Details

analyze731.0ms (1.9%)

Algorithm

1×	search
2×	egg-herbie

Rules

669×	`div-sub_binary64`
601×	`associate-/l*_binary64`
488×	`associate-/r*_binary64`
279×	`distribute-rgt-in_binary64`
273×	`associate-/l/_binary64`
259×	`distribute-lft-in_binary64`
239×	`associate-/r/_binary64`
156×	`associate-*l/_binary64`
115×	`cancel-sign-sub-inv_binary64`
112×	`distribute-rgt-neg-in_binary64`
102×	`distribute-lft-neg-in_binary64`
87×	`unswap-sqr_binary64`
75×	`distribute-neg-frac_binary64`
72×	`associate-r_binary64`
71×	`associate-l_binary64`
51×	`times-frac_binary64`
41×	`sub-neg_binary64`
39×	`unpow3_binary64`
36×	`*-commutative_binary64`
34×	`cube-mult_binary64`
27×	`exp-prod_binary64`
26×	`distribute-rgt-out_binary64`
25×	`cube-div_binary64`
24×	`sqr-pow_binary64`
22×	`neg-sub0_binary64`
21×	`neg-mul-1_binary64`
19×	`rem-sqrt-square_binary64`
17×	`distribute-neg-in_binary64`
16×	`cube-prod_binary64`
15×	`+-commutative_binary64`
14×	`pow-plus_binary64` `distribute-lft-out_binary64`
12×	`prod-exp_binary64` `distribute-lft-neg-out_binary64`
11×	`pow-sqr_binary64`
9×	`cube-unmult_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `distribute-rgt-neg-out_binary64`
8×	`div-exp_binary64` `unsub-neg_binary64` `mul-1-neg_binary64`
7×	`associate-*r/_binary64` `associate-+l+_binary64` `associate-+r+_binary64`
6×	`exp-lft-sqr_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64`
5×	`exp-sqrt_binary64` `swap-sqr_binary64`
4×	`/-rgt-identity_binary64` `*-inverses_binary64`
3×	`rec-exp_binary64` `sub0-neg_binary64` `distribute-frac-neg_binary64` `associate--r+_binary64`
2×	`remove-double-neg_binary64` `cancel-sign-sub_binary64` `distribute-rgt1-in_binary64` `associate-+l-_binary64`
1×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `exp-neg_binary64` `exp-sum_binary64` `1-exp_binary64` `exp-1-e_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-inverses_binary64` `distribute-lft-out--_binary64` `count-2_binary64` `associate-+r-_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `exp-diff_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` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-squares_binary64` `distribute-neg-out_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	23	19
2	32	19
3	55	19
4	116	11
5	296	8
6	987	8
7	4258	8
8	4892	8
9	4840	8
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.3%	24.4%	11
31.4%	44.3%	24.4%	12
31.4%	44%	24.5%	13
31.5%	43.8%	24.8%	14

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample54.0ms (0.1%)

Algorithm

1×

intervals

Results

21.0ms	80×	body	1024	valid
9.0ms	37×	body	512	valid
5.0ms	13×	body	2048	valid
5.0ms	108×	body	128	valid
2.0ms	18×	body	256	valid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify65.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

669×	`div-sub_binary64`
601×	`associate-/l*_binary64`
488×	`associate-/r*_binary64`
279×	`distribute-rgt-in_binary64`
273×	`associate-/l/_binary64`
259×	`distribute-lft-in_binary64`
239×	`associate-/r/_binary64`
156×	`associate-*l/_binary64`
115×	`cancel-sign-sub-inv_binary64`
112×	`distribute-rgt-neg-in_binary64`
102×	`distribute-lft-neg-in_binary64`
87×	`unswap-sqr_binary64`
75×	`distribute-neg-frac_binary64`
72×	`associate-r_binary64`
71×	`associate-l_binary64`
51×	`times-frac_binary64`
41×	`sub-neg_binary64`
39×	`unpow3_binary64`
36×	`*-commutative_binary64`
34×	`cube-mult_binary64`
27×	`exp-prod_binary64`
26×	`distribute-rgt-out_binary64`
25×	`cube-div_binary64`
24×	`sqr-pow_binary64`
22×	`neg-sub0_binary64`
21×	`neg-mul-1_binary64`
19×	`rem-sqrt-square_binary64`
17×	`distribute-neg-in_binary64`
16×	`cube-prod_binary64`
15×	`+-commutative_binary64`
14×	`pow-plus_binary64` `distribute-lft-out_binary64`
12×	`prod-exp_binary64` `distribute-lft-neg-out_binary64`
11×	`pow-sqr_binary64`
9×	`cube-unmult_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `distribute-rgt-neg-out_binary64`
8×	`div-exp_binary64` `unsub-neg_binary64` `mul-1-neg_binary64`
7×	`associate-*r/_binary64` `associate-+l+_binary64` `associate-+r+_binary64`
6×	`exp-lft-sqr_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64`
5×	`exp-sqrt_binary64` `swap-sqr_binary64`
4×	`/-rgt-identity_binary64` `*-inverses_binary64`
3×	`rec-exp_binary64` `sub0-neg_binary64` `distribute-frac-neg_binary64` `associate--r+_binary64`
2×	`remove-double-neg_binary64` `cancel-sign-sub_binary64` `distribute-rgt1-in_binary64` `associate-+l-_binary64`
1×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `exp-neg_binary64` `exp-sum_binary64` `1-exp_binary64` `exp-1-e_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-inverses_binary64` `distribute-lft-out--_binary64` `count-2_binary64` `associate-+r-_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `exp-diff_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` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-squares_binary64` `distribute-neg-out_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	23	19
2	32	19
3	55	19
4	116	11
5	296	8
6	987	8
7	4258	8
8	4892	8
9	4840	8

prune7.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.3b

Counts

2 → 1

Compiler

Compiled 10 to 10 computations (0% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 1 (exp.f64 x))
0.2b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

rewrite46.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

7×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64` `add-sqr-sqrt_binary64` `sqrt-prod_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64`
2×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `flip3-+_binary64` `sqrt-div_binary64` `flip-+_binary64` `distribute-lft-out_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

2 → 28

Calls

2 calls:

5.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
3.0ms	(+.f64 1 (exp.f64 x))

Compiler

Compiled 293 to 198 computations (32.4% saved)

series41.0ms (0.1%)

Error

0.2b

Counts

2 → 12

Calls

2 calls:

21.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
6.0ms	(+.f64 1 (exp.f64 x))

Compiler

Compiled 307 to 283 computations (7.8% saved)

simplify48.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

733×	`times-frac_binary64`
663×	`associate-/l*_binary64`
177×	`associate-/r/_binary64`
161×	`associate-+l+_binary64`
153×	`distribute-neg-frac_binary64`
147×	`distribute-rgt-out_binary64`
137×	`associate-/l/_binary64`
136×	`distribute-rgt-neg-in_binary64`
131×	`distribute-lft-neg-in_binary64`
101×	`associate-r_binary64`
94×	`distribute-rgt-in_binary64`
87×	`associate--l+_binary64`
86×	`distribute-lft-out_binary64`
83×	`sub-neg_binary64`
82×	`associate-+r+_binary64`
81×	`associate-l_binary64`
78×	`+-commutative_binary64`
70×	`cancel-sign-sub-inv_binary64`
68×	`distribute-rgt-out--_binary64`
62×	`distribute-lft-in_binary64`
54×	`associate-/r_binary64` `-commutative_binary64`
48×	`associate-*l/_binary64`
46×	`associate-*r/_binary64`
36×	`neg-mul-1_binary64` `neg-sub0_binary64` `sqr-pow_binary64` `unswap-sqr_binary64`
33×	`unsub-neg_binary64`
28×	`distribute-lft-out--_binary64`
15×	`exp-prod_binary64`
14×	`distribute-rgt1-in_binary64`
13×	`associate--r+_binary64` `associate-+r-_binary64`
12×	`+-rgt-identity_binary64` `associate-+l-_binary64`
8×	`cube-prod_binary64`
7×	`log-prod_binary64` `cube-unmult_binary64`
6×	`*-lft-identity_binary64` `distribute-lft1-in_binary64`
5×	`div-sub_binary64` `sub0-neg_binary64` `pow-sqr_binary64`
4×	`unpow3_binary64` `pow-plus_binary64` `prod-exp_binary64` `*-rgt-identity_binary64` `distribute-neg-in_binary64`
3×	`cube-mult_binary64` `rem-sqrt-square_binary64` `count-2_binary64`
2×	`unpow1/2_binary64` `rem-square-sqrt_binary64` `swap-sqr_binary64` `cancel-sign-sub_binary64` `distribute-lft-neg-out_binary64`
1×	`unpow2_binary64` `unpow1_binary64` `1-exp_binary64` `exp-1-e_binary64` `difference-of-sqr-1_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `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-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` `mul-1-neg_binary64` `/-rgt-identity_binary64` `remove-double-neg_binary64` `--rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-squares_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt-neg-out_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

40 → 27

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	86	545
1	211	521
2	543	490
3	1892	484
4	5074	484

prune28.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	25	3	28

Error

0.2b

Counts

28 → 3

Compiler

Compiled 355 to 271 computations (23.7% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(/.f64 1/16 (pow.f64 (sqrt.f64 2) 5))
1.6b	(pow.f64 (sqrt.f64 2) 5)
11.8b	(+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16))
15.4b	(+.f64 (+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))

rewrite380.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

30×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64` `unpow-prod-down_binary64` `times-frac_binary64`
27×	`add-log-exp_binary64`
22×	`associate-*l/_binary64`
18×	`frac-add_binary64`
16×	`sum-log_binary64`
15×	`sqrt-prod_binary64`
10×	`add-exp-log_binary64` `associate-/r*_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`pow1_binary64` `add-cbrt-cube_binary64`
5×	`sqr-pow_binary64`
4×	`associate-*r/_binary64`
3×	`pow-unpow_binary64` `pow-pow_binary64` `div-exp_binary64` `associate-/l*_binary64`
2×	`associate-+l+_binary64` `+-commutative_binary64` `pow-to-exp_binary64` `pow-exp_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `sqrt-pow2_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

4 → 119

Calls

4 calls:

19.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))
14.0ms	(+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16))
6.0ms	(/.f64 1/16 (pow.f64 (sqrt.f64 2) 5))
3.0ms	(pow.f64 (sqrt.f64 2) 5)

Compiler

Compiled 7773 to 7012 computations (9.8% saved)

series73.0ms (0.2%)

Error

0.2b

Counts

4 → 16

Calls

4 calls:

30.0ms	(+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16))
27.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2))))) (.f64 1/2 (/.f64 x (sqrt.f64 2)))) (.f64 (.f64 (/.f64 x (sqrt.f64 2)) x) 3/16)) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))
0.0ms	(pow.f64 (sqrt.f64 2) 5)
0.0ms	(/.f64 1/16 (pow.f64 (sqrt.f64 2) 5))

Compiler

Compiled 862 to 797 computations (7.5% saved)

simplify163.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

355×	`cancel-sign-sub-inv_binary64`
313×	`times-frac_binary64`
255×	`associate-r_binary64`
244×	`associate-l_binary64`
225×	`distribute-rgt-neg-in_binary64`
172×	`distribute-rgt-in_binary64`
155×	`distribute-lft-in_binary64`
148×	`*-commutative_binary64`
103×	`sqr-pow_binary64`
86×	`distribute-neg-in_binary64`
84×	`sub-neg_binary64`
77×	`exp-prod_binary64` `unswap-sqr_binary64`
75×	`+-commutative_binary64`
69×	`associate-+l+_binary64`
61×	`distribute-neg-frac_binary64`
58×	`cube-prod_binary64`
54×	`neg-mul-1_binary64` `neg-sub0_binary64` `distribute-lft-neg-out_binary64`
52×	`associate-/r*_binary64`
49×	`associate-*r/_binary64`
48×	`associate-+r+_binary64`
42×	`associate-*l/_binary64`
37×	`associate-/l*_binary64`
34×	`distribute-lft-neg-in_binary64`
33×	`swap-sqr_binary64`
27×	`exp-sum_binary64`
26×	`cube-div_binary64`
22×	`prod-exp_binary64`
21×	`unpow3_binary64`
19×	`cube-mult_binary64` `unsub-neg_binary64`
18×	`distribute-rgt-neg-out_binary64` `associate--l+_binary64`
15×	`associate-/l/_binary64`
11×	`pow-sqr_binary64`
10×	`associate--r+_binary64`
8×	`log-prod_binary64` `distribute-rgt-out--_binary64`
7×	`*-rgt-identity_binary64` `associate-/r/_binary64`
6×	`cube-unmult_binary64`
4×	`log-pow_binary64` `log-div_binary64` `difference-of-squares_binary64` `associate-+l-_binary64` `associate-+r-_binary64`
3×	`unpow1/2_binary64` `rem-sqrt-square_binary64`
2×	`pow-plus_binary64` `unpow1_binary64` `/-rgt-identity_binary64` `distribute-lft-out_binary64`
1×	`log-rec_binary64` `unpow2_binary64` `1-exp_binary64` `rem-square-sqrt_binary64` `div-sub_binary64` `*-lft-identity_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` `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` `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` `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` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out_binary64` `count-2_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

135 → 92

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	282	6819
1	745	6259
2	3026	6253
3	4973	6253

prune169.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	92	3	95

Error

0.2b

Counts

95 → 3

Compiler

Compiled 4532 to 4099 computations (9.6% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

14.4b	(cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))))
14.4b	(cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))))
14.4b	(cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))))
15.4b	(+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16)))))) (cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16))))))) (cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16))))))) (.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))

rewrite927.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

60×	`cbrt-div_binary64`
40×	`associate-*l/_binary64`
31×	`flip3-+_binary64` `flip-+_binary64`
28×	`frac-times_binary64`
26×	`frac-add_binary64`
13×	`*-un-lft-identity_binary64`
12×	`cbrt-prod_binary64`
8×	`associate-*r/_binary64`
7×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`add-log-exp_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64` `distribute-lft-out_binary64`
1×	`sum-log_binary64` `+-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

167.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16)))))) (cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16))))))) (cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16))))))) (.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))
53.0ms	(cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))))
52.0ms	(cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))))
48.0ms	(cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))))

Compiler

Compiled 17579 to 15874 computations (9.7% saved)

series425.0ms (1.1%)

Error

0.2b

Counts

4 → 32

Calls

4 calls:

96.0ms	(cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))))
94.0ms	(cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))))
92.0ms	(cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))))
32.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16)))))) (cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16))))))) (cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16))))))) (.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))

Compiler

Compiled 8295 to 7744 computations (6.6% saved)

simplify367.0ms (1%)

Algorithm

1×	egg-herbie

Rules

858×	`distribute-rgt-in_binary64`
295×	`cancel-sign-sub-inv_binary64`
292×	`associate-l_binary64`
261×	`times-frac_binary64`
253×	`associate-r_binary64`
205×	`*-commutative_binary64`
147×	`distribute-rgt-neg-in_binary64`
131×	`distribute-lft-neg-in_binary64`
124×	`unswap-sqr_binary64`
87×	`+-commutative_binary64`
80×	`distribute-lft-in_binary64`
79×	`sub-neg_binary64`
71×	`sqr-pow_binary64`
56×	`distribute-neg-in_binary64`
53×	`distribute-rgt-out_binary64`
51×	`neg-mul-1_binary64` `neg-sub0_binary64`
47×	`associate-+l+_binary64` `associate-+r+_binary64`
45×	`distribute-neg-frac_binary64`
34×	`associate-*r/_binary64`
33×	`exp-sum_binary64`
31×	`associate-/r*_binary64`
30×	`distribute-lft-neg-out_binary64`
27×	`associate-*l/_binary64`
26×	`associate--l+_binary64`
25×	`distribute-lft-out_binary64`
22×	`unsub-neg_binary64`
20×	`associate--r+_binary64`
17×	`cube-prod_binary64` `associate-/l*_binary64`
15×	`distribute-rgt-neg-out_binary64`
13×	`exp-prod_binary64` `swap-sqr_binary64`
11×	`distribute-rgt-out--_binary64`
10×	`unpow3_binary64`
9×	`cube-mult_binary64`
7×	`cube-div_binary64`
6×	`unpow1/3_binary64`
5×	`cube-unmult_binary64` `rem-3cbrt-lft_binary64` `distribute-lft-out--_binary64`
4×	`log-prod_binary64` `pow-sqr_binary64`
3×	`unpow2_binary64` `unpow1/2_binary64` `pow-plus_binary64` `unpow1_binary64` `remove-double-neg_binary64` `difference-of-squares_binary64`
2×	`log-pow_binary64` `log-div_binary64` `exp-diff_binary64` `div-sub_binary64` `associate-+l-_binary64` `associate-+r-_binary64`
1×	`log-rec_binary64` `prod-exp_binary64` `1-exp_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `cancel-sign-sub_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `pow-base-0_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `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-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_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` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `count-2_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

111 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	294	18584
1	691	18344
2	2325	17925
3	5488	17925

prune220.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	74	3	77

Error

0.2b

Counts

77 → 3

Compiler

Compiled 6985 to 6276 computations (10.2% saved)

localize77.0ms (0.2%)

Local error

Found 4 expressions with local error:

14.4b	(cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))))
14.4b	(cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))))
15.3b	(+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16)))))) (cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16))))))) (-.f64 (+.f64 (.f64 1/16 (.f64 x (.f64 x (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 5)))))) (+.f64 (.f64 37/1296 (.f64 (pow.f64 x 3) (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 17))))) (+.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 5))) (+.f64 (.f64 x 1/6) (.f64 (pow.f64 x 3) 1/36)))))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 11))) (.f64 (.f64 x x) (+.f64 1/36 (.f64 1/48 x)))))) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))
15.4b	(-.f64 (+.f64 (.f64 1/16 (.f64 x (.f64 x (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 5)))))) (+.f64 (.f64 37/1296 (.f64 (pow.f64 x 3) (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 17))))) (+.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 5))) (+.f64 (.f64 x 1/6) (.f64 (pow.f64 x 3) 1/36)))))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 11))) (.f64 (.f64 x x) (+.f64 1/36 (.f64 1/48 x)))))

rewrite15.3s (40.8%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

1258×	`associate-*r/_binary64`
880×	`cbrt-div_binary64`
596×	`frac-add_binary64`
508×	`frac-times_binary64`
471×	`flip3-+_binary64` `flip-+_binary64`
430×	`associate-*l/_binary64`
300×	`frac-sub_binary64`
20×	`add-log-exp_binary64`
10×	`flip3--_binary64` `*-un-lft-identity_binary64` `flip--_binary64`
8×	`cbrt-prod_binary64`
7×	`sum-log_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64`
6×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `associate-+l+_binary64`
4×	`diff-log_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate--r+_binary64`
3×	`sub-neg_binary64` `cancel-sign-sub-inv_binary64` `associate--l+_binary64`
2×	`pow1/3_binary64` `distribute-lft-out_binary64`
1×	`+-commutative_binary64`

Counts

4 → 391

Calls

4 calls:

176.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16)))))) (cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16))))))) (-.f64 (+.f64 (.f64 1/16 (.f64 x (.f64 x (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 5)))))) (+.f64 (.f64 37/1296 (.f64 (pow.f64 x 3) (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 17))))) (+.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 5))) (+.f64 (.f64 x 1/6) (.f64 (pow.f64 x 3) 1/36)))))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 11))) (.f64 (.f64 x x) (+.f64 1/36 (.f64 1/48 x)))))) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))
52.0ms	(cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))))
50.0ms	(cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))))
39.0ms	(-.f64 (+.f64 (.f64 1/16 (.f64 x (.f64 x (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 5)))))) (+.f64 (.f64 37/1296 (.f64 (pow.f64 x 3) (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 17))))) (+.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 5))) (+.f64 (.f64 x 1/6) (.f64 (pow.f64 x 3) 1/36)))))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 11))) (.f64 (.f64 x x) (+.f64 1/36 (.f64 1/48 x)))))

Compiler

Compiled 221107 to 199222 computations (9.9% saved)

series690.0ms (1.8%)

Error

0.2b

Counts

4 → 30

Calls

4 calls:

259.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16)))))) (cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (.f64 x 3/16))))))) (-.f64 (+.f64 (.f64 1/16 (.f64 x (.f64 x (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 5)))))) (+.f64 (.f64 37/1296 (.f64 (pow.f64 x 3) (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 17))))) (+.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 5))) (+.f64 (.f64 x 1/6) (.f64 (pow.f64 x 3) 1/36)))))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 11))) (.f64 (.f64 x x) (+.f64 1/36 (.f64 1/48 x)))))) (*.f64 (/.f64 (pow.f64 x 3) (sqrt.f64 2)) -1/16))
104.0ms	(cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))))
103.0ms	(cbrt.f64 (+.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 x 3) (+.f64 (/.f64 1/16 (pow.f64 (sqrt.f64 2) 5)) (/.f64 1/12 (sqrt.f64 2)))) (.f64 (/.f64 x (sqrt.f64 2)) (+.f64 1/2 (*.f64 x 3/16))))))
98.0ms	(-.f64 (+.f64 (.f64 1/16 (.f64 x (.f64 x (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 5)))))) (+.f64 (.f64 37/1296 (.f64 (pow.f64 x 3) (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 17))))) (+.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 5))) (+.f64 (.f64 x 1/6) (.f64 (pow.f64 x 3) 1/36)))))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 11))) (.f64 (.f64 x x) (+.f64 1/36 (.f64 1/48 x)))))

Compiler

Compiled 10485 to 9711 computations (7.4% saved)

simplify2.9s (7.9%)

Algorithm

1×	egg-herbie

Rules

1242×	`associate-l_binary64`
513×	`associate-r_binary64`
72×	`sub-neg_binary64`
63×	`cancel-sign-sub-inv_binary64`
47×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64`
25×	`sqr-pow_binary64`
14×	`unpow3_binary64` `exp-prod_binary64` `cube-mult_binary64`
10×	`associate-*r/_binary64`
7×	`cube-prod_binary64` `swap-sqr_binary64`
6×	`log-div_binary64` `difference-of-squares_binary64` `distribute-rgt-out--_binary64`
4×	`unpow1/3_binary64` `unpow2_binary64` `prod-exp_binary64`
3×	`neg-mul-1_binary64` `neg-sub0_binary64` `associate-/l_binary64` `associate-/r_binary64`
2×	`exp-sum_binary64` `mul-1-neg_binary64` `distribute-lft-neg-out_binary64` `associate-*l/_binary64`
1×	`log-rec_binary64` `div-exp_binary64` `exp-diff_binary64` `1-exp_binary64` `rem-3cbrt-lft_binary64` `rem-cube-cbrt_binary64` `rem-square-sqrt_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-out_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-prod_binary64` `pow-base-0_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` `rec-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-unmult_binary64` `cube-div_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-sqrt-square_binary64` `times-frac_binary64` `div-sub_binary64` `unsub-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` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `unswap-sqr_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64` `count-2_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` `+-commutative_binary64`

Counts

421 → 371

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2060	288790
1	5078	288790

prune12.4s (33%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	370	1	371
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	371	3	374

Error

0.2b

Counts

374 → 3

Compiler

Compiled 184354 to 165213 computations (10.4% saved)

regimes553.0ms (1.5%)

Accuracy

Total 0.0b remaining (45.9%)

Threshold costs 0.0b (45.9%)

Compiler

Compiled 11495 to 10395 computations (9.6% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`sub-neg_binary64` `cancel-sign-sub-inv_binary64` `distribute-rgt-neg-in_binary64`
1×	`1-exp_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `-lft-identity_binary64` `distribute-lft-neg-in_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` `unsub-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `*-rgt-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	26	29
2	30	29
3	31	29
4	32	29
5	28	29

end1.0ms (0%)

Compiler: Compiled 18 to 12 computations (33.3% saved)

sample1.7s (4.6%)

Algorithm

1×

intervals

Results

767.0ms	2736×	body	1024	valid
197.0ms	1295×	body	512	valid
137.0ms	2993×	body	128	valid
100.0ms	309×	body	2048	valid
62.0ms	667×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 246 to 220 computations (10.6% saved)

Details

analyze731.0ms (1.9%)

sample54.0ms (0.1%)

simplify65.0ms (0.2%)

prune7.0ms (0%)

localize5.0ms (0%)

rewrite46.0ms (0.1%)

series41.0ms (0.1%)

simplify48.0ms (0.1%)

prune28.0ms (0.1%)

localize24.0ms (0.1%)

rewrite380.0ms (1%)

series73.0ms (0.2%)

simplify163.0ms (0.4%)

prune169.0ms (0.5%)

localize35.0ms (0.1%)

rewrite927.0ms (2.5%)

series425.0ms (1.1%)

simplify367.0ms (1%)

prune220.0ms (0.6%)

localize77.0ms (0.2%)

rewrite15.3s (40.8%)

series690.0ms (1.8%)

simplify2.9s (7.9%)

prune12.4s (33%)

regimes553.0ms (1.5%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end1.0ms (0%)

sample1.7s (4.6%)

Profiling