Details

analyze1.4s (5.4%)

Algorithm

1×

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)

sample128.0ms (0.5%)

Algorithm

1×

intervals

Results

42.0ms	81×	body	1024	invalid
28.0ms	243×	body	128	valid
13.0ms	24×	body	512	invalid
11.0ms	12×	body	2048	invalid
3.0ms	22×	body	128	invalid
3.0ms	5×	body	1024	valid
2.0ms	6×	body	512	valid
2.0ms	9×	body	256	invalid
1.0ms	1×	body	2048	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify350.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

533×	`distribute-rgt-out--_binary64`
459×	`associate-/l*_binary64`
318×	`associate-/r*_binary64`
288×	`associate-*r/_binary64`
283×	`unswap-sqr_binary64` `associate-*l/_binary64`
216×	`exp-prod_binary64`
183×	`associate-/r/_binary64`
181×	`sqr-pow_binary64`
173×	`swap-sqr_binary64`
160×	`*-commutative_binary64`
155×	`distribute-rgt-neg-in_binary64`
125×	`associate-/l/_binary64`
123×	`pow-sqr_binary64`
98×	`sub-neg_binary64`
74×	`associate-l_binary64`
70×	`associate-r_binary64`
69×	`exp-sum_binary64` `div-sub_binary64`
56×	`times-frac_binary64`
55×	`cancel-sign-sub-inv_binary64`
54×	`distribute-rgt-out_binary64`
44×	`distribute-lft-out_binary64`
43×	`distribute-lft-neg-in_binary64`
40×	`unsub-neg_binary64` `distribute-lft-out--_binary64`
37×	`exp-diff_binary64` `*-lft-identity_binary64`
34×	`neg-mul-1_binary64`
29×	`distribute-rgt1-in_binary64` `distribute-rgt-in_binary64`
26×	`neg-sub0_binary64`
20×	`distribute-frac-neg_binary64`
19×	`distribute-neg-in_binary64`
17×	`distribute-neg-out_binary64`
16×	`distribute-neg-frac_binary64` `distribute-rgt-neg-out_binary64` `+-commutative_binary64`
15×	`/-rgt-identity_binary64` `distribute-lft-in_binary64`
14×	`pow-plus_binary64`
13×	`*-rgt-identity_binary64`
12×	`cube-prod_binary64` `mul0-lft_binary64` `distribute-lft-neg-out_binary64`
10×	`cube-unmult_binary64`
9×	`distribute-lft1-in_binary64` `associate--r+_binary64`
8×	`mul0-rgt_binary64` `+-inverses_binary64` `associate-+l-_binary64`
7×	`remove-double-neg_binary64` `+-rgt-identity_binary64`
6×	`sub0-neg_binary64` `div0_binary64` `associate-+r-_binary64`
5×	`unpow3_binary64` `exp-to-pow_binary64` `associate-+l+_binary64`
4×	`--rgt-identity_binary64` `+-lft-identity_binary64` `associate-+r+_binary64`
3×	`div-exp_binary64` `prod-exp_binary64` `exp-neg_binary64` `cube-div_binary64` `count-2_binary64`
2×	`associate--r-_binary64`
1×	`pow-base-1_binary64` `exp-lft-sqr_binary64` `exp-sqrt_binary64` `1-exp_binary64` `rem-exp-log_binary64` `rem-sqrt-square_binary64` `*-inverses_binary64` `associate--l+_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow2_binary64` `unpow1/2_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `rec-exp_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `cube-mult_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` `mul-1-neg_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `associate--l-_binary64`

Counts

1 → 4

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	74
1	37	72
2	62	72
3	105	72
4	249	72
5	970	72
6	3051	72
7	3583	72

prune24.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	2	2	4
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	2	3	5

Error

30.3b

Counts

5 → 3

Compiler

Compiled 254 to 87 computations (65.7% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.4b	(*.f64 (atan2.f64 x.im x.re) y.im)
27.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
27.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.7b	(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)))

rewrite116.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

30.2b

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:

8.0ms	(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)))
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)))
3.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2594 to 353 computations (86.4% saved)

series1.1s (4.3%)

Error

15.9b

Counts

4 → 61

Calls

4 calls:

508.0ms	(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)))
205.0ms	(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 6435 to 3289 computations (48.9% saved)

simplify252.0ms (1%)

Algorithm

1×	egg-herbie

Rules

392×	`cancel-sign-sub-inv_binary64`
276×	`unswap-sqr_binary64`
269×	`associate-r_binary64`
256×	`associate-l_binary64`
242×	`associate-/l/_binary64`
226×	`distribute-rgt-neg-in_binary64`
209×	`distribute-lft-neg-in_binary64`
196×	`distribute-rgt-in_binary64`
158×	`distribute-lft-in_binary64`
147×	`distribute-neg-frac_binary64`
140×	`times-frac_binary64`
135×	`sub-neg_binary64`
125×	`associate-/l*_binary64`
110×	`*-commutative_binary64`
105×	`sqr-pow_binary64`
98×	`associate-/r*_binary64`
85×	`neg-sub0_binary64`
84×	`neg-mul-1_binary64`
77×	`associate-*l/_binary64`
69×	`associate-*r/_binary64`
63×	`pow-sqr_binary64`
57×	`distribute-lft-neg-out_binary64`
53×	`+-commutative_binary64`
48×	`difference-of-squares_binary64`
40×	`pow-plus_binary64`
39×	`distribute-rgt-out_binary64`
35×	`distribute-rgt-neg-out_binary64`
34×	`unsub-neg_binary64` `associate-/r/_binary64`
33×	`associate-+r-_binary64`
27×	`associate-+l-_binary64`
25×	`distribute-neg-in_binary64`
24×	`div-sub_binary64`
20×	`cube-prod_binary64` `+-rgt-identity_binary64` `distribute-rgt-out--_binary64`
19×	`associate-+l+_binary64` `associate-+r+_binary64`
16×	`log-prod_binary64`
15×	`exp-prod_binary64` `cube-unmult_binary64` `sub0-neg_binary64`
14×	`log-div_binary64`
11×	`*-rgt-identity_binary64`
10×	`*-lft-identity_binary64`
9×	`unpow3_binary64` `distribute-lft-out--_binary64`
8×	`exp-sqrt_binary64`
7×	`cube-div_binary64` `associate--r+_binary64`
6×	`swap-sqr_binary64` `distribute-lft-out_binary64`
5×	`cancel-sign-sub_binary64` `associate--l+_binary64`
4×	`log-pow_binary64` `cube-mult_binary64`
3×	`rem-sqrt-square_binary64` `remove-double-neg_binary64` `mul0-lft_binary64` `associate--r-_binary64`
2×	`log-rec_binary64` `unpow2_binary64` `unpow1_binary64` `mul-1-neg_binary64` `--rgt-identity_binary64` `mul0-rgt_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `count-2_binary64`
1×	`exp-lft-sqr_binary64` `prod-exp_binary64` `exp-diff_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-log-exp_binary64` `rem-square-sqrt_binary64` `*-inverses_binary64` `rgt-mult-inverse_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` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `div-exp_binary64` `rec-exp_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-0_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` `/-rgt-identity_binary64` `+-lft-identity_binary64` `div0_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `distribute-frac-neg_binary64` `distribute-lft1-in_binary64` `associate--l-_binary64`

Counts

117 → 192

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	172	2606
1	372	2463
2	1040	2463
3	2651	2463

prune424.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	185	7	192
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	187	8	195

Error

16.2b

Counts

195 → 8

Compiler

Compiled 9626 to 3310 computations (65.6% saved)

localize43.0ms (0.2%)

Local error

Found 4 expressions with local error:

27.2b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.7b	(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)))))))
32.7b	(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)))
32.7b	(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)))

rewrite151.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

16.2b

Rules

6×	`add-sqr-sqrt_binary64`
5×	`pow1_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`sin-sum_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64`

Counts

4 → 39

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)))
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	(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)))))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 3576 to 793 computations (77.8% saved)

series2.4s (9.2%)

Error

16.2b

Counts

4 → 75

Calls

4 calls:

666.0ms	(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)))
656.0ms	(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)))
634.0ms	(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)))))))
246.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 16914 to 7526 computations (55.5% saved)

simplify429.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

382×	`cancel-sign-sub-inv_binary64`
285×	`associate-r_binary64`
266×	`unswap-sqr_binary64`
249×	`times-frac_binary64`
224×	`distribute-rgt-neg-in_binary64`
210×	`associate-/l*_binary64`
207×	`distribute-lft-neg-in_binary64`
204×	`associate-l_binary64`
196×	`distribute-rgt-in_binary64`
159×	`associate-/r*_binary64`
158×	`distribute-lft-in_binary64`
145×	`distribute-neg-frac_binary64`
135×	`sub-neg_binary64`
125×	`*-commutative_binary64`
86×	`sqr-pow_binary64`
85×	`neg-sub0_binary64`
84×	`neg-mul-1_binary64`
80×	`associate-*l/_binary64`
69×	`associate-*r/_binary64`
62×	`associate-/r/_binary64`
57×	`distribute-lft-neg-out_binary64`
56×	`pow-sqr_binary64`
53×	`+-commutative_binary64`
48×	`difference-of-squares_binary64`
40×	`pow-plus_binary64`
37×	`distribute-rgt-out_binary64`
35×	`distribute-rgt-neg-out_binary64`
34×	`unsub-neg_binary64`
33×	`associate-+r-_binary64`
27×	`associate-+l-_binary64`
25×	`distribute-neg-in_binary64`
24×	`div-sub_binary64`
20×	`+-rgt-identity_binary64` `distribute-rgt-out--_binary64`
17×	`associate-+l+_binary64` `associate-+r+_binary64`
15×	`sub0-neg_binary64`
12×	`cube-unmult_binary64` `cube-prod_binary64`
9×	`distribute-lft-out--_binary64`
8×	`log-div_binary64` `unpow3_binary64`
7×	`associate--r+_binary64`
6×	`distribute-lft-out_binary64`
5×	`cancel-sign-sub_binary64` `associate-/l/_binary64` `associate--l+_binary64`
4×	`log-pow_binary64` `log-prod_binary64` `cube-mult_binary64`
3×	`remove-double-neg_binary64` `mul0-lft_binary64` `associate--r-_binary64`
2×	`log-rec_binary64` `unpow2_binary64` `unpow1_binary64` `rem-sqrt-square_binary64` `mul-1-neg_binary64` `--rgt-identity_binary64` `mul0-rgt_binary64` `swap-sqr_binary64` `distribute-neg-out_binary64`
1×	`exp-diff_binary64` `1-exp_binary64` `rem-log-exp_binary64` `rem-square-sqrt_binary64` `-rgt-identity_binary64` `-inverses_binary64` `rgt-mult-inverse_binary64` `distribute-rgt1-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` `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` `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-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_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` `/-rgt-identity_binary64` `*-lft-identity_binary64` `+-lft-identity_binary64` `div0_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `distribute-frac-neg_binary64` `distribute-lft1-in_binary64` `count-2_binary64` `associate--l-_binary64`

Counts

114 → 191

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	179	4226
1	366	3969
2	1039	3969
3	2960	3969

prune715.0ms (2.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	188	3	191
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	191	8	199

Error

16.2b

Counts

199 → 8

Compiler

Compiled 17830 to 5450 computations (69.4% saved)

localize48.0ms (0.2%)

Local error

Found 4 expressions with local error:

32.7b	(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)))))))
32.7b	(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)))
32.7b	(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)))
32.7b	(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)))

rewrite180.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

16.2b

Rules

4×	`sin-sum_binary64` `pow1_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`

Counts

4 → 32

Calls

4 calls:

8.0ms	(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)))
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)))
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	(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)))))))

Compiler

Compiled 4328 to 1024 computations (76.3% saved)

series3.2s (12.3%)

Error

16.1b

Counts

4 → 78

Calls

4 calls:

756.0ms	(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)))
738.0ms	(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)))
703.0ms	(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)))))))
693.0ms	(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)))

Compiler

Compiled 26788 to 11113 computations (58.5% saved)

simplify626.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

777×	`associate-/r*_binary64`
591×	`associate-*l/_binary64`
468×	`associate-/r/_binary64`
437×	`associate-*r/_binary64`
359×	`associate-/l/_binary64`
331×	`*-commutative_binary64`
238×	`times-frac_binary64`
187×	`associate-/l*_binary64`
182×	`associate-r_binary64`
109×	`associate-l_binary64`
53×	`div-sub_binary64`
40×	`distribute-rgt-in_binary64`
39×	`cancel-sign-sub-inv_binary64`
34×	`sub-neg_binary64`
31×	`distribute-lft-in_binary64`
27×	`log-div_binary64`
24×	`associate-+r+_binary64` `+-commutative_binary64`
23×	`unsub-neg_binary64`
22×	`associate-+r-_binary64`
19×	`distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64` `associate--l-_binary64`
18×	`neg-mul-1_binary64`
16×	`neg-sub0_binary64`
15×	`log-prod_binary64` `associate--r+_binary64` `associate-+l-_binary64`
13×	`distribute-neg-in_binary64`
12×	`distribute-lft-neg-out_binary64`
10×	`pow-plus_binary64` `sqr-pow_binary64`
9×	`distribute-rgt-neg-out_binary64`
8×	`log-pow_binary64` `unswap-sqr_binary64` `associate-+l+_binary64`
7×	`pow-sqr_binary64` `associate--r-_binary64`
6×	`cube-unmult_binary64` `associate--l+_binary64`
5×	`exp-sum_binary64`
4×	`cos-neg_binary64` `sin-neg_binary64` `exp-prod_binary64` `remove-double-neg_binary64` `sub0-neg_binary64`
3×	`exp-to-pow_binary64` `mul0-lft_binary64`
2×	`log-rec_binary64` `unpow2_binary64` `unpow1_binary64` `exp-diff_binary64` `--rgt-identity_binary64` `mul0-rgt_binary64` `swap-sqr_binary64`
1×	`prod-exp_binary64` `1-exp_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `-rgt-identity_binary64` `+-rgt-identity_binary64` `-inverses_binary64` `rgt-mult-inverse_binary64` `cancel-sign-sub_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` `unpow3_binary64` `unpow1/2_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` `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` `*-lft-identity_binary64` `+-lft-identity_binary64` `div0_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_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`

Counts

110 → 187

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	134	4942
1	220	4618
2	546	4618
3	1671	4618
4	4919	4618

prune1.0s (3.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	187	8	195

Error

16.2b

Counts

195 → 8

Compiler

Compiled 25486 to 7711 computations (69.7% saved)

localize52.0ms (0.2%)

Local error

Found 4 expressions with local error:

32.7b	(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)))
32.7b	(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)))
32.7b	(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)))
32.7b	(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)))

rewrite231.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

16.2b

Rules

4×	`sin-sum_binary64` `pow1_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`

Counts

4 → 32

Calls

4 calls:

8.0ms	(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)))
8.0ms	(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)))
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)))
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)))

Compiler

Compiled 5640 to 1368 computations (75.7% saved)

series3.6s (13.7%)

Error

16.1b

Counts

4 → 80

Calls

4 calls:

789.0ms	(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)))
775.0ms	(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)))
768.0ms	(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)))
767.0ms	(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)))

Compiler

Compiled 35984 to 14839 computations (58.8% saved)

simplify672.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

781×	`associate-/r*_binary64`
592×	`associate-*l/_binary64`
466×	`associate-/r/_binary64`
448×	`associate-*r/_binary64`
358×	`associate-/l/_binary64`
325×	`*-commutative_binary64`
238×	`times-frac_binary64`
187×	`associate-/l*_binary64`
180×	`associate-r_binary64`
108×	`associate-l_binary64`
53×	`div-sub_binary64`
40×	`distribute-rgt-in_binary64`
39×	`cancel-sign-sub-inv_binary64`
34×	`sub-neg_binary64`
31×	`distribute-lft-in_binary64`
27×	`log-div_binary64`
24×	`associate-+r+_binary64` `+-commutative_binary64`
23×	`unsub-neg_binary64`
22×	`associate-+r-_binary64`
19×	`distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64` `associate--l-_binary64`
18×	`neg-mul-1_binary64`
16×	`neg-sub0_binary64`
15×	`log-prod_binary64` `associate--r+_binary64` `associate-+l-_binary64`
13×	`distribute-neg-in_binary64` `distribute-lft-neg-out_binary64`
10×	`pow-plus_binary64` `sqr-pow_binary64`
9×	`distribute-rgt-neg-out_binary64`
8×	`log-pow_binary64` `unswap-sqr_binary64` `associate-+l+_binary64`
7×	`pow-sqr_binary64` `associate--r-_binary64`
6×	`cube-unmult_binary64` `associate--l+_binary64`
5×	`exp-sum_binary64`
4×	`cos-neg_binary64` `sin-neg_binary64` `exp-prod_binary64` `sub0-neg_binary64`
3×	`exp-to-pow_binary64` `remove-double-neg_binary64` `mul0-lft_binary64`
2×	`log-rec_binary64` `unpow2_binary64` `unpow1_binary64` `exp-diff_binary64` `--rgt-identity_binary64` `mul0-rgt_binary64` `swap-sqr_binary64`
1×	`prod-exp_binary64` `1-exp_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `-rgt-identity_binary64` `+-rgt-identity_binary64` `-inverses_binary64` `rgt-mult-inverse_binary64` `cancel-sign-sub_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` `unpow3_binary64` `unpow1/2_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` `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` `*-lft-identity_binary64` `+-lft-identity_binary64` `div0_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_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`

Counts

112 → 204

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	117	5088
1	224	4764
2	550	4764
3	1675	4764
4	4923	4764

prune1.6s (5.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	204	8	212

Error

16.2b

Counts

212 → 8

Compiler

Compiled 35712 to 11383 computations (68.1% saved)

regimes1.7s (6.3%)

Accuracy

Total 0.2b remaining (1.3%)

Threshold costs 0.2b (1.3%)

Compiler

Compiled 21602 to 10720 computations (50.4% saved)

bsearch10.0ms (0%)

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

simplify18.0ms (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

Proof

(if real (<= f64 (* f64 (exp f64 (- f64 (* f64 (log f64 (sqrt f64 (+ f64 (* f64 (x re) (x re)) (* f64 (x im) (x im))))) (y re)) (* f64 (atan2 f64 (x im) (x re)) (y im)))) (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))))) 4766026668020397/9007199254740992) (* f64 (exp f64 (- f64 (* f64 (log f64 (sqrt f64 (+ f64 (* f64 (x re) (x re)) (* f64 (x im) (x im))))) (y re)) (* f64 (atan2 f64 (x im) (x re)) (y im)))) (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))))) (* f64 (exp f64 (- f64 (* f64 (log f64 (sqrt f64 (+ f64 (* f64 (x re) (x re)) (* f64 (x im) (x im))))) (y re)) (* f64 (atan2 f64 (x im) (x re)) (y im)))) (sin f64 (* f64 (y re) (atan2 f64 (x im) (x re))))))
<= *-commutative_binary64
(if real (<= f64 (* f64 (exp f64 (- f64 (* f64 (log f64 (sqrt f64 (+ f64 (* f64 (x re) (x re)) (* f64 (x im) (x im))))) (y re)) (* f64 (atan2 f64 (x im) (x re)) (y im)))) (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))))) 4766026668020397/9007199254740992) (* f64 (exp f64 (- f64 (* f64 (log f64 (sqrt f64 (+ f64 (* f64 (x re) (x re)) (* f64 (x im) (x im))))) (y re)) (* f64 (atan2 f64 (x im) (x re)) (y im)))) (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))))))) (* f64 (exp f64 (- f64 (* f64 (log f64 (sqrt f64 (+ f64 (* f64 (x re) (x re)) (* f64 (x im) (x im))))) (y re)) (* f64 (atan2 f64 (x im) (x re)) (y im)))) (sin f64 (* f64 (y re) (atan2 f64 (x im) (x re))))))
<= *-commutative_binary64
(if real (<= f64 (* f64 (exp f64 (- f64 (* f64 (log f64 (sqrt f64 (+ f64 (* f64 (x re) (x re)) (* f64 (x im) (x im))))) (y re)) (* f64 (atan2 f64 (x im) (x re)) (y im)))) (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))))))) 4766026668020397/9007199254740992) (* f64 (exp f64 (- f64 (* f64 (log f64 (sqrt f64 (+ f64 (* f64 (x re) (x re)) (* f64 (x im) (x im))))) (y re)) (* f64 (atan2 f64 (x im) (x re)) (y im)))) (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)))))) (* f64 (exp f64 (- f64 (* f64 (log f64 (sqrt f64 (+ f64 (* f64 (x re) (x re)) (* f64 (x im) (x im))))) (y re)) (* f64 (atan2 f64 (x im) (x re)) (y im)))) (sin f64 (* f64 (y re) (atan2 f64 (x im) (x re))))))

end0.0ms (0%)

sample5.7s (21.8%)

Algorithm

1×

intervals

Results

1.3s	2517×	body	1024	invalid
835.0ms	7592×	body	128	valid
328.0ms	927×	body	512	invalid
153.0ms	175×	body	2048	invalid
87.0ms	170×	body	1024	valid
71.0ms	321×	body	256	invalid
58.0ms	156×	body	512	valid
55.0ms	483×	body	128	invalid
16.0ms	72×	body	256	valid
8.0ms	10×	body	2048	valid

Compiler

Compiled 4444 to 2178 computations (51% saved)

Details

analyze1.4s (5.4%)

sample128.0ms (0.5%)

simplify350.0ms (1.3%)

prune24.0ms (0.1%)

localize22.0ms (0.1%)

rewrite116.0ms (0.4%)

series1.1s (4.3%)

simplify252.0ms (1%)

prune424.0ms (1.6%)

localize43.0ms (0.2%)

rewrite151.0ms (0.6%)

series2.4s (9.2%)

simplify429.0ms (1.6%)

prune715.0ms (2.7%)

localize48.0ms (0.2%)

rewrite180.0ms (0.7%)

series3.2s (12.3%)

simplify626.0ms (2.4%)

prune1.0s (3.9%)

localize52.0ms (0.2%)

rewrite231.0ms (0.9%)

series3.6s (13.7%)

simplify672.0ms (2.6%)

prune1.6s (5.9%)

regimes1.7s (6.3%)

bsearch10.0ms (0%)

simplify18.0ms (0.1%)

end0.0ms (0%)

sample5.7s (21.8%)

Profiling