Details

analyze450.0ms (6.4%)

Algorithm

1×	search
2×	egg-herbie

Rules

1× +-commutative_binary64 swap-a-b

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	20
1	8	20
2	8	20
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
25%	74.9%	0.1%	4
50%	50%	0.1%	5
50%	37.5%	12.6%	6
50%	25%	25.1%	7
50%	18.7%	31.3%	8
50%	12.5%	37.6%	9
50%	9.4%	40.7%	10
50%	6.2%	43.8%	11
50%	4.7%	45.4%	12
50%	3.1%	46.9%	13
50%	2.3%	47.7%	14

Symmetry

(sort a b)

Compiler

Compiled 7 to 7 computations (0% saved)

sample68.0ms (1%)

Algorithm

1×

intervals

Results

29.0ms	60×	body	1024	valid
7.0ms	142×	body	128	valid
7.0ms	31×	body	512	valid
3.0ms	21×	body	256	valid
1.0ms	2×	body	2048	valid
0.0ms	1×	body	128	overflowed

Compiler

Compiled 13 to 15 computations (-15.4% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1× +-commutative_binary64

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	8	10
2	8	10

prune4.0ms (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

28.9b

Counts

1 → 1

Compiler

Compiled 6 to 6 computations (0% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
3.4b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

rewrite44.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

28.8b

Rules

7×	`*-un-lft-identity_binary64`
4×	`log-prod_binary64` `add-log-exp_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `add-exp-log_binary64`
2×	`flip3-+_binary64` `log-div_binary64` `flip-+_binary64` `distribute-lft-out_binary64` `add-cbrt-cube_binary64`
1×	`log-pow_binary64` `rem-log-exp_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

2 → 27

Calls

2 calls:

6.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

Compiler

Compiled 363 to 92 computations (74.7% saved)

series342.0ms (4.9%)

Error

0.5b

Counts

2 → 23

Calls

2 calls:

263.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
50.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

Compiler

Compiled 751 to 569 computations (24.2% saved)

simplify122.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

633×	`cancel-sign-sub-inv_binary64`
292×	`associate-+l+_binary64`
284×	`associate-/r/_binary64`
266×	`associate-/l/_binary64`
217×	`sub-neg_binary64`
169×	`associate-+r+_binary64`
158×	`+-commutative_binary64`
137×	`times-frac_binary64`
136×	`distribute-rgt-neg-in_binary64`
134×	`associate-/l*_binary64`
132×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64`
128×	`distribute-rgt-in_binary64`
126×	`neg-sub0_binary64`
120×	`distribute-neg-frac_binary64`
105×	`distribute-lft-in_binary64`
101×	`distribute-rgt-out_binary64`
99×	`associate--l+_binary64`
94×	`associate-r_binary64`
85×	`unswap-sqr_binary64`
78×	`associate-l_binary64`
77×	`div-sub_binary64`
71×	`associate-/r*_binary64`
67×	`distribute-rgt-out--_binary64` `*-commutative_binary64`
66×	`unsub-neg_binary64`
59×	`distribute-lft-out_binary64`
58×	`prod-exp_binary64`
48×	`sqr-pow_binary64`
47×	`associate-*l/_binary64`
43×	`associate-*r/_binary64`
34×	`unpow3_binary64`
32×	`exp-prod_binary64`
28×	`distribute-lft-out--_binary64`
26×	`cube-prod_binary64`
24×	`log-prod_binary64` `cube-unmult_binary64`
20×	`associate-+r-_binary64`
19×	`pow-plus_binary64`
18×	`+-rgt-identity_binary64`
15×	`associate-+l-_binary64`
12×	`distribute-rgt1-in_binary64` `associate--r+_binary64`
8×	`log-pow_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `count-2_binary64`
7×	`cube-mult_binary64` `cube-div_binary64` `sub0-neg_binary64` `distribute-lft1-in_binary64`
6×	`distribute-neg-in_binary64`
5×	`pow-sqr_binary64` `distribute-lft-neg-out_binary64`
4×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `exp-sum_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64`
2×	`swap-sqr_binary64`
1×	`1-exp_binary64` `rem-exp-log_binary64` `distribute-rgt-neg-out_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-rec_binary64` `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` `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` `/-rgt-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` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

50 → 34

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	106	920
1	277	873
2	761	837
3	2534	826
4	4527	826
5	4990	826
6	4997	826
7	4976	826

prune46.0ms (0.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	30	4	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	31	4	35

Error

0.5b

Counts

35 → 4

Compiler

Compiled 562 to 270 computations (52% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (exp.f64 a))
0.0b	(+.f64 1 (exp.f64 a))
0.0b	(/.f64 b (+.f64 1 (exp.f64 a)))
0.1b	(log.f64 (+.f64 1 (exp.f64 a)))

rewrite105.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

28×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
7×	`distribute-lft-out_binary64` `add-exp-log_binary64`
6×	`add-cbrt-cube_binary64`
5×	`pow1_binary64`
4×	`flip3-+_binary64` `flip-+_binary64` `log-prod_binary64` `associate-/r*_binary64`
3×	`associate-/l*_binary64`
2×	`log-div_binary64` `associate-/r/_binary64` `sum-log_binary64` `+-commutative_binary64`
1×	`log-pow_binary64` `rem-log-exp_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

4 → 72

Calls

4 calls:

6.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
4.0ms	(log.f64 (+.f64 1 (exp.f64 a)))
4.0ms	(+.f64 1 (exp.f64 a))
4.0ms	(+.f64 1 (exp.f64 a))

Compiler

Compiled 1378 to 850 computations (38.3% saved)

series264.0ms (3.8%)

Error

0.5b

Counts

4 → 21

Calls

4 calls:

116.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
95.0ms	(log.f64 (+.f64 1 (exp.f64 a)))
21.0ms	(+.f64 1 (exp.f64 a))
13.0ms	(+.f64 1 (exp.f64 a))

Compiler

Compiled 710 to 557 computations (21.5% saved)

simplify125.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

426×	`cancel-sign-sub-inv_binary64`
330×	`distribute-rgt-in_binary64`
324×	`times-frac_binary64`
249×	`associate-l_binary64`
239×	`distribute-lft-in_binary64`
195×	`associate-r_binary64`
190×	`unswap-sqr_binary64`
187×	`associate-/l/_binary64`
180×	`distribute-rgt-out_binary64`
158×	`distribute-rgt-neg-in_binary64`
149×	`associate-/l*_binary64`
145×	`distribute-lft-neg-in_binary64`
129×	`distribute-lft-out_binary64`
128×	`associate-+l+_binary64`
114×	`div-sub_binary64`
109×	`sub-neg_binary64`
108×	`*-commutative_binary64`
96×	`associate-+r+_binary64`
65×	`+-commutative_binary64`
60×	`exp-sum_binary64`
58×	`associate-/r/_binary64`
57×	`sqr-pow_binary64`
55×	`associate-/r*_binary64`
53×	`log-prod_binary64` `exp-prod_binary64`
44×	`distribute-lft-out--_binary64`
43×	`distribute-rgt-out--_binary64`
40×	`distribute-neg-in_binary64`
33×	`neg-mul-1_binary64` `associate-+l-_binary64`
29×	`neg-sub0_binary64`
28×	`distribute-rgt1-in_binary64`
27×	`pow-plus_binary64`
23×	`associate--l+_binary64`
21×	`prod-exp_binary64` `associate-*l/_binary64`
20×	`distribute-lft-neg-out_binary64`
18×	`cube-prod_binary64` `*-rgt-identity_binary64`
16×	`unpow3_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft1-in_binary64`
15×	`*-lft-identity_binary64`
14×	`cube-unmult_binary64` `sub0-neg_binary64` `associate-*r/_binary64` `associate--r+_binary64`
12×	`associate-+r-_binary64`
11×	`+-rgt-identity_binary64`
10×	`associate--l-_binary64`
9×	`unsub-neg_binary64` `pow-sqr_binary64`
8×	`exp-diff_binary64`
6×	`rem-sqrt-square_binary64` `count-2_binary64`
5×	`exp-to-pow_binary64` `/-rgt-identity_binary64` `--rgt-identity_binary64`
4×	`difference-of-squares_binary64`
3×	`log-pow_binary64` `log-div_binary64` `unpow1/2_binary64` `cube-mult_binary64` `associate--r-_binary64`
2×	`unpow1_binary64` `rec-exp_binary64` `rem-exp-log_binary64` `difference-of-sqr--1_binary64` `swap-sqr_binary64`
1×	`log-rec_binary64` `unpow2_binary64` `exp-lft-sqr_binary64` `1-exp_binary64` `exp-1-e_binary64` `cube-neg_binary64` `sqr-neg_binary64` `remove-double-neg_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `difference-of-sqr-1_binary64` `distribute-neg-frac_binary64` `distribute-neg-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` `pow-base-0_binary64` `unpow1/3_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `cube-div_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `+-lft-identity_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64`

Counts

93 → 67

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	112	1217
1	229	1127
2	452	1118
3	886	1118
4	2110	1118
5	4379	1118
6	4956	1118
7	4902	1118

prune81.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	67	4	71

Error

0.5b

Counts

71 → 4

Compiler

Compiled 1284 to 812 computations (36.8% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 a) 3)
0.4b	(log.f64 (+.f64 1 (pow.f64 (exp.f64 a) 3)))
3.8b	(-.f64 (pow.f64 (exp.f64 a) 2) (exp.f64 a))
3.9b	(log.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 a) 2) (exp.f64 a))))

rewrite170.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

21×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`log-prod_binary64`
7×	`pow1_binary64`
6×	`add-exp-log_binary64` `add-log-exp_binary64`
5×	`add-cbrt-cube_binary64`
4×	`log-div_binary64` `unpow-prod-down_binary64` `difference-of-squares_binary64` `pow-pow_binary64`
3×	`distribute-lft-out_binary64` `cancel-sign-sub-inv_binary64` `pow-unpow_binary64` `exp-prod_binary64` `cube-prod_binary64`
2×	`log-pow_binary64` `flip3-+_binary64` `flip-+_binary64` `distribute-lft-out--_binary64` `rem-log-exp_binary64` `unpow2_binary64` `sqr-pow_binary64`
1×	`diff-log_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `distribute-rgt-out--_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64` `rem-cube-cbrt_binary64`

Counts

4 → 77

Calls

4 calls:

9.0ms	(log.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 a) 2) (exp.f64 a))))
7.0ms	(-.f64 (pow.f64 (exp.f64 a) 2) (exp.f64 a))
6.0ms	(log.f64 (+.f64 1 (pow.f64 (exp.f64 a) 3)))
4.0ms	(pow.f64 (exp.f64 a) 3)

Compiler

Compiled 2530 to 1632 computations (35.5% saved)

series496.0ms (7.1%)

Error

0.5b

Counts

4 → 24

Calls

4 calls:

205.0ms	(log.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 a) 2) (exp.f64 a))))
149.0ms	(log.f64 (+.f64 1 (pow.f64 (exp.f64 a) 3)))
56.0ms	(pow.f64 (exp.f64 a) 3)
51.0ms	(-.f64 (pow.f64 (exp.f64 a) 2) (exp.f64 a))

Compiler

Compiled 1468 to 1095 computations (25.4% saved)

simplify121.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

439×	`log-prod_binary64`
377×	`unswap-sqr_binary64`
315×	`cancel-sign-sub-inv_binary64`
270×	`exp-prod_binary64`
214×	`cube-prod_binary64`
204×	`*-commutative_binary64`
189×	`associate-+l+_binary64`
185×	`sub-neg_binary64`
145×	`associate-+r+_binary64`
135×	`distribute-rgt-in_binary64`
130×	`distribute-rgt-out_binary64`
123×	`distribute-lft-in_binary64`
118×	`+-commutative_binary64`
103×	`distribute-rgt-neg-in_binary64`
95×	`exp-sum_binary64`
94×	`unsub-neg_binary64`
86×	`distribute-lft-neg-in_binary64`
79×	`neg-mul-1_binary64`
78×	`neg-sub0_binary64`
70×	`difference-of-squares_binary64`
69×	`distribute-lft-out_binary64`
66×	`sqr-pow_binary64`
65×	`associate-l_binary64`
64×	`associate-r_binary64`
58×	`log-pow_binary64`
41×	`unpow3_binary64` `prod-exp_binary64`
33×	`associate--l+_binary64`
29×	`pow-plus_binary64` `cube-mult_binary64`
28×	`rem-sqrt-square_binary64`
25×	`swap-sqr_binary64`
23×	`associate-+l-_binary64` `associate-+r-_binary64`
22×	`distribute-rgt-out--_binary64`
20×	`distribute-lft-neg-out_binary64` `distribute-rgt1-in_binary64`
19×	`cube-unmult_binary64` `associate--r+_binary64`
16×	`times-frac_binary64`
13×	`pow-sqr_binary64` `distribute-lft-out--_binary64`
10×	`difference-of-sqr--1_binary64`
8×	`exp-diff_binary64` `*-lft-identity_binary64`
7×	`distribute-lft1-in_binary64` `associate--r-_binary64`
6×	`rem-exp-log_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64`
5×	`unpow1/2_binary64` `*-rgt-identity_binary64` `count-2_binary64`
4×	`+-rgt-identity_binary64`
3×	`unpow2_binary64` `unpow1_binary64` `div-sub_binary64` `difference-of-sqr-1_binary64` `associate-/l/_binary64` `associate-*r/_binary64`
2×	`associate--l-_binary64`
1×	`log-E_binary64` `exp-lft-cube_binary64` `div-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-log-exp_binary64` `cube-neg_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-neg_binary64` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `remove-double-neg_binary64` `associate-/r/_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-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-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `rec-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `cube-div_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `sqr-abs_binary64` `/-rgt-identity_binary64` `sub0-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` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `associate-/r_binary64` `associate-*l/_binary64`

Counts

101 → 62

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	1549
1	374	1426
2	997	1395
3	3536	1395
4	4854	1395
5	5046	1395

prune115.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	60	6	66

Error

0.5b

Counts

66 → 6

Compiler

Compiled 1976 to 1287 computations (34.9% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 a) 3)
0.4b	(log.f64 (+.f64 1 (pow.f64 (exp.f64 a) 3)))
3.9b	(log.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 (exp.f64 a) 2) 1) (exp.f64 a))))
3.9b	(log.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 (exp.f64 a) 2) 1) (exp.f64 a))))

rewrite269.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

25×	`*-un-lft-identity_binary64`
22×	`log-prod_binary64`
17×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`sqrt-prod_binary64`
10×	`pow1_binary64`
7×	`log-pow_binary64` `add-exp-log_binary64`
6×	`log-div_binary64`
5×	`add-cbrt-cube_binary64`
4×	`sqrt-div_binary64` `distribute-lft-out--_binary64` `add-log-exp_binary64` `pow-pow_binary64`
3×	`distribute-lft-out_binary64` `rem-log-exp_binary64` `unpow-prod-down_binary64` `pow-unpow_binary64` `exp-prod_binary64` `cube-prod_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3--_binary64` `flip--_binary64` `difference-of-squares_binary64`
1×	`flip3-+_binary64` `flip-+_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64` `rem-cube-cbrt_binary64` `sqr-pow_binary64`

Counts

4 → 85

Calls

4 calls:

10.0ms	(log.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 (exp.f64 a) 2) 1) (exp.f64 a))))
10.0ms	(log.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 (exp.f64 a) 2) 1) (exp.f64 a))))
6.0ms	(log.f64 (+.f64 1 (pow.f64 (exp.f64 a) 3)))
4.0ms	(pow.f64 (exp.f64 a) 3)

Compiler

Compiled 3991 to 2669 computations (33.1% saved)

series685.0ms (9.7%)

Error

0.5b

Counts

4 → 24

Calls

4 calls:

226.0ms	(log.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 (exp.f64 a) 2) 1) (exp.f64 a))))
203.0ms	(log.f64 (sqrt.f64 (-.f64 (+.f64 (pow.f64 (exp.f64 a) 2) 1) (exp.f64 a))))
146.0ms	(log.f64 (+.f64 1 (pow.f64 (exp.f64 a) 3)))
62.0ms	(pow.f64 (exp.f64 a) 3)

Compiler

Compiled 2200 to 1603 computations (27.1% saved)

simplify97.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

703×	`difference-of-squares_binary64`
246×	`unswap-sqr_binary64`
222×	`cancel-sign-sub-inv_binary64`
172×	`distribute-rgt-in_binary64`
169×	`*-commutative_binary64`
167×	`log-prod_binary64` `exp-prod_binary64`
159×	`distribute-lft-in_binary64`
152×	`associate-+l+_binary64`
142×	`sqr-pow_binary64`
138×	`cube-prod_binary64`
117×	`associate-+r+_binary64`
106×	`sub-neg_binary64`
82×	`+-commutative_binary64`
73×	`distribute-rgt-neg-in_binary64`
70×	`exp-sum_binary64`
65×	`distribute-rgt-out_binary64`
62×	`distribute-lft-neg-in_binary64`
55×	`associate-l_binary64` `associate-r_binary64`
43×	`pow-sqr_binary64`
42×	`neg-mul-1_binary64` `neg-sub0_binary64`
35×	`prod-exp_binary64`
33×	`distribute-lft-out_binary64`
30×	`unsub-neg_binary64`
29×	`unpow3_binary64` `associate--l+_binary64`
28×	`swap-sqr_binary64`
26×	`log-pow_binary64`
25×	`difference-of-sqr-1_binary64`
23×	`pow-plus_binary64`
22×	`*-lft-identity_binary64`
20×	`*-rgt-identity_binary64`
18×	`cube-mult_binary64` `associate-+r-_binary64`
17×	`cube-unmult_binary64`
16×	`+-rgt-identity_binary64` `difference-of-sqr--1_binary64`
15×	`rem-sqrt-square_binary64` `associate-+l-_binary64`
12×	`distribute-rgt-out--_binary64`
10×	`distribute-lft-neg-out_binary64`
9×	`sub0-neg_binary64` `distribute-rgt1-in_binary64`
7×	`distribute-lft-out--_binary64`
6×	`count-2_binary64`
5×	`rem-exp-log_binary64`
3×	`unpow1/2_binary64` `distribute-lft1-in_binary64` `associate-/l/_binary64` `associate-*r/_binary64`
2×	`unpow2_binary64` `unpow1_binary64`
1×	`exp-to-pow_binary64` `exp-lft-cube_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-log-exp_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `+-inverses_binary64` `distribute-rgt-neg-out_binary64` `associate-/r/_binary64` `associate-/l*_binary64` `associate--r+_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-rec_binary64` `log-div_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_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` `cube-div_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `times-frac_binary64` `div-sub_binary64` `/-rgt-identity_binary64` `remove-double-neg_binary64` `--rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `associate-/r_binary64` `associate-*l/_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

109 → 54

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	154	2152
1	310	2008
2	816	1971
3	2696	1949
4	5620	1949

prune130.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	1	3	4
Picked	0	1	1
Done	1	0	1
Total	55	5	60

Error

0.5b

Counts

60 → 5

Compiler

Compiled 2346 to 1569 computations (33.1% saved)

regimes452.0ms (6.4%)

Accuracy

Total 0.5b remaining (46.3%)

Threshold costs 0.5b (46.3%)

Compiler

Compiled 5239 to 3773 computations (28% saved)

bsearch0.0ms (0%)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`1-exp_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `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` `exp-1-e_binary64` `exp-0_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `unsub-neg_binary64` `sub-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `cancel-sign-sub-inv_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	47
1	24	47
2	23	47

Compiler

Compiled 60 to 44 computations (26.7% saved)

end0.0ms (0%)

sample2.8s (39.5%)

Algorithm

1×

intervals

Results

918.0ms	1971×	body	1024	valid
222.0ms	948×	body	512	valid
194.0ms	4392×	body	128	valid
135.0ms	208×	body	2048	valid
61.0ms	481×	body	256	valid
6.0ms	142×	body	128	overflowed

Compiler

Compiled 825 to 601 computations (27.2% saved)

Details

analyze450.0ms (6.4%)

sample68.0ms (1%)

simplify10.0ms (0.1%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

rewrite44.0ms (0.6%)

series342.0ms (4.9%)

simplify122.0ms (1.7%)

prune46.0ms (0.7%)

localize8.0ms (0.1%)

rewrite105.0ms (1.5%)

series264.0ms (3.8%)

simplify125.0ms (1.8%)

prune81.0ms (1.2%)

localize17.0ms (0.2%)

rewrite170.0ms (2.4%)

series496.0ms (7.1%)

simplify121.0ms (1.7%)

prune115.0ms (1.6%)

localize20.0ms (0.3%)

rewrite269.0ms (3.8%)

series685.0ms (9.7%)

simplify97.0ms (1.4%)

prune130.0ms (1.8%)

regimes452.0ms (6.4%)

bsearch0.0ms (0%)

simplify12.0ms (0.2%)

end0.0ms (0%)

sample2.8s (39.5%)

Profiling