Metrics for Quotient of sum of exps

analyze95.0ms (4.8%)

Algorithm

1×	search
2×	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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	9	26
2	9	26
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
25%	74.9%	0.1%	3
62.4%	37.5%	0.1%	4
68.7%	31.2%	0.1%	5
68.7%	18.7%	12.6%	6
68.7%	18.7%	12.6%	7
68.7%	12.5%	18.8%	8
68.7%	12.5%	18.8%	9
68.7%	9.4%	22%	10
68.7%	9.4%	22%	11
68.7%	7.8%	23.5%	12
68.7%	7.8%	23.5%	13
68.7%	7%	24.3%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample20.0ms (1%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
0.0ms	19×	body	128	overflowed

Compiler

Compiled 17 to 15 computations (11.8% 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	7	13
1	8	13
2	8	13

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

0.5b

Counts

1 → 1

Compiler

Compiled 8 to 6 computations (25% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
0.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

rewrite46.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

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

Counts

2 → 45

Calls

2 calls:

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

Compiler

Compiled 674 to 135 computations (80% saved)

series68.0ms (3.4%)

Error

0.0b

Counts

2 → 22

Calls

2 calls:

38.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
17.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

Compiler

Compiled 855 to 607 computations (29% saved)

simplify100.0ms (5%)

Algorithm

1×	egg-herbie

Rules

496×	`associate-/l/_binary64`
363×	`cancel-sign-sub-inv_binary64`
330×	`div-sub_binary64`
223×	`associate-+l+_binary64`
221×	`distribute-rgt-in_binary64`
193×	`distribute-lft-in_binary64`
174×	`sub-neg_binary64`
160×	`associate-/l*_binary64`
136×	`+-commutative_binary64`
135×	`associate-+r+_binary64`
118×	`distribute-neg-frac_binary64`
116×	`times-frac_binary64`
111×	`associate-/r*_binary64`
104×	`distribute-rgt-neg-in_binary64`
100×	`distribute-lft-neg-in_binary64`
83×	`*-commutative_binary64`
82×	`associate-l_binary64`
78×	`associate-r_binary64`
71×	`distribute-rgt-out_binary64`
68×	`associate-*l/_binary64`
64×	`associate--l+_binary64`
62×	`unswap-sqr_binary64`
54×	`associate-*r/_binary64`
52×	`sqr-pow_binary64`
51×	`associate-/r/_binary64`
43×	`exp-prod_binary64`
41×	`neg-mul-1_binary64` `neg-sub0_binary64`
37×	`associate-+l-_binary64`
36×	`unsub-neg_binary64` `associate-+r-_binary64`
32×	`cube-prod_binary64`
31×	`distribute-lft-out_binary64`
30×	`exp-sum_binary64`
29×	`distribute-rgt-out--_binary64`
25×	`*-rgt-identity_binary64`
22×	`cube-unmult_binary64`
20×	`unpow3_binary64`
19×	`associate--r+_binary64`
18×	`prod-exp_binary64` `+-rgt-identity_binary64`
16×	`exp-diff_binary64`
15×	`*-lft-identity_binary64`
12×	`pow-plus_binary64` `sub0-neg_binary64`
11×	`distribute-rgt1-in_binary64`
10×	`distribute-neg-in_binary64` `distribute-lft-out--_binary64`
8×	`difference-of-squares_binary64`
7×	`distribute-lft1-in_binary64`
6×	`log-prod_binary64` `cube-mult_binary64` `pow-sqr_binary64` `distribute-lft-neg-out_binary64`
5×	`log-div_binary64` `div-exp_binary64` `rem-sqrt-square_binary64` `count-2_binary64`
4×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `/-rgt-identity_binary64`
3×	`rec-exp_binary64`
2×	`log-pow_binary64` `rem-log-exp_binary64` `cube-div_binary64` `associate--l-_binary64`
1×	`exp-to-pow_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `sqr-neg_binary64` `remove-double-neg_binary64` `--rgt-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `distribute-rgt-neg-out_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` `pow-base-0_binary64` `unpow1/3_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-neg_binary64` `e-exp-1_binary64` `exp-0_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` `*-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` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64`

Counts

67 → 53

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	126	1364
1	319	1293
2	872	1279
3	2517	1251
4	4607	1251
5	5214	1251

prune35.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	51	3	54

Error

0b

Counts

54 → 3

Compiler

Compiled 771 to 257 computations (66.7% saved)

localize14.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (exp.f64 b) (exp.f64 a))
0.3b	(*.f64 (sqrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a)))) (sqrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a)))))
0.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a)))
0.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a)))

rewrite179.0ms (9%)

Algorithm

1×	rewrite-expression-head

Error

0b

Rules

122×	`*-un-lft-identity_binary64`
98×	`sqrt-prod_binary64`
96×	`add-sqr-sqrt_binary64`
92×	`times-frac_binary64`
62×	`add-cube-cbrt_binary64`
29×	`swap-sqr_binary64`
27×	`distribute-lft-out_binary64`
21×	`associate-l_binary64` `associate-r_binary64`
19×	`pow1_binary64`
12×	`associate-/r/_binary64`
10×	`add-cbrt-cube_binary64`
9×	`unswap-sqr_binary64`
8×	`add-exp-log_binary64` `associate-/r*_binary64` `pow1/2_binary64` `sqrt-pow1_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64` `div-inv_binary64` `associate-/l*_binary64`
5×	`pow-prod-up_binary64`
4×	`rem-sqrt-square_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64`
2×	`div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `sqr-abs_binary64`
1×	`pow2_binary64` `pow-plus_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `sqrt-unprod_binary64` `rem-square-sqrt_binary64` `frac-times_binary64` `associate-l/_binary64` `associate-r/_binary64` `*-commutative_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

4 → 188

Calls

4 calls:

26.0ms	(*.f64 (sqrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a)))) (sqrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a)))))
7.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a)))
7.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a)))
4.0ms	(+.f64 (exp.f64 b) (exp.f64 a))

Compiler

Compiled 4501 to 610 computations (86.4% saved)

series134.0ms (6.7%)

Error

0b

Counts

4 → 37

Calls

4 calls:

39.0ms	(*.f64 (sqrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a)))) (sqrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a)))))
29.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a)))
27.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a)))
19.0ms	(+.f64 (exp.f64 b) (exp.f64 a))

Compiler

Compiled 2047 to 1181 computations (42.3% saved)

simplify195.0ms (9.8%)

Algorithm

1×	egg-herbie

Rules

523×	`times-frac_binary64`
451×	`associate-/l*_binary64`
219×	`associate-*l/_binary64`
213×	`associate-/r*_binary64`
194×	`associate-+l+_binary64`
155×	`associate-*r/_binary64`
152×	`associate-/l/_binary64`
129×	`associate-l_binary64` `associate-r_binary64`
119×	`distribute-rgt-in_binary64`
106×	`distribute-lft-in_binary64`
102×	`associate-/r/_binary64`
86×	`unswap-sqr_binary64`
73×	`cancel-sign-sub-inv_binary64`
65×	`associate--l+_binary64`
63×	`log-prod_binary64`
54×	`log-div_binary64`
53×	`+-commutative_binary64`
51×	`*-commutative_binary64`
49×	`sub-neg_binary64`
40×	`*-rgt-identity_binary64` `sqr-pow_binary64`
38×	`associate-+l-_binary64`
36×	`associate-+r-_binary64` `associate-+r+_binary64`
33×	`rem-sqrt-square_binary64`
31×	`*-lft-identity_binary64`
30×	`distribute-rgt-neg-in_binary64`
28×	`distribute-neg-frac_binary64`
26×	`rem-square-sqrt_binary64`
24×	`distribute-lft-neg-in_binary64`
22×	`exp-prod_binary64`
21×	`associate--r+_binary64`
18×	`neg-mul-1_binary64` `neg-sub0_binary64`
15×	`cube-prod_binary64`
14×	`distribute-rgt-out_binary64`
10×	`cube-unmult_binary64` `unsub-neg_binary64` `swap-sqr_binary64`
9×	`prod-exp_binary64`
8×	`div-sub_binary64` `distribute-neg-in_binary64` `distribute-lft-out_binary64`
7×	`cube-div_binary64` `distribute-lft-neg-out_binary64`
6×	`log-pow_binary64` `unpow3_binary64` `count-2_binary64`
5×	`cube-mult_binary64` `pow-sqr_binary64`
4×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `/-rgt-identity_binary64` `distribute-rgt-out--_binary64`
3×	`pow-plus_binary64` `distribute-rgt1-in_binary64`
2×	`log-rec_binary64` `+-rgt-identity_binary64` `distribute-lft1-in_binary64` `distribute-lft-out--_binary64` `associate--l-_binary64`
1×	`exp-diff_binary64` `exp-sum_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-log-exp_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `difference-of-squares_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` `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-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `mul-1-neg_binary64` `remove-double-neg_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` `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`

Counts

225 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	5394
1	440	5040
2	1482	4953
3	4896	4953
4	5004	4953

prune80.0ms (4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	148	3	151

Error

0b

Counts

151 → 3

Compiler

Compiled 2277 to 563 computations (75.3% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (+.f64 1 (exp.f64 b)))
0.0b	(+.f64 1 (exp.f64 b))

rewrite51.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0b

Rules

21×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
11×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`add-exp-log_binary64`
5×	`distribute-lft-out_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `associate-/r*_binary64`
3×	`pow1_binary64` `associate-/l*_binary64`
2×	`flip3-+_binary64` `flip-+_binary64` `div-exp_binary64` `associate-/r/_binary64`
1×	`sum-log_binary64` `+-commutative_binary64` `inv-pow_binary64` `pow-flip_binary64` `1-exp_binary64` `rec-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

2 → 49

Calls

2 calls:

5.0ms	(/.f64 1 (+.f64 1 (exp.f64 b)))
3.0ms	(+.f64 1 (exp.f64 b))

Compiler

Compiled 565 to 413 computations (26.9% saved)

series21.0ms (1%)

Error

0b

Counts

2 → 10

Calls

2 calls:

8.0ms	(/.f64 1 (+.f64 1 (exp.f64 b)))
6.0ms	(+.f64 1 (exp.f64 b))

Compiler

Compiled 149 to 156 computations (-4.7% saved)

simplify125.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

430×	`cancel-sign-sub-inv_binary64`
352×	`sub-neg_binary64`
301×	`times-frac_binary64`
296×	`unswap-sqr_binary64`
223×	`sqr-pow_binary64`
205×	`distribute-rgt-out_binary64`
203×	`*-commutative_binary64`
189×	`div-sub_binary64`
186×	`associate-+r-_binary64`
177×	`distribute-rgt-in_binary64`
143×	`unsub-neg_binary64`
141×	`exp-prod_binary64`
134×	`associate-/l*_binary64`
131×	`+-commutative_binary64`
119×	`distribute-lft-out_binary64` `associate-l_binary64`
108×	`neg-mul-1_binary64`
106×	`neg-sub0_binary64`
104×	`distribute-neg-in_binary64`
97×	`associate-+l+_binary64`
95×	`associate-r_binary64`
93×	`associate-+r+_binary64`
92×	`distribute-rgt-neg-in_binary64`
87×	`pow-sqr_binary64`
84×	`associate--r+_binary64`
75×	`distribute-lft-in_binary64`
72×	`associate-/r*_binary64`
70×	`distribute-lft-neg-in_binary64`
68×	`associate--l+_binary64`
66×	`*-rgt-identity_binary64`
57×	`associate-+l-_binary64`
51×	`associate-*l/_binary64`
50×	`cube-prod_binary64` `associate-/l/_binary64`
46×	`distribute-rgt1-in_binary64`
44×	`associate-/r/_binary64`
41×	`unpow3_binary64`
39×	`associate--l-_binary64`
38×	`pow-plus_binary64`
32×	`/-rgt-identity_binary64`
30×	`associate--r-_binary64`
28×	`distribute-lft1-in_binary64`
27×	`associate-*r/_binary64`
21×	`*-lft-identity_binary64`
20×	`distribute-rgt-out--_binary64`
18×	`distribute-lft-neg-out_binary64`
17×	`rem-sqrt-square_binary64`
16×	`prod-exp_binary64` `cube-unmult_binary64` `remove-double-neg_binary64`
12×	`difference-of-squares_binary64` `distribute-rgt-neg-out_binary64`
10×	`--rgt-identity_binary64` `distribute-lft-out--_binary64`
9×	`div-exp_binary64` `rec-exp_binary64` `cube-div_binary64` `sub0-neg_binary64`
8×	`unpow2_binary64` `exp-sum_binary64` `+-lft-identity_binary64`
7×	`unpow1_binary64` `cube-mult_binary64` `distribute-neg-frac_binary64`
6×	`unpow1/2_binary64` `div0_binary64` `remove-double-div_binary64`
5×	`exp-diff_binary64` `+-rgt-identity_binary64`
4×	`log-div_binary64` `difference-of-sqr--1_binary64` `swap-sqr_binary64` `count-2_binary64`
3×	`log-prod_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `difference-of-sqr-1_binary64`
2×	`log-rec_binary64` `exp-lft-sqr_binary64` `sqr-neg_binary64` `mul-1-neg_binary64` `+-inverses_binary64` `distribute-neg-out_binary64`
1×	`exp-lft-cube_binary64` `exp-neg_binary64` `1-exp_binary64` `exp-1-e_binary64` `cube-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` `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` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `rem-square-sqrt_binary64` `*-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64`

Counts

59 → 47

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	76	744
1	167	691
2	324	688
3	590	688
4	1381	688
5	2695	688
6	4148	688
7	4958	688
8	4793	688

prune28.0ms (1.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	47	3	50

Error

0b

Counts

50 → 3

Compiler

Compiled 409 to 301 computations (26.4% saved)

regimes192.0ms (9.7%)

Accuracy

Total 0.6b remaining (98.3%)

Threshold costs 0.6b (98.3%)

Compiler

Compiled 2018 to 1687 computations (16.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

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 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 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 *-commutative_binary64

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	8	13
2	8	13

end1.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

sample583.0ms (29.3%)

Algorithm

1×

intervals

Results

227.0ms	8000×	body	128	valid
15.0ms	687×	body	128	overflowed

Compiler

Compiled 61 to 53 computations (13.1% saved)

Details

analyze95.0ms (4.8%)

sample20.0ms (1%)

simplify9.0ms (0.4%)

prune1.0ms (0.1%)

localize6.0ms (0.3%)

rewrite46.0ms (2.3%)

series68.0ms (3.4%)

simplify100.0ms (5%)

prune35.0ms (1.7%)

localize14.0ms (0.7%)

rewrite179.0ms (9%)

series134.0ms (6.7%)

simplify195.0ms (9.8%)

prune80.0ms (4%)

localize4.0ms (0.2%)

rewrite51.0ms (2.6%)

series21.0ms (1%)

simplify125.0ms (6.3%)

prune28.0ms (1.4%)

regimes192.0ms (9.7%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample583.0ms (29.3%)

Profiling