8	10

end1.0ms (0%)

Compiler: Compiled 7 to 6 computations (14.3% saved)

sample450.0ms (20.8%)

Algorithm

1×

intervals

Results

176.0ms

8000×

body

128

valid

Compiler

Compiled 49 to 42 computations (14.3% saved)

Details

analyze24.0ms (1.1%)

sample13.0ms (0.6%)

simplify8.0ms (0.4%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

rewrite39.0ms (1.8%)

series15.0ms (0.7%)

simplify108.0ms (5%)

prune27.0ms (1.3%)

localize8.0ms (0.4%)

rewrite274.0ms (12.7%)

series75.0ms (3.5%)

simplify333.0ms (15.4%)

prune118.0ms (5.5%)

localize7.0ms (0.3%)

rewrite265.0ms (12.2%)

series26.0ms (1.2%)

simplify151.0ms (7%)

prune33.0ms (1.5%)

regimes178.0ms (8.3%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample450.0ms (20.8%)

Profiling