Details

analyze101.0ms (3.8%)

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)

sample16.0ms (0.6%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
0.0ms	15×	body	128	overflowed

Compiler

Compiled 17 to 15 computations (11.8% saved)

simplify13.0ms (0.5%)

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 (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite38.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

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

Counts

1 → 33

Calls

1 calls:

7.0ms

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

Compiler

Compiled 505 to 102 computations (79.8% saved)

series50.0ms (1.9%)

Error

0.0b

Counts

1 → 11

Calls

1 calls:

36.0ms

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

Compiler

Compiled 683 to 472 computations (30.9% saved)

simplify117.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

307×	`sub-neg_binary64`
273×	`associate-/l*_binary64`
266×	`times-frac_binary64`
190×	`distribute-rgt-out_binary64`
189×	`associate-/r*_binary64`
161×	`distribute-neg-frac_binary64`
160×	`distribute-rgt-neg-in_binary64`
155×	`distribute-lft-neg-in_binary64`
125×	`associate-+l+_binary64`
121×	`distribute-rgt-in_binary64`
118×	`unswap-sqr_binary64`
117×	`associate-*l/_binary64`
113×	`associate--l+_binary64`
111×	`distribute-lft-in_binary64`
109×	`associate--r+_binary64`
104×	`distribute-rgt-out--_binary64`
87×	`associate-r_binary64` `+-commutative_binary64`
84×	`associate-l_binary64`
83×	`associate-/r/_binary64`
81×	`associate-+r+_binary64`
80×	`associate-/l/_binary64` `associate-*r/_binary64`
77×	`*-commutative_binary64`
74×	`cancel-sign-sub-inv_binary64`
61×	`unsub-neg_binary64`
54×	`distribute-neg-in_binary64`
51×	`neg-mul-1_binary64`
50×	`neg-sub0_binary64`
49×	`sqr-pow_binary64`
43×	`div-sub_binary64`
38×	`*-rgt-identity_binary64`
29×	`associate-+l-_binary64`
28×	`associate-+r-_binary64`
26×	`exp-prod_binary64`
20×	`unpow3_binary64` `prod-exp_binary64`
18×	`+-rgt-identity_binary64`
17×	`cube-prod_binary64`
15×	`*-lft-identity_binary64`
12×	`pow-plus_binary64` `cube-unmult_binary64`
11×	`sub0-neg_binary64`
10×	`exp-sum_binary64` `distribute-rgt1-in_binary64`
9×	`exp-diff_binary64`
8×	`difference-of-squares_binary64`
7×	`distribute-lft-neg-out_binary64`
6×	`log-prod_binary64`
5×	`log-pow_binary64` `log-div_binary64` `cube-mult_binary64` `pow-sqr_binary64` `associate--l-_binary64`
4×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `cube-div_binary64` `rem-sqrt-square_binary64` `/-rgt-identity_binary64` `distribute-lft1-in_binary64` `distribute-lft-out_binary64`
3×	`div-exp_binary64`
2×	`rec-exp_binary64` `swap-sqr_binary64` `cancel-sign-sub_binary64` `count-2_binary64`
1×	`exp-to-pow_binary64` `1-exp_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `remove-double-neg_binary64` `--rgt-identity_binary64` `div0_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-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-1-e_binary64` `exp-0_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` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_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` `distribute-frac-neg_binary64` `distribute-neg-out_binary64`

Counts

44 → 37

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	114	1183
1	285	1129
2	866	1100
3	3218	1080
4	4952	1080
5	4997	1080
6	4954	1080

prune35.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	34	3	37
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	35	3	38

Error

Counts

38 → 3

Compiler

Compiled 653 to 246 computations (62.3% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3)
0.3b	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3))
0.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a)))

rewrite116.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

78×	`*-un-lft-identity_binary64`
60×	`times-frac_binary64`
46×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
42×	`cbrt-prod_binary64`
36×	`unpow-prod-down_binary64` `cube-prod_binary64`
16×	`distribute-lft-out_binary64`
10×	`associate-/r/_binary64`
8×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
5×	`div-inv_binary64` `flip3-+_binary64` `flip-+_binary64`
4×	`pow1_binary64` `associate-/r*_binary64`
3×	`add-log-exp_binary64` `associate-/l*_binary64` `pow-unpow_binary64`
2×	`div-exp_binary64` `cbrt-undiv_binary64` `cube-div_binary64` `unpow3_binary64` `cube-mult_binary64` `sqr-pow_binary64` `pow-exp_binary64` `rem-cube-cbrt_binary64`
1×	`frac-2neg_binary64` `clear-num_binary64` `pow1/3_binary64` `cbrt-div_binary64` `rem-cbrt-cube_binary64` `pow-pow_binary64` `pow-to-exp_binary64`

Counts

3 → 141

Calls

3 calls:

9.0ms	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3))
9.0ms	(pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3)
7.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a)))

Compiler

Compiled 2025 to 615 computations (69.6% saved)

series170.0ms (6.4%)

Error

Counts

3 → 32

Calls

3 calls:

65.0ms	(pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3)
40.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a)))
35.0ms	(cbrt.f64 (pow.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 b) (exp.f64 a))) 3))

Compiler

Compiled 2149 to 1549 computations (27.9% saved)

simplify184.0ms (6.9%)

Algorithm

1×	egg-herbie

Rules

487×	`unswap-sqr_binary64`
230×	`distribute-rgt-in_binary64`
202×	`distribute-lft-in_binary64`
156×	`cancel-sign-sub-inv_binary64`
144×	`sqr-pow_binary64`
134×	`log-div_binary64`
131×	`associate-/l*_binary64`
115×	`sub-neg_binary64`
108×	`times-frac_binary64`
93×	`associate-*l/_binary64`
88×	`associate-*r/_binary64`
87×	`log-prod_binary64`
82×	`associate-/r*_binary64`
71×	`associate-r_binary64`
70×	`cube-div_binary64` `distribute-neg-frac_binary64`
62×	`exp-prod_binary64`
60×	`+-commutative_binary64`
58×	`distribute-rgt-neg-in_binary64` `associate-l_binary64`
52×	`distribute-lft-neg-in_binary64`
49×	`distribute-neg-in_binary64`
48×	`cube-prod_binary64`
46×	`*-commutative_binary64`
42×	`log-pow_binary64` `unpow3_binary64`
41×	`cube-mult_binary64`
37×	`associate--l+_binary64`
35×	`neg-mul-1_binary64` `neg-sub0_binary64` `swap-sqr_binary64`
32×	`associate-+l+_binary64`
31×	`associate-/l/_binary64` `associate--r+_binary64`
26×	`rem-cbrt-cube_binary64`
25×	`*-rgt-identity_binary64` `associate-+r+_binary64`
24×	`unsub-neg_binary64`
19×	`associate-/r/_binary64`
14×	`distribute-rgt-out_binary64`
13×	`rem-sqrt-square_binary64` `pow-sqr_binary64`
11×	`*-lft-identity_binary64`
10×	`distribute-lft-neg-out_binary64`
9×	`pow-plus_binary64` `div-sub_binary64` `distribute-lft-out_binary64`
8×	`prod-exp_binary64` `cube-unmult_binary64`
5×	`log-rec_binary64` `unpow1/2_binary64` `unpow1_binary64` `distribute-rgt-out--_binary64`
4×	`unpow2_binary64` `/-rgt-identity_binary64` `distribute-rgt-neg-out_binary64`
3×	`rem-log-exp_binary64` `rem-cube-cbrt_binary64` `rem-square-sqrt_binary64` `distribute-rgt1-in_binary64` `associate-+r-_binary64`
2×	`+-rgt-identity_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `count-2_binary64`
1×	`rec-exp_binary64` `exp-diff_binary64` `1-exp_binary64` `rem-3cbrt-lft_binary64` `distribute-lft1-in_binary64` `associate-+l-_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `pow-base-0_binary64` `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` `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` `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` `associate--l-_binary64`

Counts

173 → 133

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	236	5014
1	650	4655
2	2279	4516
3	4959	4516
4	5025	4516

prune64.0ms (2.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	133	3	136

Error

Counts

136 → 3

Compiler

Compiled 1588 to 781 computations (50.8% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

rewrite242.0ms (9.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

109×	`*-un-lft-identity_binary64`
73×	`times-frac_binary64`
52×	`add-sqr-sqrt_binary64`
40×	`add-cube-cbrt_binary64`
31×	`cancel-sign-sub-inv_binary64`
23×	`distribute-lft-out_binary64`
17×	`unpow-prod-down_binary64`
11×	`add-exp-log_binary64` `distribute-lft-out--_binary64`
9×	`unpow2_binary64` `add-log-exp_binary64` `div-inv_binary64`
8×	`add-cbrt-cube_binary64` `associate-/r*_binary64`
6×	`pow1_binary64` `associate-/l*_binary64`
5×	`sqr-pow_binary64` `difference-of-squares_binary64`
4×	`distribute-rgt-out_binary64` `associate-/r/_binary64`
3×	`pow-unpow_binary64` `frac-sub_binary64` `flip3-+_binary64` `flip-+_binary64` `div-exp_binary64`
2×	`diff-log_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64`
1×	`pow-pow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `sum-log_binary64` `frac-add_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `associate--l+_binary64` `inv-pow_binary64` `pow-flip_binary64` `1-exp_binary64` `rec-exp_binary64`

Counts

4 → 152

Calls

4 calls:

55.0ms	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (/.f64 a (+.f64 1 (exp.f64 b)))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)))
8.0ms	(/.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)

Compiler

Compiled 4346 to 2853 computations (34.4% saved)

series122.0ms (4.6%)

Error

Counts

4 → 28

Calls

4 calls:

60.0ms	(-.f64 (+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (/.f64 a (+.f64 1 (exp.f64 b)))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)))
20.0ms	(/.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)

Compiler

Compiled 1355 to 1031 computations (23.9% saved)

simplify157.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

589×	`distribute-rgt-in_binary64`
551×	`distribute-lft-in_binary64`
207×	`exp-prod_binary64`
132×	`distribute-neg-frac_binary64`
129×	`cancel-sign-sub-inv_binary64`
122×	`distribute-rgt-neg-in_binary64`
114×	`sub-neg_binary64`
112×	`associate-*l/_binary64`
109×	`*-commutative_binary64`
101×	`neg-sub0_binary64`
98×	`associate-*r/_binary64`
92×	`neg-mul-1_binary64`
90×	`associate-/r*_binary64`
83×	`distribute-lft-neg-in_binary64`
81×	`associate-/l*_binary64`
77×	`distribute-lft-neg-out_binary64`
73×	`div-sub_binary64`
71×	`times-frac_binary64` `+-commutative_binary64`
70×	`distribute-rgt-out_binary64`
58×	`associate-l_binary64`
57×	`sqr-pow_binary64`
50×	`associate-/l/_binary64`
49×	`distribute-frac-neg_binary64` `associate-r_binary64`
48×	`distribute-rgt-neg-out_binary64`
47×	`unswap-sqr_binary64`
45×	`log-prod_binary64`
41×	`distribute-neg-in_binary64`
31×	`cube-prod_binary64` `distribute-rgt-out--_binary64` `associate-/r/_binary64` `associate-+l+_binary64`
24×	`unpow3_binary64` `associate-+r+_binary64`
20×	`cube-div_binary64` `*-rgt-identity_binary64` `distribute-lft-out_binary64`
19×	`exp-sum_binary64`
17×	`swap-sqr_binary64` `associate--l+_binary64`
15×	`log-div_binary64` `unsub-neg_binary64`
14×	`distribute-rgt1-in_binary64`
13×	`pow-plus_binary64` `*-lft-identity_binary64` `associate-+r-_binary64`
11×	`log-pow_binary64`
9×	`pow-sqr_binary64`
8×	`/-rgt-identity_binary64`
7×	`unpow2_binary64`
6×	`unpow1/2_binary64` `unpow1_binary64` `exp-diff_binary64` `cube-unmult_binary64` `cube-mult_binary64` `+-rgt-identity_binary64` `difference-of-squares_binary64`
5×	`div-exp_binary64` `div0_binary64` `associate--r+_binary64`
4×	`prod-exp_binary64` `distribute-lft1-in_binary64` `distribute-lft-out--_binary64`
3×	`log-rec_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64`
2×	`rem-3cbrt-lft_binary64`
1×	`1-exp_binary64` `rem-3cbrt-rft_binary64` `mul-1-neg_binary64` `remove-double-neg_binary64` `+-lft-identity_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `count-2_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` `rec-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `*-inverses_binary64` `+-inverses_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `cancel-sign-sub_binary64` `distribute-neg-out_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

180 → 157

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	303	4119
1	748	3865
2	2105	3403
3	4799	3403
4	5000	3403

prune104.0ms (3.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

160 → 3

Compiler

Compiled 2579 to 1731 computations (32.9% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite50.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

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)

series23.0ms (0.9%)

Error

Counts

2 → 12

Calls

2 calls:

9.0ms	(/.f64 1 (+.f64 1 (exp.f64 b)))
6.0ms	(+.f64 1 (exp.f64 b))

Compiler

Compiled 194 to 195 computations (-0.5% saved)

simplify91.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

494×	`unswap-sqr_binary64`
479×	`sub-neg_binary64`
415×	`cancel-sign-sub-inv_binary64`
315×	`*-commutative_binary64`
301×	`times-frac_binary64`
212×	`distribute-rgt-neg-in_binary64`
201×	`associate-+r-_binary64`
192×	`associate-l_binary64`
180×	`distribute-lft-neg-in_binary64`
175×	`distribute-rgt-in_binary64`
154×	`associate-r_binary64`
143×	`distribute-rgt-out_binary64`
134×	`associate-/l*_binary64`
122×	`associate--r+_binary64`
119×	`associate-+l+_binary64`
117×	`sqr-pow_binary64`
115×	`neg-mul-1_binary64`
108×	`neg-sub0_binary64`
105×	`associate-+r+_binary64`
103×	`associate--l+_binary64`
101×	`associate-+l-_binary64`
99×	`distribute-neg-in_binary64`
78×	`distribute-lft-out_binary64`
72×	`associate-/r*_binary64`
71×	`div-sub_binary64` `distribute-lft-in_binary64`
67×	`exp-prod_binary64`
66×	`*-rgt-identity_binary64`
62×	`+-commutative_binary64`
58×	`associate--l-_binary64`
54×	`unsub-neg_binary64`
51×	`associate-*l/_binary64`
50×	`associate-/l/_binary64`
46×	`associate--r-_binary64`
44×	`associate-/r/_binary64`
34×	`pow-sqr_binary64`
32×	`cube-prod_binary64` `distribute-rgt1-in_binary64`
31×	`distribute-lft-neg-out_binary64`
27×	`associate-*r/_binary64`
24×	`sub0-neg_binary64`
23×	`*-lft-identity_binary64`
21×	`remove-double-neg_binary64`
20×	`pow-plus_binary64`
18×	`distribute-rgt-out--_binary64`
17×	`cube-unmult_binary64` `distribute-lft1-in_binary64`
15×	`--rgt-identity_binary64`
14×	`+-rgt-identity_binary64`
12×	`/-rgt-identity_binary64` `difference-of-squares_binary64`
11×	`distribute-rgt-neg-out_binary64`
10×	`+-lft-identity_binary64`
9×	`rem-sqrt-square_binary64`
8×	`unpow3_binary64`
7×	`exp-sum_binary64` `cube-div_binary64` `distribute-lft-out--_binary64`
6×	`swap-sqr_binary64`
5×	`prod-exp_binary64`
4×	`log-div_binary64` `unpow1/2_binary64` `div-exp_binary64` `exp-diff_binary64` `cube-mult_binary64` `difference-of-sqr--1_binary64` `count-2_binary64`
3×	`rec-exp_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `remove-double-div_binary64` `difference-of-sqr-1_binary64`
2×	`log-rec_binary64` `log-prod_binary64` `unpow1_binary64` `exp-lft-sqr_binary64` `mul-1-neg_binary64` `+-inverses_binary64` `distribute-neg-out_binary64`
1×	`unpow2_binary64` `exp-lft-cube_binary64` `exp-neg_binary64` `1-exp_binary64` `exp-1-e_binary64` `cube-neg_binary64` `sqr-neg_binary64` `distribute-neg-frac_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` `div0_binary64` `*-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64`

Counts

61 → 49

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	86	785
1	194	732
2	405	729
3	775	729
4	1945	729
5	3755	729
6	5289	729

prune29.0ms (1.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	49	3	52

Error

Counts

52 → 3

Compiler

Compiled 437 to 324 computations (25.9% saved)

regimes295.0ms (11.1%)

Accuracy

Total 0.7b remaining (96.2%)

Threshold costs 0.7b (96.2%)

Compiler

Compiled 3653 to 2954 computations (19.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1× 1-exp_binary64 /-rgt-identity_binary64 *-commutative_binary64 +-commutative_binary64

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	15	22
2	14	22

end1.0ms (0%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

sample609.0ms (22.9%)

Algorithm

1×

intervals

Results

234.0ms	8000×	body	128	valid
15.0ms	686×	body	128	overflowed

Compiler

Compiled 72 to 67 computations (6.9% saved)

Details

analyze101.0ms (3.8%)

sample16.0ms (0.6%)

simplify13.0ms (0.5%)

prune1.0ms (0%)

localize5.0ms (0.2%)

rewrite38.0ms (1.4%)

series50.0ms (1.9%)

simplify117.0ms (4.4%)

prune35.0ms (1.3%)

localize7.0ms (0.3%)

rewrite116.0ms (4.4%)

series170.0ms (6.4%)

simplify184.0ms (6.9%)

prune64.0ms (2.4%)

localize13.0ms (0.5%)

rewrite242.0ms (9.1%)

series122.0ms (4.6%)

simplify157.0ms (5.9%)

prune104.0ms (3.9%)

localize4.0ms (0.1%)

rewrite50.0ms (1.9%)

series23.0ms (0.9%)

simplify91.0ms (3.4%)

prune29.0ms (1.1%)

regimes295.0ms (11.1%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample609.0ms (22.9%)

Profiling