Metrics for math.log/1 on complex, real part

analyze24.0ms (1%)

Algorithm

1×	search
2×	egg-herbie

Rules

1× +-commutative_binary64 swap-re-im

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 1-exp_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-unmult_binary64 cube-mult_binary64 cube-div_binary64 cube-prod_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate-*l*_binary64 associate-*r*_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64 *-commutative_binary64

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	9	28
2	9	28
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
74.9%	25%	0.1%	3
87.4%	12.5%	0.1%	4
93.7%	6.2%	0.1%	5
96.8%	3.1%	0.1%	6
98.3%	1.6%	0.1%	7
99.1%	0.8%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Symmetry

(sort re im)

Compiler

Compiled 10 to 8 computations (20% saved)

sample26.0ms (1.1%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 19 to 17 computations (10.5% saved)

simplify9.0ms (0.4%)

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 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 1-exp_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-unmult_binary64 cube-mult_binary64 cube-div_binary64 cube-prod_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate-*l*_binary64 associate-*r*_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64 *-commutative_binary64

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	9	14
2	9	14

prune1.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

29.5b

Counts

1 → 1

Compiler

Compiled 9 to 7 computations (22.2% saved)

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

27.5b

(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))

rewrite19.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

29.5b

Rules

3×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-div_binary64` `*-un-lft-identity_binary64`
1×	`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

1 → 15

Calls

1 calls:

4.0ms

(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))

Compiler

Compiled 259 to 69 computations (73.4% saved)

series49.0ms (2.1%)

Error

0.3b

Counts

1 → 18

Calls

1 calls:

39.0ms

(sqrt.f64 (+.f64 (*.f64 re re) (*.f64 im im)))

Compiler

Compiled 512 to 430 computations (16% saved)

simplify66.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

550×	`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`
152×	`associate-l_binary64`
140×	`associate-/l*_binary64`
139×	`distribute-rgt-in_binary64`
99×	`sub-neg_binary64`
86×	`associate-/r*_binary64`
62×	`associate-*l/_binary64`
57×	`*-commutative_binary64`
52×	`associate-*r/_binary64`
49×	`distribute-rgt-out_binary64`
44×	`difference-of-squares_binary64`
35×	`+-commutative_binary64`
34×	`sqr-pow_binary64`
28×	`distribute-rgt-out--_binary64`
24×	`distribute-lft-neg-out_binary64`
21×	`associate-+l-_binary64` `associate-+r-_binary64`
20×	`pow-plus_binary64`
19×	`cube-unmult_binary64` `+-rgt-identity_binary64`
16×	`cube-prod_binary64` `distribute-lft-out_binary64`
14×	`distribute-lft-in_binary64`
13×	`distribute-lft-out--_binary64` `associate-+l+_binary64`
12×	`unpow3_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64` `associate-/r/_binary64`
11×	`unsub-neg_binary64` `sub0-neg_binary64`
6×	`associate--r+_binary64`
5×	`associate--l+_binary64` `associate-+r+_binary64`
4×	`cube-mult_binary64` `cube-div_binary64` `rem-sqrt-square_binary64` `pow-sqr_binary64`
2×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `sqr-neg_binary64` `mul-1-neg_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64`
1×	`1-exp_binary64` `rem-square-sqrt_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

33 → 20

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	65	520
1	176	501
2	508	501
3	2175	501
4	4285	501
5	5050	501

prune14.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	18	2	20
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	18	3	21

Error

2.6b

Counts

21 → 3

Compiler

Compiled 236 to 129 computations (45.3% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im)))
6.1b	(log.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))))
7.3b	(/.f64 (*.f64 re re) im)

rewrite49.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

9×	`add-exp-log_binary64`
8×	`add-cbrt-cube_binary64`
6×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
4×	`pow1_binary64`
3×	`times-frac_binary64` `associate-/r*_binary64` `log-prod_binary64`
2×	`div-exp_binary64` `cbrt-undiv_binary64` `flip3-+_binary64` `log-div_binary64` `flip-+_binary64`
1×	`prod-exp_binary64` `cbrt-unprod_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64` `associate-/l*_binary64` `log-pow_binary64` `rem-log-exp_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

3 → 46

Calls

3 calls:

5.0ms	(/.f64 (*.f64 re re) im)
3.0ms	(+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im)))
3.0ms	(log.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))))

Compiler

Compiled 833 to 386 computations (53.7% saved)

series93.0ms (3.9%)

Error

0.3b

Counts

3 → 29

Calls

3 calls:

33.0ms	(log.f64 (+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im))))
30.0ms	(+.f64 im (.f64 1/2 (/.f64 (.f64 re re) im)))
17.0ms	(/.f64 (*.f64 re re) im)

Compiler

Compiled 718 to 637 computations (11.3% saved)

simplify97.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

336×	`associate-*l/_binary64`
324×	`associate-*r/_binary64`
305×	`cancel-sign-sub-inv_binary64`
270×	`times-frac_binary64`
259×	`associate-l_binary64`
239×	`associate-/l*_binary64`
214×	`associate-r_binary64`
207×	`distribute-neg-frac_binary64`
183×	`unswap-sqr_binary64`
181×	`sub-neg_binary64`
147×	`div-sub_binary64`
141×	`associate-/l/_binary64` `associate-/r*_binary64`
104×	`cube-prod_binary64` `*-commutative_binary64`
89×	`cube-div_binary64`
84×	`log-prod_binary64`
77×	`associate-/r/_binary64`
76×	`log-div_binary64`
72×	`unsub-neg_binary64`
61×	`distribute-neg-in_binary64`
60×	`associate-+r-_binary64`
59×	`distribute-rgt-in_binary64`
58×	`neg-sub0_binary64`
54×	`neg-mul-1_binary64`
52×	`+-commutative_binary64`
50×	`unpow3_binary64` `distribute-lft-in_binary64`
48×	`sqr-pow_binary64`
43×	`distribute-lft-neg-out_binary64`
42×	`distribute-rgt-neg-in_binary64`
41×	`associate-+r+_binary64`
39×	`associate-+l-_binary64`
38×	`exp-prod_binary64` `cube-mult_binary64` `swap-sqr_binary64` `associate-+l+_binary64`
35×	`distribute-lft-neg-in_binary64`
26×	`associate--r-_binary64`
17×	`distribute-rgt-neg-out_binary64`
15×	`associate--l-_binary64` `associate--l+_binary64`
14×	`cube-unmult_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `distribute-rgt-out_binary64`
11×	`pow-plus_binary64`
9×	`*-rgt-identity_binary64`
8×	`log-pow_binary64` `+-rgt-identity_binary64` `distribute-rgt-out--_binary64`
6×	`log-rec_binary64` `*-lft-identity_binary64` `remove-double-neg_binary64` `pow-sqr_binary64` `distribute-neg-out_binary64` `associate--r+_binary64`
5×	`rem-sqrt-square_binary64` `distribute-frac-neg_binary64`
4×	`prod-exp_binary64`
3×	`unpow1/2_binary64` `/-rgt-identity_binary64` `cancel-sign-sub_binary64` `distribute-lft-out--_binary64` `count-2_binary64`
2×	`unpow2_binary64` `unpow1_binary64` `exp-sum_binary64` `mul-1-neg_binary64` `+-inverses_binary64` `difference-of-squares_binary64` `distribute-lft-out_binary64`
1×	`1-exp_binary64` `exp-1-e_binary64` `rem-exp-log_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-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-square-sqrt_binary64` `+-lft-identity_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`

Counts

75 → 54

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	118	1225
1	280	1077
2	787	1071
3	3331	1063
4	4661	1063
5	5095	1063

prune27.0ms (1.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	54	3	57

Error

0.1b

Counts

57 → 3

Compiler

Compiled 552 to 282 computations (48.9% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 im (.f64 1/2 (.f64 re (/.f64 re im))))
0.1b	(*.f64 re (/.f64 re im))
6.1b	(log.f64 (+.f64 im (.f64 1/2 (.f64 re (/.f64 re im)))))

rewrite58.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

17×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
12×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
10×	`times-frac_binary64`
9×	`add-exp-log_binary64`
8×	`add-cbrt-cube_binary64`
6×	`pow1_binary64`
5×	`add-log-exp_binary64`
3×	`log-prod_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `log-div_binary64` `flip-+_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64`
1×	`log-pow_binary64` `rem-log-exp_binary64` `pow-prod-down_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `div-inv_binary64` `-commutative_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

3 → 57

Calls

3 calls:

7.0ms	(*.f64 re (/.f64 re im))
3.0ms	(+.f64 im (.f64 1/2 (.f64 re (/.f64 re im))))
3.0ms	(log.f64 (+.f64 im (.f64 1/2 (.f64 re (/.f64 re im)))))

Compiler

Compiled 1023 to 462 computations (54.8% saved)

series88.0ms (3.7%)

Error

0.1b

Counts

3 → 29

Calls

3 calls:

31.0ms	(log.f64 (+.f64 im (.f64 1/2 (.f64 re (/.f64 re im)))))
30.0ms	(+.f64 im (.f64 1/2 (.f64 re (/.f64 re im))))
19.0ms	(*.f64 re (/.f64 re im))

Compiler

Compiled 718 to 637 computations (11.3% saved)

simplify132.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

367×	`times-frac_binary64`
316×	`associate-*r/_binary64`
306×	`associate-*l/_binary64`
290×	`associate-/l*_binary64`
278×	`cancel-sign-sub-inv_binary64`
262×	`distribute-rgt-neg-in_binary64`
205×	`*-commutative_binary64`
196×	`distribute-neg-frac_binary64`
162×	`sub-neg_binary64`
153×	`unswap-sqr_binary64`
148×	`associate-/r*_binary64`
107×	`log-div_binary64`
97×	`associate-l_binary64`
94×	`associate-/l/_binary64`
93×	`associate-r_binary64`
89×	`log-prod_binary64`
86×	`cube-div_binary64`
75×	`unsub-neg_binary64`
72×	`distribute-neg-in_binary64`
71×	`neg-mul-1_binary64`
69×	`neg-sub0_binary64` `distribute-rgt-in_binary64`
67×	`sqr-pow_binary64`
63×	`associate-/r/_binary64`
61×	`exp-prod_binary64`
60×	`swap-sqr_binary64` `distribute-lft-neg-in_binary64` `distribute-lft-in_binary64`
51×	`cube-prod_binary64`
48×	`+-commutative_binary64`
46×	`associate-+r-_binary64`
41×	`*-rgt-identity_binary64`
40×	`*-lft-identity_binary64`
39×	`distribute-lft-neg-out_binary64`
38×	`associate-+r+_binary64`
37×	`associate-+l+_binary64`
33×	`distribute-rgt-out_binary64`
32×	`unpow3_binary64`
28×	`associate-+l-_binary64`
25×	`/-rgt-identity_binary64`
24×	`associate--r-_binary64`
23×	`cube-mult_binary64`
15×	`sub0-neg_binary64` `distribute-rgt-out--_binary64` `associate--l+_binary64`
13×	`distribute-rgt-neg-out_binary64`
12×	`div-sub_binary64` `pow-sqr_binary64`
11×	`log-rec_binary64` `--rgt-identity_binary64` `associate--r+_binary64`
10×	`cube-unmult_binary64` `associate--l-_binary64`
9×	`log-pow_binary64`
8×	`remove-double-neg_binary64` `+-rgt-identity_binary64`
7×	`pow-plus_binary64`
6×	`unpow1/2_binary64` `prod-exp_binary64` `rem-sqrt-square_binary64`
5×	`remove-double-div_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-lft-out_binary64`
4×	`distribute-lft-out--_binary64`
3×	`cancel-sign-sub_binary64`
2×	`unpow2_binary64` `unpow1_binary64` `exp-sum_binary64` `mul-1-neg_binary64` `+-inverses_binary64` `difference-of-squares_binary64` `count-2_binary64`
1×	`1-exp_binary64` `exp-1-e_binary64` `rem-exp-log_binary64` `rem-square-sqrt_binary64` `*-inverses_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-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` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64`

Counts

86 → 66

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	137	1361
1	336	1198
2	1041	1186
3	3337	1170
4	4764	1170
5	4989	1166
6	4963	1166

prune26.0ms (1.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	66	3	69

Error

0.1b

Counts

69 → 3

Compiler

Compiled 681 to 342 computations (49.8% saved)

localize3.0ms (0.1%)

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 0.1b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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 1-exp_binary64 exp-1-e_binary64 exp-0_binary64 rem-log-exp_binary64 rem-exp-log_binary64 cube-unmult_binary64 cube-mult_binary64 cube-div_binary64 cube-prod_binary64 cube-neg_binary64 rem-3cbrt-rft_binary64 rem-3cbrt-lft_binary64 rem-cbrt-cube_binary64 rem-cube-cbrt_binary64 sqr-abs_binary64 sqr-neg_binary64 rem-sqrt-square_binary64 rem-square-sqrt_binary64 times-frac_binary64 div-sub_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-neg_binary64 mul-1-neg_binary64 /-rgt-identity_binary64 *-rgt-identity_binary64 *-lft-identity_binary64 remove-double-neg_binary64 sub0-neg_binary64 --rgt-identity_binary64 +-rgt-identity_binary64 +-lft-identity_binary64 mul0-rgt_binary64 mul0-lft_binary64 div0_binary64 *-inverses_binary64 +-inverses_binary64 lft-mult-inverse_binary64 rgt-mult-inverse_binary64 remove-double-div_binary64 pow-sqr_binary64 sqr-pow_binary64 difference-of-sqr--1_binary64 difference-of-sqr-1_binary64 difference-of-squares_binary64 unswap-sqr_binary64 swap-sqr_binary64 cancel-sign-sub-inv_binary64 cancel-sign-sub_binary64 distribute-neg-frac_binary64 distribute-frac-neg_binary64 distribute-neg-out_binary64 distribute-neg-in_binary64 distribute-rgt-neg-out_binary64 distribute-lft-neg-out_binary64 distribute-rgt-neg-in_binary64 distribute-lft-neg-in_binary64 distribute-rgt1-in_binary64 distribute-lft1-in_binary64 distribute-rgt-out--_binary64 distribute-rgt-out_binary64 distribute-lft-out--_binary64 distribute-lft-out_binary64 distribute-rgt-in_binary64 distribute-lft-in_binary64 count-2_binary64 associate-/l/_binary64 associate-/r/_binary64 associate-/l*_binary64 associate-/r*_binary64 associate-*l/_binary64 associate-*r/_binary64 associate-*l*_binary64 associate-*r*_binary64 associate--r-_binary64 associate--l-_binary64 associate--l+_binary64 associate--r+_binary64 associate-+l-_binary64 associate-+r-_binary64 associate-+l+_binary64 associate-+r+_binary64 *-commutative_binary64 +-commutative_binary64

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune1.0ms (0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	2	2
Total	3	3

Error

0.1b

Counts

3 → 3

Compiler

Compiled 0 to 0 computations (0% saved)

regimes580.0ms (24.6%)

Accuracy

Total 6.8b remaining (97.9%)

Threshold costs 0b (0%)

Compiler

Compiled 1501 to 1245 computations (17.1% saved)

bsearch31.0ms (1.3%)

Steps

Iters	Range		Point
4	1.3615758364165824e+110	9.61176686499161e+110	3.0994021608132516e+110
9	1.5726615535625908e-159	3.4693918181042096e-150	3.5598012421053094e-159

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64` `+-commutative_binary64`
1×	`neg-sub0_binary64` `sub-neg_binary64` `mul-1-neg_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` `unsub-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	46
1	30	46
2	32	46
3	33	46
4	34	46
5	34	46

end7.0ms (0.3%)

Compiler: Compiled 90 to 63 computations (30% saved)

sample917.0ms (39%)

Algorithm

1×

intervals

Results

384.0ms

8000×

body

128

valid

Compiler

Compiled 65 to 59 computations (9.2% saved)

Details

analyze24.0ms (1%)

sample26.0ms (1.1%)

simplify9.0ms (0.4%)

prune1.0ms (0.1%)

localize8.0ms (0.3%)

rewrite19.0ms (0.8%)

series49.0ms (2.1%)

simplify66.0ms (2.8%)

prune14.0ms (0.6%)

localize8.0ms (0.3%)

rewrite49.0ms (2.1%)

series93.0ms (3.9%)

simplify97.0ms (4.1%)

prune27.0ms (1.1%)

localize7.0ms (0.3%)

rewrite58.0ms (2.5%)

series88.0ms (3.7%)

simplify132.0ms (5.6%)

prune26.0ms (1.1%)

localize3.0ms (0.1%)

rewrite2.0ms (0.1%)

series0.0ms (0%)

simplify8.0ms (0.3%)

prune1.0ms (0%)

regimes580.0ms (24.6%)

bsearch31.0ms (1.3%)

simplify5.0ms (0.2%)

end7.0ms (0.3%)

sample917.0ms (39%)

Profiling