Details

analyze239.0ms (8%)

Algorithm

1×	search
2×	egg-herbie

Rules

644×	`sub-neg_binary64` `distribute-rgt-out--_binary64`
602×	`cancel-sign-sub-inv_binary64`
586×	`neg-mul-1_binary64`
568×	`neg-sub0_binary64`
418×	`distribute-neg-frac_binary64`
414×	`associate-*l/_binary64`
308×	`associate-*r/_binary64`
288×	`distribute-frac-neg_binary64`
274×	`unsub-neg_binary64`
248×	`associate-l_binary64`
241×	`remove-double-neg_binary64`
226×	`distribute-rgt-neg-in_binary64`
206×	`div-sub_binary64`
199×	`associate-/r*_binary64`
192×	`associate-r_binary64`
172×	`associate-/l*_binary64`
165×	`distribute-lft-neg-in_binary64`
142×	`distribute-lft-out--_binary64`
122×	`associate-/r/_binary64`
110×	`times-frac_binary64`
78×	`distribute-rgt-in_binary64`
76×	`distribute-rgt-neg-out_binary64`
70×	`distribute-lft-neg-out_binary64`
61×	`distribute-lft-in_binary64`
58×	`swap-sqr_binary64`
50×	`cancel-sign-sub_binary64` `associate-/l/_binary64`
44×	`+-lft-identity_binary64`
40×	`distribute-rgt-out_binary64`
38×	`distribute-rgt1-in_binary64`
33×	`*-commutative_binary64`
32×	`associate--r-_binary64`
30×	`unswap-sqr_binary64` `distribute-neg-in_binary64` `+-commutative_binary64`
26×	`*-lft-identity_binary64`
25×	`*-rgt-identity_binary64`
24×	`associate--r+_binary64`
20×	`mul0-rgt_binary64` `mul0-lft_binary64`
19×	`/-rgt-identity_binary64`
18×	`div0_binary64`
17×	`sqr-neg_binary64`
14×	`distribute-neg-out_binary64` `associate-+r-_binary64`
13×	`sub0-neg_binary64`
10×	`distribute-lft1-in_binary64` `associate-+r+_binary64`
8×	`mul-1-neg_binary64`
6×	`associate-+l-_binary64`
4×	`+-rgt-identity_binary64` `*-inverses_binary64`
2×	`lft-mult-inverse_binary64` `rgt-mult-inverse_binary64`
1×	`1-exp_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` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `--rgt-identity_binary64` `+-inverses_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` `distribute-lft-out_binary64` `count-2_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate-+l+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	28	26
2	82	20
3	166	20
4	309	20
5	785	20
6	2306	20
7	3560	20
8	4466	20
9	4777	20
10	5000	20
11	4754	20
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
56.2%	43.7%	0.1%	7
56.2%	43.7%	0.1%	8
76.5%	23.4%	0.1%	9
76.5%	23.4%	0.1%	10
87.8%	12.1%	0.1%	11
87.8%	12.1%	0.1%	12
93.8%	6.1%	0.1%	13
93.8%	6.1%	0.1%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample19.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 19 to 17 computations (10.5% saved)

simplify157.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

761×	`div-sub_binary64`
595×	`times-frac_binary64`
506×	`neg-mul-1_binary64`
502×	`neg-sub0_binary64`
378×	`sub-neg_binary64`
372×	`distribute-neg-frac_binary64`
319×	`*-commutative_binary64`
315×	`unsub-neg_binary64`
301×	`associate-/l*_binary64`
281×	`distribute-lft-neg-out_binary64`
280×	`distribute-rgt-neg-out_binary64`
273×	`remove-double-neg_binary64`
245×	`cancel-sign-sub-inv_binary64`
237×	`associate-/r/_binary64`
231×	`associate-/r*_binary64`
218×	`distribute-frac-neg_binary64`
195×	`associate-*l/_binary64`
172×	`+-commutative_binary64`
171×	`associate-/l/_binary64`
163×	`associate--r+_binary64`
140×	`unswap-sqr_binary64`
129×	`associate-l_binary64`
127×	`distribute-rgt-neg-in_binary64`
110×	`associate-*r/_binary64`
107×	`swap-sqr_binary64`
101×	`associate-+l-_binary64`
79×	`cancel-sign-sub_binary64`
76×	`distribute-rgt-out--_binary64` `distribute-rgt-in_binary64` `associate-r_binary64`
74×	`distribute-lft-neg-in_binary64`
67×	`distribute-rgt-out_binary64`
63×	`+-lft-identity_binary64`
54×	`associate--r-_binary64`
53×	`associate--l-_binary64`
51×	`distribute-neg-in_binary64`
49×	`distribute-lft-in_binary64`
43×	`distribute-neg-out_binary64`
35×	`/-rgt-identity_binary64` `*-lft-identity_binary64`
31×	`div0_binary64`
30×	`mul0-rgt_binary64` `mul0-lft_binary64` `distribute-lft-out--_binary64` `associate-+r-_binary64`
28×	`*-rgt-identity_binary64`
27×	`associate--l+_binary64`
26×	`associate-+r+_binary64`
25×	`remove-double-div_binary64`
23×	`sqr-neg_binary64`
22×	`sub0-neg_binary64`
20×	`associate-+l+_binary64`
18×	`--rgt-identity_binary64`
13×	`distribute-lft-out_binary64`
11×	`mul-1-neg_binary64`
9×	`+-rgt-identity_binary64`
6×	`lft-mult-inverse_binary64`
4×	`distribute-rgt1-in_binary64`
2×	`*-inverses_binary64`
1×	`1-exp_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` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `+-inverses_binary64` `rgt-mult-inverse_binary64` `pow-sqr_binary64` `sqr-pow_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `distribute-lft1-in_binary64` `count-2_binary64`

Counts

1 → 1

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	52	10
3	112	10
4	200	10
5	417	10
6	697	10
7	2421	10
8	3775	10
9	3836	10
10	4261	10
11	4709	10
12	4977	10
13	5248	10

prune3.0ms (0.1%)

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

0.0b

Counts

2 → 1

Compiler

Compiled 14 to 14 computations (0% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

rewrite24.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

7×	`*-un-lft-identity_binary64`
3×	`add-log-exp_binary64`
2×	`times-frac_binary64` `distribute-lft-out_binary64`
1×	`sum-log_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `frac-add_binary64` `flip3-+_binary64` `flip-+_binary64` `+-commutative_binary64`

Counts

1 → 14

Calls

1 calls:

13.0ms

(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

Compiler

Compiled 200 to 154 computations (23% saved)

series32.0ms (1.1%)

Error

0.0b

Counts

1 → 12

Calls

1 calls:

28.0ms

(+.f64 (/.f64 1/2 y) (/.f64 -1/2 x))

Compiler

Compiled 167 to 171 computations (-2.4% saved)

simplify90.0ms (3%)

Algorithm

1×	egg-herbie

Rules

884×	`div-sub_binary64`
324×	`distribute-rgt-in_binary64`
310×	`associate-*l/_binary64`
292×	`distribute-lft-in_binary64`
267×	`neg-mul-1_binary64`
265×	`associate-/l*_binary64`
213×	`distribute-neg-frac_binary64`
206×	`associate-*r/_binary64`
188×	`distribute-rgt-out_binary64`
162×	`neg-sub0_binary64`
157×	`associate-l_binary64`
152×	`*-commutative_binary64`
148×	`associate-r_binary64`
134×	`associate-/r*_binary64`
125×	`distribute-lft-out_binary64`
124×	`sub-neg_binary64`
112×	`cancel-sign-sub-inv_binary64` `distribute-rgt-neg-out_binary64`
110×	`distribute-frac-neg_binary64`
107×	`distribute-lft-neg-out_binary64`
91×	`associate-/r/_binary64`
78×	`distribute-rgt-neg-in_binary64`
65×	`sqr-pow_binary64`
62×	`exp-prod_binary64` `cube-prod_binary64`
61×	`distribute-lft-neg-in_binary64` `associate-/l/_binary64`
56×	`unsub-neg_binary64`
54×	`remove-double-neg_binary64`
50×	`associate-+l+_binary64`
48×	`associate-+r+_binary64`
37×	`distribute-rgt-out--_binary64`
36×	`*-rgt-identity_binary64` `unswap-sqr_binary64`
33×	`*-lft-identity_binary64`
29×	`+-commutative_binary64`
28×	`mul0-rgt_binary64` `mul0-lft_binary64`
24×	`associate-+l-_binary64`
23×	`distribute-neg-out_binary64`
22×	`exp-sum_binary64` `associate-+r-_binary64`
21×	`exp-diff_binary64`
18×	`times-frac_binary64`
15×	`sub0-neg_binary64`
14×	`unpow3_binary64` `swap-sqr_binary64`
13×	`log-prod_binary64` `distribute-lft-out--_binary64`
12×	`+-rgt-identity_binary64`
11×	`cube-mult_binary64` `cube-neg_binary64`
10×	`cube-div_binary64`
9×	`distribute-neg-in_binary64`
8×	`cube-unmult_binary64` `div0_binary64` `difference-of-squares_binary64`
7×	`/-rgt-identity_binary64` `associate--r-_binary64`
6×	`sqr-neg_binary64` `pow-sqr_binary64` `associate--l-_binary64`
4×	`unpow1/2_binary64` `pow-plus_binary64` `mul-1-neg_binary64`
3×	`--rgt-identity_binary64` `associate--r+_binary64`
2×	`associate--l+_binary64`
1×	`prod-exp_binary64` `1-exp_binary64` `exp-1-e_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-pow_binary64` `log-rec_binary64` `log-div_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow2_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` `div-exp_binary64` `rec-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `rem-square-sqrt_binary64` `+-lft-identity_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-rgt1-in_binary64` `distribute-lft1-in_binary64` `count-2_binary64`

Counts

26 → 16

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	326
1	121	296
2	311	293
3	1160	293
4	3527	293
5	4260	293
6	4996	293
7	4854	293

prune9.0ms (0.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	15	1	16
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	15	2	17

Error

0.0b

Counts

17 → 2

Compiler

Compiled 170 to 132 computations (22.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
0.5b	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
0.5b	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
0.6b	(*.f64 (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x))) (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x))))

rewrite276.0ms (9.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

121×	`add-sqr-sqrt_binary64`
92×	`cbrt-prod_binary64`
91×	`*-un-lft-identity_binary64`
70×	`times-frac_binary64`
37×	`distribute-lft-out--_binary64`
33×	`cbrt-div_binary64`
29×	`add-cube-cbrt_binary64`
28×	`difference-of-squares_binary64`
17×	`swap-sqr_binary64`
15×	`associate-l_binary64` `associate-r_binary64`
14×	`div-inv_binary64`
11×	`pow1_binary64` `frac-sub_binary64` `flip3--_binary64` `flip--_binary64`
9×	`pow1/3_binary64` `frac-times_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
3×	`associate-l/_binary64` `associate-r/_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`pow2_binary64` `pow-plus_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `*-commutative_binary64`

Counts

4 → 153

Calls

4 calls:

39.0ms	(*.f64 (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x))) (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x))))
14.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
13.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
13.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))

Compiler

Compiled 5483 to 4269 computations (22.1% saved)

series264.0ms (8.8%)

Error

0.0b

Counts

4 → 54

Calls

4 calls:

69.0ms	(*.f64 (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x))) (cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x))))
46.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
46.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
46.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))

Compiler

Compiled 4603 to 3914 computations (15% saved)

simplify213.0ms (7.1%)

Algorithm

1×	egg-herbie

Rules

450×	`times-frac_binary64`
347×	`associate-/l*_binary64`
296×	`associate-/r*_binary64`
241×	`neg-mul-1_binary64`
226×	`cancel-sign-sub-inv_binary64`
170×	`distribute-rgt-neg-in_binary64`
165×	`associate-r_binary64`
159×	`distribute-lft-neg-in_binary64`
145×	`associate-l_binary64`
122×	`*-commutative_binary64`
103×	`sub-neg_binary64`
97×	`distribute-neg-frac_binary64`
91×	`sqr-pow_binary64`
75×	`unswap-sqr_binary64`
73×	`distribute-rgt-in_binary64`
72×	`neg-sub0_binary64` `associate-*r/_binary64`
69×	`associate-/r/_binary64`
67×	`exp-prod_binary64`
55×	`+-commutative_binary64`
48×	`distribute-lft-in_binary64`
45×	`associate-*l/_binary64`
44×	`distribute-neg-in_binary64`
43×	`*-rgt-identity_binary64`
35×	`log-prod_binary64`
32×	`exp-sum_binary64` `div-sub_binary64`
26×	`associate--r+_binary64`
24×	`*-lft-identity_binary64`
22×	`cube-prod_binary64`
21×	`unsub-neg_binary64`
19×	`distribute-lft-neg-out_binary64`
17×	`unpow1/3_binary64`
12×	`associate-/l/_binary64` `associate-+l+_binary64`
11×	`pow-plus_binary64`
10×	`exp-diff_binary64` `associate-+r+_binary64`
9×	`cube-div_binary64`
8×	`log-pow_binary64` `unpow3_binary64` `exp-neg_binary64` `cube-unmult_binary64` `rem-sqrt-square_binary64` `pow-sqr_binary64`
7×	`exp-to-pow_binary64` `/-rgt-identity_binary64` `distribute-rgt-neg-out_binary64`
5×	`rem-exp-log_binary64` `cube-mult_binary64` `swap-sqr_binary64` `distribute-rgt-out_binary64` `associate--l+_binary64`
4×	`log-div_binary64` `unpow1/2_binary64` `exp-lft-sqr_binary64` `difference-of-squares_binary64`
3×	`unpow2_binary64` `unpow1_binary64`
2×	`rem-3cbrt-lft_binary64` `count-2_binary64`
1×	`1-exp_binary64` `exp-1-e_binary64` `rem-3cbrt-rft_binary64` `sqr-neg_binary64` `rem-square-sqrt_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-rec_binary64` `pow-base-0_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `cube-neg_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_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-lft-out--_binary64` `distribute-lft-out_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate-+l-_binary64` `associate-+r-_binary64`

Counts

207 → 182

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	302	6437
1	680	6145
2	1982	5832
3	4709	5642
4	4988	5642

prune161.0ms (5.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	181	3	184

Error

0.0b

Counts

184 → 3

Compiler

Compiled 5036 to 3839 computations (23.8% saved)

localize21.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (+.f64 (/.f64 -1/2 x) (/.f64 1/2 y))) (cbrt.f64 1/2))
0.5b	(cbrt.f64 (-.f64 (/.f64 1 y) (/.f64 1 x)))
0.5b	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
0.5b	(cbrt.f64 (+.f64 (/.f64 -1/2 x) (/.f64 1/2 y)))

rewrite200.0ms (6.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

59×	`add-sqr-sqrt_binary64`
51×	`*-un-lft-identity_binary64`
48×	`cbrt-prod_binary64`
32×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
13×	`difference-of-squares_binary64`
12×	`cbrt-div_binary64` `distribute-lft-out--_binary64`
8×	`associate-l_binary64`
6×	`pow1_binary64` `add-exp-log_binary64` `div-inv_binary64` `associate-r_binary64`
5×	`pow1/3_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64`
3×	`associate-*l/_binary64`
2×	`frac-add_binary64` `flip3-+_binary64` `flip-+_binary64` `frac-sub_binary64` `flip3--_binary64` `flip--_binary64` `pow-prod-down_binary64`
1×	`prod-exp_binary64` `cbrt-unprod_binary64` `*-commutative_binary64`

Counts

4 → 102

Calls

4 calls:

26.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 -1/2 x) (/.f64 1/2 y))) (cbrt.f64 1/2))
14.0ms	(cbrt.f64 (-.f64 (/.f64 1 y) (/.f64 1 x)))
13.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
13.0ms	(cbrt.f64 (+.f64 (/.f64 -1/2 x) (/.f64 1/2 y)))

Compiler

Compiled 3671 to 2929 computations (20.2% saved)

series246.0ms (8.2%)

Error

0.0b

Counts

4 → 48

Calls

4 calls:

56.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 -1/2 x) (/.f64 1/2 y))) (cbrt.f64 1/2))
47.0ms	(cbrt.f64 (+.f64 (/.f64 -1/2 x) (/.f64 1/2 y)))
47.0ms	(cbrt.f64 (-.f64 (/.f64 1/2 y) (/.f64 1/2 x)))
43.0ms	(cbrt.f64 (-.f64 (/.f64 1 y) (/.f64 1 x)))

Compiler

Compiled 4517 to 3880 computations (14.1% saved)

simplify152.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

825×	`times-frac_binary64`
479×	`associate-/l*_binary64`
281×	`cancel-sign-sub-inv_binary64`
223×	`distribute-rgt-neg-in_binary64`
195×	`distribute-lft-neg-in_binary64`
143×	`distribute-neg-frac_binary64`
124×	`associate-r_binary64` `*-commutative_binary64`
116×	`sub-neg_binary64`
111×	`associate-l_binary64`
96×	`associate-/r/_binary64` `associate-/r*_binary64`
92×	`sqr-pow_binary64`
91×	`associate-*r/_binary64`
87×	`div-sub_binary64`
83×	`neg-mul-1_binary64` `neg-sub0_binary64`
77×	`+-commutative_binary64`
63×	`distribute-rgt-in_binary64` `associate-*l/_binary64`
60×	`associate-/l/_binary64`
38×	`exp-sum_binary64` `distribute-lft-in_binary64`
36×	`distribute-neg-in_binary64`
30×	`exp-prod_binary64`
28×	`distribute-lft-neg-out_binary64`
27×	`/-rgt-identity_binary64`
25×	`cube-prod_binary64`
21×	`associate--r+_binary64`
20×	`*-rgt-identity_binary64`
19×	`log-prod_binary64` `cube-div_binary64`
17×	`unpow1/3_binary64` `unsub-neg_binary64` `*-lft-identity_binary64`
15×	`distribute-rgt-out_binary64`
12×	`distribute-rgt-neg-out_binary64` `associate-+l+_binary64` `associate-+r+_binary64`
11×	`swap-sqr_binary64` `distribute-rgt-out--_binary64`
10×	`unpow3_binary64`
9×	`difference-of-squares_binary64`
8×	`cube-mult_binary64` `unswap-sqr_binary64`
7×	`log-div_binary64`
6×	`cube-unmult_binary64` `distribute-frac-neg_binary64`
5×	`exp-diff_binary64` `rem-exp-log_binary64` `distribute-lft-out_binary64`
4×	`log-pow_binary64` `exp-neg_binary64` `rem-sqrt-square_binary64` `pow-sqr_binary64` `associate--l+_binary64`
3×	`unpow1/2_binary64` `exp-to-pow_binary64` `rem-3cbrt-lft_binary64`
2×	`log-rec_binary64` `unpow2_binary64` `pow-plus_binary64` `unpow1_binary64`
1×	`rec-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `cube-neg_binary64` `rem-cube-cbrt_binary64` `distribute-neg-out_binary64` `distribute-lft-out--_binary64` `associate-+l-_binary64` `associate-+r-_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `pow-base-0_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` `prod-exp_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-square-sqrt_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-rgt1-in_binary64` `distribute-lft1-in_binary64` `count-2_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

150 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	318	3582
1	753	3510
2	2045	3489
3	4841	3417
4	4964	3417

prune119.0ms (4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	134	3	137

Error

0.0b

Counts

137 → 3

Compiler

Compiled 3863 to 3050 computations (21% saved)

regimes166.0ms (5.5%)

Accuracy

Total 0.0b remaining (31.7%)

Threshold costs 0.0b (31.7%)

Compiler

Compiled 2104 to 1864 computations (11.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

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	8	10
1	9	10
2	9	10

end1.0ms (0%)

Compiler: Compiled 7 to 7 computations (0% saved)

sample584.0ms (19.5%)

Algorithm

1×

intervals

Results

235.0ms	8000×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 89 to 87 computations (2.2% saved)

Details

analyze239.0ms (8%)

sample19.0ms (0.6%)

simplify157.0ms (5.3%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

rewrite24.0ms (0.8%)

series32.0ms (1.1%)

simplify90.0ms (3%)

prune9.0ms (0.3%)

localize10.0ms (0.3%)

rewrite276.0ms (9.2%)

series264.0ms (8.8%)

simplify213.0ms (7.1%)

prune161.0ms (5.4%)

localize21.0ms (0.7%)

rewrite200.0ms (6.7%)

series246.0ms (8.2%)

simplify152.0ms (5.1%)

prune119.0ms (4%)

regimes166.0ms (5.5%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample584.0ms (19.5%)

Profiling