Details

analyze1.6s (10.1%)

Algorithm

1×	search
2×	egg-herbie

Rules

392×	`times-frac_binary64`
391×	`associate-/l*_binary64`
329×	`associate-/r*_binary64`
280×	`unswap-sqr_binary64`
232×	`associate-*r/_binary64`
224×	`associate-*l/_binary64`
197×	`sqr-pow_binary64`
138×	`exp-sum_binary64`
126×	`exp-prod_binary64`
91×	`associate-/r/_binary64`
87×	`pow-sqr_binary64`
70×	`associate-l_binary64`
69×	`*-commutative_binary64`
57×	`associate-/l/_binary64`
49×	`associate-r_binary64`
45×	`sub-neg_binary64`
44×	`exp-diff_binary64`
38×	`+-commutative_binary64`
35×	`neg-mul-1_binary64`
33×	`distribute-neg-in_binary64`
28×	`neg-sub0_binary64` `cancel-sign-sub-inv_binary64`
26×	`distribute-rgt-neg-in_binary64`
19×	`distribute-lft-neg-out_binary64`
17×	`exp-neg_binary64`
14×	`unsub-neg_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64`
12×	`exp-to-pow_binary64`
10×	`div-sub_binary64` `distribute-frac-neg_binary64`
7×	`div-exp_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `sub0-neg_binary64` `distribute-lft-neg-in_binary64` `associate-+l-_binary64` `associate-+r-_binary64` `associate-+l+_binary64`
6×	`+-rgt-identity_binary64`
5×	`rem-exp-log_binary64`
4×	`mul0-rgt_binary64` `mul0-lft_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` `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` `prod-exp_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_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` `mul-1-neg_binary64` `/-rgt-identity_binary64` `remove-double-neg_binary64` `--rgt-identity_binary64` `+-lft-identity_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `swap-sqr_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-neg-out_binary64` `distribute-rgt-neg-out_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` `count-2_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	94	518
1	184	504
2	327	504
3	572	504
4	1474	504
5	4923	504
6	5006	504
0	4	4
1	4	4

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
9.4%	90.4%	0.2%	6
17.2%	82.7%	0.2%	7
19.5%	80.3%	0.2%	8
30.8%	69%	0.2%	9
35.5%	64.3%	0.2%	10
42.4%	57.4%	0.2%	11
47.1%	52.7%	0.2%	12
49%	50.8%	0.2%	13
50.1%	49.7%	0.2%	14

Compiler

Compiled 38 to 20 computations (47.4% saved)

sample122.0ms (0.8%)

Algorithm

1×

intervals

Results

38.0ms	74×	body	1024	invalid
31.0ms	243×	body	128	valid
12.0ms	35×	body	512	invalid
6.0ms	7×	body	2048	invalid
3.0ms	6×	body	1024	valid
3.0ms	12×	body	256	invalid
2.0ms	6×	body	512	valid
2.0ms	15×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify65.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

892×	`unswap-sqr_binary64`
461×	`associate-/l*_binary64`
323×	`associate-/r*_binary64`
296×	`associate-*l/_binary64`
286×	`associate-*r/_binary64`
284×	`sqr-pow_binary64`
201×	`*-commutative_binary64`
184×	`associate-/r/_binary64`
175×	`pow-sqr_binary64`
125×	`associate-/l/_binary64`
94×	`div-sub_binary64`
74×	`exp-sum_binary64` `associate-l_binary64`
68×	`associate-r_binary64`
60×	`sub-neg_binary64`
56×	`times-frac_binary64`
51×	`exp-prod_binary64`
47×	`neg-mul-1_binary64`
42×	`distribute-rgt-in_binary64`
37×	`*-lft-identity_binary64` `cancel-sign-sub-inv_binary64`
34×	`exp-diff_binary64`
26×	`neg-sub0_binary64`
24×	`swap-sqr_binary64` `distribute-rgt-neg-in_binary64`
20×	`cube-prod_binary64` `distribute-frac-neg_binary64` `distribute-lft-in_binary64`
19×	`unsub-neg_binary64`
16×	`distribute-rgt-neg-out_binary64` `distribute-lft-neg-in_binary64`
15×	`/-rgt-identity_binary64`
14×	`*-rgt-identity_binary64` `+-commutative_binary64`
12×	`unpow3_binary64` `cube-unmult_binary64` `distribute-neg-frac_binary64` `distribute-lft-neg-out_binary64` `associate--r+_binary64`
10×	`mul0-rgt_binary64` `mul0-lft_binary64`
9×	`+-rgt-identity_binary64` `distribute-neg-in_binary64`
8×	`pow-plus_binary64`
7×	`+-lft-identity_binary64`
6×	`sub0-neg_binary64` `associate-+l-_binary64`
5×	`exp-to-pow_binary64` `remove-double-neg_binary64`
4×	`unpow2_binary64` `exp-neg_binary64` `cube-mult_binary64` `div0_binary64`
3×	`log-pow_binary64` `--rgt-identity_binary64` `associate--r-_binary64` `associate-+l+_binary64`
2×	`cube-div_binary64` `associate-+r+_binary64`
1×	`log-rec_binary64` `log-div_binary64` `log-prod_binary64` `div-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-exp-log_binary64` `cancel-sign-sub_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` `unpow1/3_binary64` `unpow1/2_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` `prod-exp_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_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` `mul-1-neg_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `distribute-neg-out_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` `count-2_binary64` `associate--l-_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	74
1	37	72
2	62	72
3	105	72
4	245	72
5	968	72
6	2998	72
7	4028	72
8	4444	72
9	4944	72

prune10.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

33.1b

Counts

2 → 2

Compiler

Compiled 109 to 57 computations (47.7% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.7b	(*.f64 (atan2.f64 x.im x.re) y.im)
28.3b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
29.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
29.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite120.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

33.0b

Rules

12×	`add-sqr-sqrt_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-l_binary64` `associate-r_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64`
1×	`sin-sum_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

7.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
6.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2594 to 353 computations (86.4% saved)

series1.1s (7.1%)

Error

22.3b

Counts

4 → 62

Calls

4 calls:

512.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
210.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
209.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
106.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 6605 to 3384 computations (48.8% saved)

simplify133.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

402×	`distribute-rgt-neg-in_binary64`
338×	`associate-r_binary64`
306×	`unswap-sqr_binary64` `associate-l_binary64`
299×	`times-frac_binary64`
278×	`distribute-neg-frac_binary64`
225×	`associate-/l*_binary64`
204×	`div-sub_binary64`
148×	`associate-/r*_binary64`
142×	`*-commutative_binary64`
139×	`sub-neg_binary64`
100×	`cancel-sign-sub-inv_binary64`
94×	`neg-sub0_binary64`
91×	`neg-mul-1_binary64`
86×	`associate-*l/_binary64`
80×	`distribute-lft-neg-in_binary64`
70×	`associate-*r/_binary64`
54×	`sqr-pow_binary64`
53×	`+-commutative_binary64`
44×	`difference-of-squares_binary64`
42×	`distribute-neg-in_binary64`
41×	`associate-/r/_binary64`
38×	`distribute-lft-neg-out_binary64`
35×	`unsub-neg_binary64`
33×	`associate-+r-_binary64`
31×	`distribute-rgt-in_binary64`
25×	`associate-+l-_binary64`
23×	`cube-unmult_binary64` `distribute-lft-in_binary64`
22×	`cube-prod_binary64` `distribute-rgt-neg-out_binary64`
20×	`pow-plus_binary64` `+-rgt-identity_binary64`
17×	`log-prod_binary64`
15×	`sub0-neg_binary64` `associate-+l+_binary64`
12×	`log-div_binary64` `unpow3_binary64` `exp-prod_binary64`
11×	`associate-+r+_binary64`
10×	`*-lft-identity_binary64`
9×	`*-rgt-identity_binary64`
8×	`pow-sqr_binary64` `cancel-sign-sub_binary64`
7×	`distribute-rgt-out--_binary64` `associate--r+_binary64`
6×	`log-pow_binary64` `rem-sqrt-square_binary64`
5×	`associate--l+_binary64`
4×	`sin-neg_binary64` `log-rec_binary64` `unpow1/2_binary64` `cube-mult_binary64` `cube-div_binary64` `remove-double-neg_binary64` `swap-sqr_binary64` `distribute-rgt-out_binary64`
3×	`associate--r-_binary64`
2×	`cos-neg_binary64` `unpow2_binary64` `unpow1_binary64` `mul-1-neg_binary64` `--rgt-identity_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64`
1×	`exp-diff_binary64` `exp-sum_binary64` `1-exp_binary64` `exp-1-e_binary64` `cube-neg_binary64` `sqr-neg_binary64` `rem-square-sqrt_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `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-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_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-rgt1-in_binary64` `distribute-lft1-in_binary64` `count-2_binary64` `associate-/l/_binary64` `associate--l-_binary64`

Counts

118 → 74

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	178	2653
1	387	2488
2	945	2488
3	3259	2488
4	4723	2488
5	4993	2488

prune160.0ms (1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	66	8	74
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	67	9	76

Error

22.3b

Counts

76 → 9

Compiler

Compiled 3512 to 1177 computations (66.5% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

29.7b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
29.7b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
29.7b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
29.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite316.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

22.3b

Rules

20×	`*-un-lft-identity_binary64`
18×	`sqrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-div_binary64`
6×	`unpow-prod-down_binary64` `distribute-lft-out_binary64`
4×	`pow1/2_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64`

Counts

4 → 66

Calls

4 calls:

10.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 5748 to 2873 computations (50% saved)

series1.2s (7.6%)

Error

22.3b

Counts

4 → 72

Calls

4 calls:

250.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
241.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
237.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
233.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))

Compiler

Compiled 13896 to 8199 computations (41% saved)

simplify123.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

551×	`cancel-sign-sub-inv_binary64`
382×	`distribute-rgt-neg-in_binary64`
371×	`distribute-lft-neg-in_binary64`
367×	`neg-mul-1_binary64`
361×	`neg-sub0_binary64`
298×	`unswap-sqr_binary64`
278×	`distribute-neg-frac_binary64`
210×	`times-frac_binary64`
188×	`div-sub_binary64` `associate-r_binary64`
153×	`associate-l_binary64`
140×	`associate-/l*_binary64`
139×	`distribute-rgt-in_binary64`
102×	`sub-neg_binary64`
86×	`associate-/r*_binary64`
62×	`associate-*l/_binary64`
58×	`*-commutative_binary64`
52×	`associate-*r/_binary64`
49×	`distribute-rgt-out_binary64`
45×	`difference-of-squares_binary64`
38×	`+-commutative_binary64`
32×	`sqr-pow_binary64`
28×	`distribute-rgt-out--_binary64`
24×	`distribute-lft-neg-out_binary64`
22×	`associate-+r-_binary64`
21×	`associate-+l-_binary64`
20×	`pow-plus_binary64`
19×	`cube-unmult_binary64` `+-rgt-identity_binary64`
16×	`cube-prod_binary64` `distribute-lft-out_binary64`
14×	`unpow3_binary64` `distribute-lft-in_binary64`
13×	`distribute-lft-out--_binary64` `associate-+l+_binary64`
12×	`distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64` `associate-/r/_binary64`
11×	`unsub-neg_binary64` `sub0-neg_binary64`
6×	`cube-mult_binary64` `pow-sqr_binary64` `associate--r+_binary64`
5×	`rem-sqrt-square_binary64` `associate--l+_binary64` `associate-+r+_binary64`
4×	`cube-div_binary64`
2×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `sqr-neg_binary64` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_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` `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` `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-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-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-sqr-1_binary64` `swap-sqr_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `count-2_binary64` `associate-/l/_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

138 → 71

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	95	2538
1	184	2454
2	513	2454
3	2180	2454
4	4288	2454
5	5052	2454

prune302.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	71	9	80

Error

22.3b

Counts

80 → 9

Compiler

Compiled 6212 to 3212 computations (48.3% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.7b	(*.f64 (atan2.f64 x.im x.re) y.im)
28.3b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))
29.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
29.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite114.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

22.3b

Rules

12×	`add-sqr-sqrt_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-l_binary64` `associate-r_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64`
1×	`sin-sum_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

7.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2538 to 332 computations (86.9% saved)

series1.1s (6.9%)

Error

22.3b

Counts

4 → 62

Calls

4 calls:

494.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 y.re (atan2.f64 x.im x.re))))
208.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
205.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
110.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 6448 to 3276 computations (49.2% saved)

simplify131.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

402×	`distribute-rgt-neg-in_binary64`
338×	`associate-r_binary64`
306×	`unswap-sqr_binary64` `associate-l_binary64`
299×	`times-frac_binary64`
278×	`distribute-neg-frac_binary64`
225×	`associate-/l*_binary64`
204×	`div-sub_binary64`
148×	`associate-/r*_binary64`
142×	`*-commutative_binary64`
139×	`sub-neg_binary64`
100×	`cancel-sign-sub-inv_binary64`
94×	`neg-sub0_binary64`
91×	`neg-mul-1_binary64`
86×	`associate-*l/_binary64`
80×	`distribute-lft-neg-in_binary64`
70×	`associate-*r/_binary64`
54×	`sqr-pow_binary64`
53×	`+-commutative_binary64`
44×	`difference-of-squares_binary64`
42×	`distribute-neg-in_binary64`
41×	`associate-/r/_binary64`
38×	`distribute-lft-neg-out_binary64`
35×	`unsub-neg_binary64`
33×	`associate-+r-_binary64`
31×	`distribute-rgt-in_binary64`
25×	`associate-+l-_binary64`
23×	`cube-unmult_binary64` `distribute-lft-in_binary64`
22×	`cube-prod_binary64` `distribute-rgt-neg-out_binary64`
20×	`pow-plus_binary64` `+-rgt-identity_binary64`
17×	`log-prod_binary64`
15×	`sub0-neg_binary64` `associate-+l+_binary64`
12×	`log-div_binary64` `unpow3_binary64` `exp-prod_binary64`
11×	`associate-+r+_binary64`
10×	`*-lft-identity_binary64`
9×	`*-rgt-identity_binary64`
8×	`pow-sqr_binary64` `cancel-sign-sub_binary64`
7×	`distribute-rgt-out--_binary64` `associate--r+_binary64`
6×	`log-pow_binary64` `rem-sqrt-square_binary64`
5×	`associate--l+_binary64`
4×	`sin-neg_binary64` `log-rec_binary64` `unpow1/2_binary64` `cube-mult_binary64` `cube-div_binary64` `remove-double-neg_binary64` `swap-sqr_binary64` `distribute-rgt-out_binary64`
3×	`associate--r-_binary64`
2×	`cos-neg_binary64` `unpow2_binary64` `unpow1_binary64` `mul-1-neg_binary64` `--rgt-identity_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64`
1×	`exp-diff_binary64` `exp-sum_binary64` `1-exp_binary64` `exp-1-e_binary64` `cube-neg_binary64` `sqr-neg_binary64` `rem-square-sqrt_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `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-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_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-rgt1-in_binary64` `distribute-lft1-in_binary64` `count-2_binary64` `associate-/l/_binary64` `associate--l-_binary64`

Counts

118 → 74

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	175	2653
1	383	2488
2	941	2488
3	3255	2488
4	4719	2488
5	4993	2488

prune151.0ms (0.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	74	9	83

Error

22.3b

Counts

83 → 9

Compiler

Compiled 3365 to 1093 computations (67.5% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

13.4b	(cbrt.f64 (pow.f64 (sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))))))) 3))
28.3b	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))))))
29.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
29.7b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))

rewrite181.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

22.3b

Rules

13×	`*-un-lft-identity_binary64`
12×	`cbrt-prod_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
8×	`sqrt-prod_binary64`
6×	`pow1_binary64`
5×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`cube-prod_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `distribute-lft-out_binary64` `rem-sqrt-square_binary64`
1×	`sin-sum_binary64` `pow1/3_binary64` `unpow3_binary64` `cube-mult_binary64` `sqr-pow_binary64` `rem-cbrt-cube_binary64`

Counts

4 → 61

Calls

4 calls:

9.0ms	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
5.0ms	(cbrt.f64 (pow.f64 (sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))))))) 3))
5.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 3307 to 1470 computations (55.5% saved)

series1.4s (8.6%)

Error

22.3b

Counts

4 → 63

Calls

4 calls:

512.0ms	(cbrt.f64 (pow.f64 (sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))))))) 3))
387.0ms	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))))))
208.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
164.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))

Compiler

Compiled 7174 to 4270 computations (40.5% saved)

simplify161.0ms (1%)

Algorithm

1×	egg-herbie

Rules

516×	`unswap-sqr_binary64`
344×	`associate-r_binary64`
299×	`times-frac_binary64`
288×	`associate-l_binary64`
278×	`distribute-neg-frac_binary64`
225×	`associate-/l*_binary64`
203×	`div-sub_binary64`
148×	`associate-/r*_binary64`
142×	`sub-neg_binary64`
128×	`*-commutative_binary64`
101×	`cancel-sign-sub-inv_binary64`
94×	`neg-sub0_binary64`
91×	`neg-mul-1_binary64`
89×	`distribute-rgt-neg-in_binary64`
86×	`associate-*l/_binary64`
80×	`distribute-lft-neg-in_binary64`
70×	`associate-*r/_binary64`
65×	`sqr-pow_binary64`
54×	`+-commutative_binary64`
52×	`rem-sqrt-square_binary64`
45×	`difference-of-squares_binary64`
41×	`associate-/r/_binary64`
40×	`pow-plus_binary64`
35×	`unsub-neg_binary64`
34×	`associate-+r-_binary64`
31×	`distribute-rgt-in_binary64`
30×	`cube-unmult_binary64`
26×	`unpow3_binary64` `cube-prod_binary64`
25×	`associate-+l-_binary64`
23×	`distribute-lft-in_binary64`
22×	`log-prod_binary64`
20×	`+-rgt-identity_binary64`
15×	`exp-prod_binary64` `sub0-neg_binary64`
13×	`pow-sqr_binary64` `distribute-lft-neg-out_binary64` `associate-+l+_binary64`
12×	`log-div_binary64`
11×	`log-pow_binary64` `cube-mult_binary64`
9×	`associate-+r+_binary64`
8×	`cancel-sign-sub_binary64` `distribute-neg-in_binary64`
7×	`distribute-rgt-out--_binary64` `associate--r+_binary64`
5×	`distribute-rgt-neg-out_binary64` `associate--l+_binary64`
4×	`sin-neg_binary64` `log-rec_binary64` `unpow2_binary64` `cube-div_binary64` `rem-cbrt-cube_binary64` `remove-double-neg_binary64` `distribute-rgt-out_binary64`
3×	`rem-square-sqrt_binary64` `associate--r-_binary64`
2×	`cos-neg_binary64` `unpow1/2_binary64` `unpow1_binary64` `mul-1-neg_binary64` `--rgt-identity_binary64` `swap-sqr_binary64`
1×	`1-exp_binary64` `rem-3cbrt-lft_binary64` `rem-cube-cbrt_binary64` `distribute-lft-out--_binary64` `distribute-lft-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` `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-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-neg_binary64` `rem-3cbrt-rft_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-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` `associate-/l/_binary64` `associate--l-_binary64`

Counts

124 → 83

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	200	3804
1	366	3537
2	887	3537
3	3372	3537
4	4824	3523
5	5142	3523

prune177.0ms (1.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	82	10	92

Error

22.3b

Counts

92 → 10

Compiler

Compiled 3799 to 1627 computations (57.2% saved)

regimes1.5s (9.5%)

Accuracy

Total 0.2b remaining (1.1%)

Threshold costs 0.2b (1.1%)

Compiler

Compiled 15022 to 9465 computations (37% saved)

bsearch10.0ms (0.1%)

Compiler: Compiled 37 to 19 computations (48.6% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-mul-1_binary64` `neg-sub0_binary64`
2×	`cancel-sign-sub-inv_binary64` `distribute-rgt-neg-in_binary64`
1×	`distribute-lft-neg-out_binary64` `distribute-lft-neg-in_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` `unsub-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_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	203
1	41	203
2	51	203
3	57	203
4	61	203
5	62	203
6	62	203

end0.0ms (0%)

sample5.7s (35.5%)

Algorithm

1×

intervals

Results

1.3s	2537×	body	1024	invalid
853.0ms	7617×	body	128	valid
341.0ms	964×	body	512	invalid
153.0ms	183×	body	2048	invalid
89.0ms	160×	body	1024	valid
83.0ms	357×	body	256	invalid
56.0ms	491×	body	128	invalid
44.0ms	129×	body	512	valid
19.0ms	82×	body	256	valid
10.0ms	12×	body	2048	valid

Compiler

Compiled 3128 to 1927 computations (38.4% saved)

Details

analyze1.6s (10.1%)

sample122.0ms (0.8%)

simplify65.0ms (0.4%)

prune10.0ms (0.1%)

localize23.0ms (0.1%)

rewrite120.0ms (0.7%)

series1.1s (7.1%)

simplify133.0ms (0.8%)

prune160.0ms (1%)

localize36.0ms (0.2%)

rewrite316.0ms (2%)

series1.2s (7.6%)

simplify123.0ms (0.8%)

prune302.0ms (1.9%)

localize22.0ms (0.1%)

rewrite114.0ms (0.7%)

series1.1s (6.9%)

simplify131.0ms (0.8%)

prune151.0ms (0.9%)

localize31.0ms (0.2%)

rewrite181.0ms (1.1%)

series1.4s (8.6%)

simplify161.0ms (1%)

prune177.0ms (1.1%)

regimes1.5s (9.5%)

bsearch10.0ms (0.1%)

simplify10.0ms (0.1%)

end0.0ms (0%)

sample5.7s (35.5%)

Profiling