Metrics for Linear.Quaternion:$clog from linear-1.19.1.3

analyze94.0ms (5.2%)

Algorithm

1×	search
2×	egg-herbie

Rules

2× +-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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	11	18
2	11	18
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	50%	6.3%	6
43.7%	43.7%	12.6%	7
59.3%	26.5%	14.1%	8
59.3%	22.6%	18%	9
67.1%	13.7%	19.2%	10
67.1%	11.5%	21.4%	11
71%	6.9%	22%	12
71%	5.8%	23.2%	13
73%	3.5%	23.5%	14

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample15.0ms (0.8%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
0.0ms	8×	body	128	nan

Compiler

Compiled 13 to 13 computations (0% saved)

simplify9.0ms (0.5%)

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	6	9
1	7	9
2	7	9

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

20.8b

Counts

1 → 1

Compiler

Compiled 6 to 5 computations (16.7% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (*.f64 x x) y)
19.4b	(sqrt.f64 (+.f64 (*.f64 x x) y))

rewrite29.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

20.8b

Rules

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

Counts

2 → 26

Calls

2 calls:

4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
4.0ms	(+.f64 (*.f64 x x) y)

Compiler

Compiled 340 to 89 computations (73.8% saved)

series48.0ms (2.6%)

Error

0.0b

Counts

2 → 23

Calls

2 calls:

21.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
18.0ms	(+.f64 (*.f64 x x) y)

Compiler

Compiled 337 to 303 computations (10.1% saved)

simplify65.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

621×	`cancel-sign-sub-inv_binary64`
466×	`times-frac_binary64`
270×	`*-commutative_binary64`
240×	`unswap-sqr_binary64`
239×	`associate-/l*_binary64`
196×	`associate-/r*_binary64`
195×	`distribute-rgt-in_binary64`
176×	`distribute-lft-in_binary64`
153×	`associate-*l/_binary64`
142×	`associate-l_binary64`
137×	`associate-*r/_binary64`
126×	`associate-r_binary64`
114×	`difference-of-squares_binary64`
101×	`distribute-rgt-neg-in_binary64`
100×	`sub-neg_binary64`
99×	`distribute-lft-neg-in_binary64`
98×	`distribute-rgt-out_binary64`
85×	`div-sub_binary64`
84×	`associate-+l+_binary64`
83×	`neg-mul-1_binary64`
81×	`neg-sub0_binary64`
77×	`associate-+r+_binary64`
75×	`distribute-lft-out_binary64`
71×	`distribute-neg-frac_binary64`
68×	`sqr-pow_binary64`
52×	`unsub-neg_binary64` `associate-/l/_binary64`
46×	`associate-/r/_binary64`
19×	`pow-plus_binary64` `associate-+l-_binary64`
18×	`exp-prod_binary64` `pow-sqr_binary64` `+-commutative_binary64`
15×	`distribute-rgt-out--_binary64`
14×	`cube-unmult_binary64`
13×	`sub0-neg_binary64` `associate-+r-_binary64`
12×	`distribute-lft-neg-out_binary64`
11×	`cube-prod_binary64` `+-rgt-identity_binary64`
9×	`mul0-rgt_binary64` `mul0-lft_binary64`
7×	`unpow3_binary64` `distribute-lft-out--_binary64`
6×	`distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64` `associate--r+_binary64`
5×	`div0_binary64`
4×	`exp-sum_binary64` `rem-sqrt-square_binary64`
3×	`unpow2_binary64` `cube-mult_binary64` `swap-sqr_binary64` `associate--l+_binary64`
2×	`unpow1/2_binary64` `unpow1_binary64`
1×	`log-prod_binary64` `prod-exp_binary64` `1-exp_binary64` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `remove-double-neg_binary64` `+-lft-identity_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` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-div_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `--rgt-identity_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

49 → 34

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	522
1	149	483
2	345	483
3	1156	477
4	3756	477
5	5029	477

prune16.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	31	3	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	31	4	35

Error

0b

Counts

35 → 4

Compiler

Compiled 294 to 115 computations (60.9% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (cbrt.f64 (+.f64 y (*.f64 x x))))
0.3b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 y (.f64 x x)))) (sqrt.f64 (cbrt.f64 (+.f64 y (*.f64 x x)))))
20.3b	(cbrt.f64 (+.f64 y (*.f64 x x)))
20.3b	(cbrt.f64 (+.f64 y (*.f64 x x)))

rewrite57.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

0b

Rules

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

Counts

4 → 74

Calls

4 calls:

8.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 y (.f64 x x)))) (sqrt.f64 (cbrt.f64 (+.f64 y (*.f64 x x)))))
3.0ms	(sqrt.f64 (cbrt.f64 (+.f64 y (*.f64 x x))))
3.0ms	(cbrt.f64 (+.f64 y (*.f64 x x)))
2.0ms	(cbrt.f64 (+.f64 y (*.f64 x x)))

Compiler

Compiled 1735 to 259 computations (85.1% saved)

series123.0ms (6.8%)

Error

0b

Counts

4 → 30

Calls

4 calls:

32.0ms	(cbrt.f64 (+.f64 y (*.f64 x x)))
30.0ms	(cbrt.f64 (+.f64 y (*.f64 x x)))
30.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 y (.f64 x x)))) (sqrt.f64 (cbrt.f64 (+.f64 y (*.f64 x x)))))
19.0ms	(sqrt.f64 (cbrt.f64 (+.f64 y (*.f64 x x))))

Compiler

Compiled 1554 to 1259 computations (19% saved)

simplify132.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

445×	`associate-l_binary64`
354×	`log-prod_binary64`
325×	`neg-mul-1_binary64`
313×	`associate-r_binary64`
245×	`distribute-rgt-in_binary64`
226×	`distribute-lft-in_binary64`
221×	`unswap-sqr_binary64`
156×	`sqr-pow_binary64`
149×	`cancel-sign-sub-inv_binary64`
140×	`unsub-neg_binary64`
137×	`distribute-rgt-neg-in_binary64`
125×	`distribute-lft-neg-in_binary64`
116×	`distribute-lft-neg-out_binary64`
111×	`distribute-rgt-neg-out_binary64`
101×	`distribute-rgt-out_binary64`
89×	`*-commutative_binary64`
82×	`exp-sum_binary64`
81×	`exp-prod_binary64`
77×	`sub-neg_binary64`
66×	`neg-sub0_binary64`
65×	`*-lft-identity_binary64`
62×	`cube-prod_binary64`
60×	`*-rgt-identity_binary64`
57×	`div-sub_binary64`
44×	`pow-sqr_binary64`
38×	`unpow3_binary64` `rem-sqrt-square_binary64`
37×	`associate-/r*_binary64`
31×	`log-pow_binary64` `pow-plus_binary64`
29×	`associate-+l+_binary64` `+-commutative_binary64`
28×	`cube-unmult_binary64`
26×	`exp-diff_binary64`
24×	`associate-+r+_binary64`
22×	`distribute-rgt-out--_binary64`
21×	`mul0-rgt_binary64` `mul0-lft_binary64`
20×	`exp-neg_binary64` `distribute-neg-in_binary64`
18×	`associate-+l-_binary64`
17×	`prod-exp_binary64` `sub0-neg_binary64`
15×	`distribute-lft-out_binary64`
14×	`cube-mult_binary64`
13×	`associate-+r-_binary64`
12×	`exp-to-pow_binary64` `cube-div_binary64` `swap-sqr_binary64` `associate-/l/_binary64`
11×	`log-div_binary64` `unpow1/3_binary64`
8×	`times-frac_binary64` `+-rgt-identity_binary64` `count-2_binary64` `associate--r+_binary64`
6×	`difference-of-squares_binary64` `distribute-neg-out_binary64`
5×	`+-lft-identity_binary64`
4×	`unpow2_binary64` `unpow1/2_binary64` `associate--r-_binary64`
3×	`log-rec_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `mul-1-neg_binary64` `remove-double-neg_binary64` `distribute-neg-frac_binary64` `distribute-lft-out--_binary64` `associate-/l*_binary64` `associate--l+_binary64`
2×	`unpow1_binary64` `div-exp_binary64` `distribute-frac-neg_binary64` `distribute-lft1-in_binary64` `associate-*r/_binary64`
1×	`unpow-1_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-3cbrt-lft_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-square-sqrt_binary64` `--rgt-identity_binary64` `+-inverses_binary64` `cancel-sign-sub_binary64` `distribute-rgt1-in_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` `pow-base-0_binary64` `pow-base-1_binary64` `unpow0_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `rec-exp_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `/-rgt-identity_binary64` `div0_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` `associate-/r/_binary64` `associate-l/_binary64`

Counts

104 → 88

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	1884
1	235	1812
2	600	1803
3	1572	1803
4	3214	1803
5	4476	1803
6	4914	1803

prune238.0ms (13.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	88	4	92

Error

0b

Counts

92 → 4

Compiler

Compiled 1445 to 308 computations (78.7% saved)

localize2.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

0b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

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

simplify8.0ms (0.4%)

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 (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

0b

Counts

4 → 4

Compiler

Compiled 7 to 6 computations (14.3% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite40.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0b

Rules

15×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
10×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64` `times-frac_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64` `add-log-exp_binary64`
3×	`associate-l_binary64`
2×	`prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64`
1×	`pow-prod-down_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `div-inv_binary64` `-commutative_binary64` `sum-log_binary64` `flip3-+_binary64` `flip-+_binary64` `+-commutative_binary64`

Counts

2 → 43

Calls

2 calls:

7.0ms	(*.f64 1/2 (/.f64 y x))
3.0ms	(+.f64 x (*.f64 1/2 (/.f64 y x)))

Compiler

Compiled 597 to 308 computations (48.4% saved)

series40.0ms (2.2%)

Error

0b

Counts

2 → 18

Calls

2 calls:

23.0ms	(+.f64 x (*.f64 1/2 (/.f64 y x)))
15.0ms	(*.f64 1/2 (/.f64 y x))

Compiler

Compiled 206 to 176 computations (14.6% saved)

simplify110.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

615×	`associate-/l*_binary64`
586×	`associate-*l/_binary64`
518×	`associate-*r/_binary64`
317×	`times-frac_binary64`
293×	`associate-/l/_binary64`
200×	`distribute-rgt-out_binary64`
195×	`distribute-rgt-in_binary64`
173×	`distribute-lft-in_binary64` `associate-/r*_binary64`
171×	`associate-/r/_binary64`
166×	`associate-l_binary64`
146×	`distribute-neg-frac_binary64`
124×	`cancel-sign-sub-inv_binary64`
122×	`associate-r_binary64`
111×	`distribute-rgt-neg-in_binary64`
108×	`div-sub_binary64`
106×	`sub-neg_binary64`
97×	`*-commutative_binary64`
95×	`distribute-lft-neg-in_binary64`
82×	`neg-mul-1_binary64`
79×	`neg-sub0_binary64`
75×	`unsub-neg_binary64`
63×	`sqr-pow_binary64`
48×	`log-div_binary64`
37×	`distribute-rgt-out--_binary64`
36×	`distribute-lft-neg-out_binary64`
29×	`unpow3_binary64`
28×	`cube-div_binary64`
26×	`distribute-rgt-neg-out_binary64`
25×	`log-prod_binary64`
21×	`distribute-lft-out_binary64`
19×	`*-lft-identity_binary64` `unswap-sqr_binary64`
17×	`distribute-neg-in_binary64`
16×	`+-commutative_binary64`
14×	`associate-+l+_binary64`
13×	`/-rgt-identity_binary64`
12×	`cube-prod_binary64` `*-rgt-identity_binary64` `div0_binary64` `pow-sqr_binary64`
9×	`cube-unmult_binary64` `remove-double-neg_binary64` `associate-+r-_binary64`
8×	`distribute-neg-out_binary64` `associate-+l-_binary64` `associate-+r+_binary64`
7×	`+-rgt-identity_binary64`
6×	`mul0-rgt_binary64` `mul0-lft_binary64` `swap-sqr_binary64` `distribute-frac-neg_binary64`
5×	`cube-mult_binary64` `sub0-neg_binary64`
3×	`exp-prod_binary64`
2×	`pow-plus_binary64` `exp-sum_binary64` `remove-double-div_binary64` `difference-of-squares_binary64` `associate--l+_binary64`
1×	`log-rec_binary64` `unpow1/2_binary64` `prod-exp_binary64` `1-exp_binary64` `*-inverses_binary64` `distribute-lft-out--_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow2_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `--rgt-identity_binary64` `+-lft-identity_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `cancel-sign-sub_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `count-2_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--r+_binary64`

Counts

61 → 24

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	655
1	223	634
2	596	633
3	1550	633
4	4356	633
5	4600	633
6	4941	633
7	4926	633

prune9.0ms (0.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	24	4	28

Error

0b

Counts

28 → 4

Compiler

Compiled 178 to 100 computations (43.8% saved)

regimes167.0ms (9.3%)

Accuracy

Total 0.0b remaining (51.8%)

Threshold costs 0.0b (51.8%)

Compiler

Compiled 477 to 396 computations (17% saved)

bsearch13.0ms (0.7%)

Steps

Iters	Range		Point
2	6.065591002021895e+149	2.046222803097852e+153	2.6947295261630386e+152
7	-9.025511892909482e+157	-1.2538627596973678e+154	-1.3207608804161588e+154

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`neg-sub0_binary64` `sub-neg_binary64` `mul-1-neg_binary64` `*-commutative_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `unpow1_binary64` `e-exp-1_binary64` `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	15	25
1	18	25
2	20	25
3	21	25
4	22	25
5	22	25

end1.0ms (0%)

Compiler: Compiled 17 to 12 computations (29.4% saved)

sample566.0ms (31.4%)

Algorithm

1×

intervals

Results

216.0ms	8000×	body	128	valid
4.0ms	158×	body	128	nan

Compiler

Compiled 86 to 70 computations (18.6% saved)

Details

analyze94.0ms (5.2%)

sample15.0ms (0.8%)

simplify9.0ms (0.5%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

rewrite29.0ms (1.6%)

series48.0ms (2.6%)

simplify65.0ms (3.6%)

prune16.0ms (0.9%)

localize8.0ms (0.4%)

rewrite57.0ms (3.2%)

series123.0ms (6.8%)

simplify132.0ms (7.3%)

prune238.0ms (13.2%)

localize2.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify8.0ms (0.4%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

rewrite40.0ms (2.2%)

series40.0ms (2.2%)

simplify110.0ms (6.1%)

prune9.0ms (0.5%)

regimes167.0ms (9.3%)

bsearch13.0ms (0.7%)

simplify4.0ms (0.2%)

end1.0ms (0%)

sample566.0ms (31.4%)

Profiling