Details

analyze105.0ms (2.1%)

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 fabs-div_binary64 fabs-mul_binary64 fabs-sqr_binary64 fabs-neg_binary64 fabs-sub_binary64 fabs-fabs_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)

sample22.0ms (0.4%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
0.0ms	22×	body	128	overflowed

Compiler

Compiled 17 to 15 computations (11.8% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1× +-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%)

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)

localize5.0ms (0.1%)

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)))

rewrite59.0ms (1.2%)

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:

7.0ms	(/.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)

series279.0ms (5.6%)

Error

0.0b

Counts

2 → 24

Calls

2 calls:

237.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
15.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

Compiler

Compiled 1053 to 741 computations (29.6% saved)

simplify64.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

459×	`associate-+l+_binary64`
381×	`times-frac_binary64`
378×	`associate-/l*_binary64`
242×	`associate--l+_binary64`
236×	`associate-/r*_binary64`
209×	`associate--r+_binary64`
152×	`associate-*l/_binary64`
141×	`associate-l_binary64`
139×	`associate-r_binary64`
133×	`distribute-rgt-in_binary64`
112×	`distribute-lft-in_binary64`
102×	`associate-*r/_binary64`
100×	`cancel-sign-sub-inv_binary64`
98×	`associate-/r/_binary64`
96×	`sub-neg_binary64`
93×	`associate-/l/_binary64`
90×	`+-commutative_binary64`
82×	`associate-+r+_binary64`
49×	`associate-+l-_binary64`
46×	`distribute-neg-in_binary64`
44×	`associate-+r-_binary64`
34×	`sqr-pow_binary64`
30×	`*-commutative_binary64`
24×	`neg-mul-1_binary64` `neg-sub0_binary64` `distribute-neg-frac_binary64`
20×	`unsub-neg_binary64` `distribute-rgt-out_binary64`
19×	`distribute-rgt-neg-in_binary64`
16×	`*-rgt-identity_binary64`
15×	`distribute-lft-neg-in_binary64`
12×	`unswap-sqr_binary64` `distribute-lft-out_binary64`
11×	`div-sub_binary64`
9×	`prod-exp_binary64`
8×	`associate--l-_binary64`
6×	`unpow3_binary64` `cube-mult_binary64`
5×	`*-lft-identity_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt1-in_binary64`
4×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `exp-prod_binary64` `cube-unmult_binary64` `cube-prod_binary64` `/-rgt-identity_binary64`
3×	`log-div_binary64` `distribute-rgt-out--_binary64`
2×	`cube-div_binary64` `distribute-lft1-in_binary64` `count-2_binary64`
1×	`exp-diff_binary64` `1-exp_binary64` `rem-log-exp_binary64` `sub0-neg_binary64` `difference-of-squares_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-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-pow_binary64` `log-rec_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `pow-plus_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` `exp-sum_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `fabs-div_binary64` `fabs-mul_binary64` `fabs-sqr_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `remove-double-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` `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

69 → 55

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	157	1672
1	411	1601
2	1328	1560
3	5229	1560

prune59.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	51	4	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	4	56

Error

Counts

56 → 4

Compiler

Compiled 1007 to 414 computations (58.9% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (exp.f64 b) (exp.f64 a))
0.0b	(/.f64 1 (/.f64 (+.f64 (exp.f64 b) (exp.f64 a)) (exp.f64 a)))
0.5b	(/.f64 (+.f64 (exp.f64 b) (exp.f64 a)) (exp.f64 a))

rewrite149.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

3 → 133

Calls

3 calls:

9.0ms	(/.f64 1 (/.f64 (+.f64 (exp.f64 b) (exp.f64 a)) (exp.f64 a)))
7.0ms	(/.f64 (+.f64 (exp.f64 b) (exp.f64 a)) (exp.f64 a))
4.0ms	(+.f64 (exp.f64 b) (exp.f64 a))

Compiler

Compiled 2437 to 700 computations (71.3% saved)

series108.0ms (2.2%)

Error

Counts

3 → 36

Calls

3 calls:

38.0ms	(/.f64 1 (/.f64 (+.f64 (exp.f64 b) (exp.f64 a)) (exp.f64 a)))
22.0ms	(/.f64 (+.f64 (exp.f64 b) (exp.f64 a)) (exp.f64 a))
15.0ms	(+.f64 (exp.f64 b) (exp.f64 a))

Compiler

Compiled 1465 to 1044 computations (28.7% saved)

simplify171.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

781×	`times-frac_binary64`
346×	`associate-/r/_binary64`
312×	`associate-/l/_binary64`
192×	`distribute-rgt-in_binary64`
166×	`cancel-sign-sub-inv_binary64`
154×	`distribute-lft-in_binary64`
131×	`neg-mul-1_binary64`
125×	`sub-neg_binary64`
123×	`+-commutative_binary64`
116×	`div-sub_binary64`
111×	`associate-+r+_binary64`
103×	`associate-/l*_binary64`
85×	`associate-+l+_binary64`
82×	`*-commutative_binary64`
78×	`associate-*l/_binary64`
72×	`associate-/r*_binary64`
70×	`associate-r_binary64`
60×	`associate-*r/_binary64`
51×	`distribute-rgt-neg-in_binary64` `associate-l_binary64`
50×	`distribute-neg-in_binary64`
47×	`associate--l+_binary64`
40×	`distribute-lft-neg-in_binary64`
38×	`unsub-neg_binary64` `sqr-pow_binary64`
36×	`*-rgt-identity_binary64`
33×	`exp-prod_binary64` `cube-prod_binary64` `associate--r+_binary64`
32×	`neg-sub0_binary64` `distribute-neg-frac_binary64`
30×	`distribute-rgt-out_binary64`
27×	`prod-exp_binary64`
19×	`*-lft-identity_binary64` `distribute-lft-neg-out_binary64`
18×	`distribute-rgt-neg-out_binary64`
15×	`unswap-sqr_binary64`
14×	`/-rgt-identity_binary64`
13×	`unpow3_binary64`
12×	`distribute-lft-out_binary64`
11×	`log-div_binary64` `exp-sum_binary64` `cube-unmult_binary64` `distribute-rgt1-in_binary64`
10×	`log-prod_binary64` `distribute-frac-neg_binary64`
8×	`cube-mult_binary64`
7×	`div-exp_binary64`
6×	`cube-div_binary64` `associate-+r-_binary64`
5×	`log-rec_binary64` `swap-sqr_binary64`
4×	`unpow2_binary64` `unpow1/2_binary64` `pow-plus_binary64` `unpow1_binary64` `rec-exp_binary64` `rem-sqrt-square_binary64` `remove-double-div_binary64` `distribute-rgt-out--_binary64`
3×	`cube-neg_binary64` `sqr-neg_binary64` `+-rgt-identity_binary64` `distribute-lft1-in_binary64` `count-2_binary64`
2×	`log-pow_binary64` `exp-diff_binary64` `rem-log-exp_binary64` `distribute-lft-out--_binary64` `associate--r-_binary64`
1×	`exp-neg_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-exp-log_binary64` `sub0-neg_binary64` `+-lft-identity_binary64` `div0_binary64` `difference-of-squares_binary64` `distribute-neg-out_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` `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` `e-exp-1_binary64` `exp-0_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `fabs-div_binary64` `fabs-mul_binary64` `fabs-sqr_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `remove-double-neg_binary64` `--rgt-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `pow-sqr_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `cancel-sign-sub_binary64` `associate--l-_binary64`

Counts

169 → 156

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	250	4379
1	656	4111
2	2206	4013
3	4666	4013
4	4963	4013

prune105.0ms (2.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	155	1	156
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	157	3	160

Error

Counts

160 → 3

Compiler

Compiled 2138 to 745 computations (65.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
0.3b	(/.f64 1 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
0.5b	(/.f64 (sqrt.f64 (+.f64 (exp.f64 b) (exp.f64 a))) (exp.f64 a))
0.5b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (/.f64 (sqrt.f64 (+.f64 (exp.f64 b) (exp.f64 a))) (exp.f64 a)))

rewrite739.0ms (14.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

1851×	`times-frac_binary64`
1135×	`*-un-lft-identity_binary64`
794×	`add-sqr-sqrt_binary64`
793×	`add-cube-cbrt_binary64`
684×	`sqrt-prod_binary64`
171×	`distribute-lft-out_binary64`
58×	`sqrt-div_binary64`
57×	`div-inv_binary64`
55×	`associate-/r/_binary64`
37×	`associate-/l*_binary64`
35×	`associate-/r*_binary64`
29×	`flip3-+_binary64` `flip-+_binary64`
27×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`
19×	`div-exp_binary64`
10×	`cbrt-undiv_binary64`
7×	`pow1_binary64`
4×	`add-log-exp_binary64`
3×	`1-exp_binary64` `rec-exp_binary64` `frac-2neg_binary64` `clear-num_binary64` `associate-/l/_binary64` `pow-flip_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64`
1×	`inv-pow_binary64` `rem-sqrt-square_binary64`

Counts

4 → 863

Calls

4 calls:

38.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (/.f64 (sqrt.f64 (+.f64 (exp.f64 b) (exp.f64 a))) (exp.f64 a)))
8.0ms	(/.f64 (sqrt.f64 (+.f64 (exp.f64 b) (exp.f64 a))) (exp.f64 a))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
4.0ms	(sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 21773 to 5217 computations (76% saved)

series221.0ms (4.5%)

Error

Counts

4 → 48

Calls

4 calls:

48.0ms	(/.f64 1 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
47.0ms	(/.f64 (sqrt.f64 (+.f64 (exp.f64 b) (exp.f64 a))) (exp.f64 a))
37.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (/.f64 (sqrt.f64 (+.f64 (exp.f64 b) (exp.f64 a))) (exp.f64 a)))
34.0ms	(sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 4000 to 2785 computations (30.4% saved)

simplify1.1s (22.7%)

Algorithm

1×	egg-herbie

Rules

567×	`associate-*l/_binary64`
512×	`associate-/r/_binary64`
363×	`associate-/r*_binary64`
279×	`associate-/l/_binary64`
277×	`associate-/l*_binary64`
225×	`associate-*r/_binary64`
176×	`times-frac_binary64`
162×	`associate-l_binary64`
125×	`sub-neg_binary64`
91×	`cancel-sign-sub-inv_binary64`
84×	`neg-mul-1_binary64`
83×	`neg-sub0_binary64`
75×	`*-commutative_binary64`
70×	`+-commutative_binary64`
36×	`associate-+r+_binary64`
33×	`unsub-neg_binary64` `distribute-neg-in_binary64`
32×	`associate-r_binary64`
30×	`sqr-pow_binary64`
28×	`/-rgt-identity_binary64`
23×	`distribute-rgt-neg-in_binary64`
22×	`log-div_binary64`
19×	`distribute-lft-neg-in_binary64`
18×	`associate--l+_binary64`
17×	`*-rgt-identity_binary64`
16×	`exp-prod_binary64`
13×	`log-prod_binary64` `distribute-rgt-out_binary64` `associate--r+_binary64`
12×	`cube-prod_binary64`
11×	`distribute-lft-out_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64`
8×	`prod-exp_binary64` `cube-unmult_binary64` `rem-sqrt-square_binary64`
7×	`*-lft-identity_binary64` `distribute-neg-frac_binary64`
6×	`log-rec_binary64` `unpow3_binary64` `cube-mult_binary64` `cube-div_binary64`
5×	`unswap-sqr_binary64`
4×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `rem-square-sqrt_binary64` `div-sub_binary64` `distribute-lft-neg-out_binary64` `associate--l-_binary64`
3×	`distribute-rgt-out--_binary64`
2×	`rec-exp_binary64` `sub0-neg_binary64` `remove-double-div_binary64` `count-2_binary64` `associate-+r-_binary64`
1×	`1-exp_binary64` `rem-log-exp_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `fabs-mul_binary64` `sqr-abs_binary64` `difference-of-squares_binary64` `swap-sqr_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-pow_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `pow-plus_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` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `fabs-div_binary64` `fabs-sqr_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-neg_binary64` `mul-1-neg_binary64` `remove-double-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` `pow-sqr_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-lft-out--_binary64` `associate-+l-_binary64` `associate-+l+_binary64`

Counts

911 → 863

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	771	50266
1	2187	46433
2	4743	44468
3	4970	44468

prune292.0ms (5.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	863	0	863
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	863	3	866

Error

Counts

866 → 3

Compiler

Compiled 10893 to 3212 computations (70.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (exp.f64 b))
0.0b	(/.f64 a (+.f64 1 (exp.f64 b)))
0.0b	(pow.f64 (+.f64 1 (exp.f64 b)) 2)
0.0b	(/.f64 1 (+.f64 1 (exp.f64 b)))

rewrite134.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

44×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `times-frac_binary64`
11×	`add-exp-log_binary64`
10×	`distribute-lft-out_binary64`
8×	`add-cbrt-cube_binary64` `associate-/r*_binary64`
6×	`pow1_binary64` `add-log-exp_binary64` `associate-/l*_binary64`
4×	`associate-/r/_binary64` `unpow-prod-down_binary64`
3×	`div-exp_binary64` `flip3-+_binary64` `flip-+_binary64` `pow-unpow_binary64`
2×	`cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64`
1×	`inv-pow_binary64` `pow-flip_binary64` `1-exp_binary64` `rec-exp_binary64` `pow-pow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `unpow2_binary64` `sqr-pow_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

4 → 101

Calls

4 calls:

5.0ms	(/.f64 1 (+.f64 1 (exp.f64 b)))
5.0ms	(/.f64 a (+.f64 1 (exp.f64 b)))
4.0ms	(pow.f64 (+.f64 1 (exp.f64 b)) 2)
3.0ms	(+.f64 1 (exp.f64 b))

Compiler

Compiled 2551 to 1685 computations (33.9% saved)

series75.0ms (1.5%)

Error

Counts

4 → 25

Calls

4 calls:

24.0ms	(/.f64 a (+.f64 1 (exp.f64 b)))
12.0ms	(/.f64 1 (+.f64 1 (exp.f64 b)))
10.0ms	(pow.f64 (+.f64 1 (exp.f64 b)) 2)
9.0ms	(+.f64 1 (exp.f64 b))

Compiler

Compiled 1263 to 959 computations (24.1% saved)

simplify146.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

495×	`unswap-sqr_binary64`
478×	`distribute-rgt-in_binary64`
286×	`log-prod_binary64`
227×	`times-frac_binary64`
224×	`exp-prod_binary64`
187×	`cancel-sign-sub-inv_binary64`
185×	`associate-l_binary64`
180×	`cube-prod_binary64`
151×	`associate-/r*_binary64`
146×	`associate-/l*_binary64`
144×	`associate-r_binary64`
136×	`distribute-rgt-out_binary64`
105×	`*-commutative_binary64`
99×	`sub-neg_binary64`
95×	`distribute-lft-out_binary64`
87×	`sqr-pow_binary64`
86×	`associate-/l/_binary64`
73×	`associate-+l+_binary64`
68×	`distribute-rgt-neg-in_binary64` `+-commutative_binary64`
67×	`associate-*l/_binary64`
61×	`log-div_binary64`
58×	`distribute-lft-neg-in_binary64`
56×	`associate-/r/_binary64`
54×	`associate-+r+_binary64`
52×	`cube-div_binary64`
47×	`distribute-lft-in_binary64`
44×	`swap-sqr_binary64`
43×	`log-pow_binary64`
41×	`associate-*r/_binary64`
37×	`unpow3_binary64`
35×	`cube-unmult_binary64`
32×	`fabs-mul_binary64`
30×	`*-rgt-identity_binary64`
27×	`pow-plus_binary64` `exp-sum_binary64`
25×	`associate-+l-_binary64` `associate-+r-_binary64`
22×	`neg-mul-1_binary64` `pow-sqr_binary64`
21×	`neg-sub0_binary64`
17×	`cube-mult_binary64`
16×	`*-lft-identity_binary64` `distribute-rgt1-in_binary64`
14×	`rem-sqrt-square_binary64`
13×	`/-rgt-identity_binary64` `distribute-neg-in_binary64` `associate--r+_binary64`
12×	`distribute-neg-frac_binary64` `associate--l+_binary64`
11×	`unpow1/2_binary64` `+-rgt-identity_binary64`
10×	`log-rec_binary64` `fabs-div_binary64` `distribute-rgt-out--_binary64`
9×	`sub0-neg_binary64`
7×	`prod-exp_binary64` `div-sub_binary64`
6×	`unpow2_binary64` `unsub-neg_binary64` `distribute-lft1-in_binary64`
5×	`unpow1_binary64` `distribute-lft-neg-out_binary64`
4×	`distribute-lft-out--_binary64`
2×	`fabs-sqr_binary64` `+-lft-identity_binary64` `distribute-rgt-neg-out_binary64` `count-2_binary64` `associate--l-_binary64`
1×	`rec-exp_binary64` `exp-diff_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-3cbrt-rft_binary64` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `--rgt-identity_binary64` `+-inverses_binary64` `difference-of-sqr-1_binary64` `distribute-frac-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` `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` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `remove-double-neg_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-neg-out_binary64` `associate--r-_binary64`

Counts

126 → 82

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	1604
1	336	1505
2	798	1490
3	2348	1487
4	4373	1487
5	4915	1487
6	4920	1487

prune55.0ms (1.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	82	3	85

Error

Counts

85 → 3

Compiler

Compiled 1293 to 861 computations (33.4% saved)

regimes381.0ms (7.7%)

Accuracy

Total 0.7b remaining (98.9%)

Threshold costs 0.7b (98.9%)

Compiler

Compiled 5272 to 3828 computations (27.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1× 1-exp_binary64 +-commutative_binary64

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	12	16
2	11	16

end1.0ms (0%)

Compiler: Compiled 10 to 8 computations (20% saved)

sample619.0ms (12.5%)

Algorithm

1×

intervals

Results

234.0ms	8000×	body	128	valid
16.0ms	704×	body	128	overflowed

Compiler

Compiled 80 to 71 computations (11.3% saved)

Details

analyze105.0ms (2.1%)

sample22.0ms (0.4%)

simplify10.0ms (0.2%)

prune1.0ms (0%)

localize5.0ms (0.1%)

rewrite59.0ms (1.2%)

series279.0ms (5.6%)

simplify64.0ms (1.3%)

prune59.0ms (1.2%)

localize6.0ms (0.1%)

rewrite149.0ms (3%)

series108.0ms (2.2%)

simplify171.0ms (3.5%)

prune105.0ms (2.1%)

localize11.0ms (0.2%)

rewrite739.0ms (14.9%)

series221.0ms (4.5%)

simplify1.1s (22.7%)

prune292.0ms (5.9%)

localize11.0ms (0.2%)

rewrite134.0ms (2.7%)

series75.0ms (1.5%)

simplify146.0ms (2.9%)

prune55.0ms (1.1%)

regimes381.0ms (7.7%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample619.0ms (12.5%)

Profiling