Details

analyze32.0ms (1.4%)

Algorithm

1×	search
2×	egg-herbie

Rules

32×	`distribute-rgt-in_binary64`
27×	`cancel-sign-sub-inv_binary64`
26×	`distribute-lft-in_binary64`
25×	`sub-neg_binary64`
17×	`div-sub_binary64`
16×	`distribute-lft-neg-out_binary64`
15×	`unsub-neg_binary64` `distribute-rgt-neg-in_binary64`
14×	`associate-/l*_binary64`
13×	`neg-mul-1_binary64` `distribute-rgt-neg-out_binary64` `associate-/r*_binary64`
12×	`associate--r+_binary64`
10×	`distribute-neg-frac_binary64`
9×	`neg-sub0_binary64`
8×	`distribute-neg-in_binary64` `distribute-lft-neg-in_binary64`
7×	`associate-l_binary64` `*-commutative_binary64`
6×	`-lft-identity_binary64` `associate-l/_binary64` `associate-r_binary64` `associate--r-_binary64` `+-commutative_binary64`
5×	`sub0-neg_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-*r/_binary64` `associate-+l-_binary64`
3×	`*-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `associate--l+_binary64` `associate-+l+_binary64`
2×	`/-rgt-identity_binary64` `remove-double-neg_binary64` `div0_binary64` `distribute-rgt1-in_binary64` `associate--l-_binary64`
1×	`1-exp_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64` `associate-+r-_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-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` `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` `mul-1-neg_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_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-rgt-out_binary64` `count-2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	14	9
2	17	9
3	21	9
4	28	9
5	35	9
6	52	9
7	78	9
8	97	9
9	131	9
10	183	9
11	192	9
12	207	9
13	205	9
14	168	9
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
62.5%	25%	12.5%	4
68.7%	12.5%	18.8%	5
71.8%	6.2%	21.9%	6
73.4%	3.1%	23.5%	7
74.2%	1.6%	24.3%	8
74.6%	0.8%	24.6%	9
75%	0.4%	24.6%	10
75.1%	0.2%	24.7%	11
75.1%	0.1%	24.8%	12
75.1%	0%	24.8%	13
75.2%	0%	24.8%	14

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample30.0ms (1.3%)

Algorithm

1×

intervals

Results

13.0ms	84×	body	1024	valid
5.0ms	53×	body	512	valid
2.0ms	87×	body	128	valid
2.0ms	9×	body	2048	valid
1.0ms	23×	body	256	valid

Compiler

Compiled 13 to 12 computations (7.7% saved)

simplify17.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

32×	`distribute-rgt-in_binary64`
27×	`cancel-sign-sub-inv_binary64`
26×	`distribute-lft-in_binary64`
25×	`sub-neg_binary64`
17×	`div-sub_binary64`
16×	`distribute-lft-neg-out_binary64`
15×	`unsub-neg_binary64` `distribute-rgt-neg-in_binary64`
14×	`associate-/l*_binary64`
13×	`neg-mul-1_binary64` `distribute-rgt-neg-out_binary64` `associate-/r*_binary64`
12×	`associate--r+_binary64`
10×	`distribute-neg-frac_binary64`
9×	`neg-sub0_binary64`
8×	`distribute-neg-in_binary64` `distribute-lft-neg-in_binary64`
7×	`associate-l_binary64` `*-commutative_binary64`
6×	`-lft-identity_binary64` `associate-l/_binary64` `associate-r_binary64` `associate--r-_binary64` `+-commutative_binary64`
5×	`sub0-neg_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-*r/_binary64` `associate-+l-_binary64`
3×	`*-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `associate--l+_binary64` `associate-+l+_binary64`
2×	`/-rgt-identity_binary64` `remove-double-neg_binary64` `div0_binary64` `distribute-rgt1-in_binary64` `associate--l-_binary64`
1×	`1-exp_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64` `associate-+r-_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-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` `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` `mul-1-neg_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_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-rgt-out_binary64` `count-2_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	14	9
2	17	9
3	21	9
4	28	9
5	35	9
6	52	9
7	78	9
8	97	9
9	131	9
10	183	9
11	192	9
12	207	9
13	205	9
14	168	9

prune1.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

42.8b

Counts

1 → 1

Compiler

Compiled 6 to 5 computations (16.7% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 (exp.f64 x) 1) x)
4.9b	(-.f64 (exp.f64 x) 1)

rewrite89.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

42.8b

Rules

35×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
7×	`associate-/l*_binary64`
5×	`difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`cancel-sign-sub-inv_binary64` `associate-/r*_binary64`
2×	`pow1_binary64` `flip3--_binary64` `flip--_binary64` `associate-/l/_binary64`
1×	`diff-log_binary64` `sub-neg_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

2 → 64

Calls

2 calls:

6.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
5.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 754 to 428 computations (43.2% saved)

series30.0ms (1.3%)

Error

0.0b

Counts

2 → 12

Calls

2 calls:

9.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
8.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 230 to 186 computations (19.1% saved)

simplify90.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

486×	`associate-/l*_binary64`
359×	`associate-*l/_binary64`
294×	`associate-/l/_binary64` `associate-/r*_binary64`
268×	`distribute-rgt-in_binary64`
267×	`associate-/r/_binary64`
239×	`distribute-lft-in_binary64`
185×	`div-sub_binary64`
137×	`neg-mul-1_binary64`
120×	`cube-div_binary64`
117×	`exp-prod_binary64`
111×	`log-div_binary64`
86×	`times-frac_binary64`
82×	`associate-l_binary64`
81×	`distribute-rgt-out_binary64`
78×	`cube-prod_binary64` `associate-r_binary64`
65×	`log-prod_binary64`
58×	`*-commutative_binary64`
57×	`distribute-lft-out_binary64`
56×	`distribute-lft-neg-out_binary64`
54×	`distribute-rgt-neg-out_binary64`
50×	`associate-+l+_binary64` `+-commutative_binary64`
45×	`sub-neg_binary64`
39×	`associate-+r+_binary64`
38×	`exp-sum_binary64` `distribute-frac-neg_binary64`
32×	`associate-*r/_binary64`
28×	`sqr-pow_binary64` `distribute-neg-frac_binary64`
26×	`exp-diff_binary64` `cancel-sign-sub-inv_binary64` `distribute-rgt-neg-in_binary64`
23×	`unswap-sqr_binary64`
21×	`neg-sub0_binary64`
19×	`distribute-lft-neg-in_binary64`
18×	`unpow3_binary64` `distribute-neg-in_binary64`
15×	`unsub-neg_binary64`
14×	`cube-neg_binary64` `sqr-neg_binary64`
13×	`prod-exp_binary64` `cube-unmult_binary64` `/-rgt-identity_binary64` `*-lft-identity_binary64`
12×	`mul-1-neg_binary64` `*-rgt-identity_binary64` `distribute-rgt1-in_binary64`
11×	`log-rec_binary64`
10×	`cube-mult_binary64`
9×	`div-exp_binary64` `exp-neg_binary64`
8×	`swap-sqr_binary64`
7×	`pow-plus_binary64` `rec-exp_binary64`
6×	`rem-sqrt-square_binary64`
5×	`distribute-lft1-in_binary64` `associate-+r-_binary64`
4×	`cancel-sign-sub_binary64`
3×	`log-pow_binary64` `unpow1/2_binary64` `fabs-mul_binary64` `pow-sqr_binary64` `difference-of-sqr-1_binary64` `count-2_binary64`
2×	`fabs-div_binary64` `remove-double-neg_binary64` `+-rgt-identity_binary64` `associate--r+_binary64` `associate-+l-_binary64`
1×	`unpow2_binary64` `unpow1_binary64` `exp-lft-sqr_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-3cbrt-lft_binary64` `fabs-sqr_binary64` `sub0-neg_binary64` `div0_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `associate--r-_binary64` `associate--l-_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-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-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-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `rem-square-sqrt_binary64` `--rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `difference-of-squares_binary64` `distribute-neg-out_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `associate--l+_binary64`

Counts

76 → 40

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	116	1147
1	249	1094
2	556	1082
3	1324	1076
4	4327	1076
5	4968	1076

prune23.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	3	41

Error

Counts

41 → 3

Compiler

Compiled 326 to 197 computations (39.6% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1/6 (*.f64 x 1/24))
0.0b	(.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (*.f64 x 1/24)))))
0.2b	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
0.3b	(*.f64 x 1/24)

rewrite80.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

16×	`add-sqr-sqrt_binary64`
10×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
9×	`associate-l_binary64` `associate-r_binary64`
6×	`add-log-exp_binary64`
4×	`associate-*r/_binary64`
3×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64` `flip3-+_binary64` `flip-+_binary64`
2×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64`
1×	`sum-log_binary64` `+-commutative_binary64`

Counts

4 → 73

Calls

4 calls:

6.0ms	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
5.0ms	(.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (*.f64 x 1/24)))))
4.0ms	(*.f64 x 1/24)
3.0ms	(+.f64 1/6 (*.f64 x 1/24))

Compiler

Compiled 1414 to 1092 computations (22.8% saved)

series68.0ms (2.9%)

Error

Counts

4 → 24

Calls

4 calls:

22.0ms	(.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (*.f64 x 1/24)))))
13.0ms	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
10.0ms	(+.f64 1/6 (*.f64 x 1/24))
8.0ms	(*.f64 x 1/24)

Compiler

Compiled 600 to 515 computations (14.2% saved)

simplify115.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

769×	`distribute-rgt-in_binary64`
755×	`distribute-lft-in_binary64`
285×	`*-commutative_binary64`
254×	`sub-neg_binary64`
163×	`associate-l_binary64`
148×	`sqr-pow_binary64`
138×	`associate--r+_binary64`
132×	`associate-r_binary64`
130×	`unswap-sqr_binary64`
119×	`distribute-rgt-neg-in_binary64`
117×	`neg-mul-1_binary64`
113×	`neg-sub0_binary64`
111×	`distribute-neg-in_binary64`
104×	`exp-prod_binary64`
103×	`unsub-neg_binary64`
97×	`distribute-lft-neg-in_binary64`
82×	`associate-+l+_binary64`
81×	`cancel-sign-sub-inv_binary64`
80×	`associate-+r+_binary64`
60×	`*-lft-identity_binary64`
58×	`*-rgt-identity_binary64`
49×	`exp-sum_binary64`
48×	`distribute-rgt-out_binary64`
39×	`pow-sqr_binary64`
32×	`swap-sqr_binary64`
28×	`+-commutative_binary64`
27×	`distribute-lft-neg-out_binary64`
25×	`log-prod_binary64`
20×	`distribute-rgt-neg-out_binary64`
19×	`cube-prod_binary64`
18×	`associate-+l-_binary64`
15×	`associate--l+_binary64`
12×	`unpow1/2_binary64`
10×	`sub0-neg_binary64`
9×	`distribute-rgt-out--_binary64`
7×	`unpow3_binary64` `associate-+r-_binary64`
5×	`pow-plus_binary64` `+-rgt-identity_binary64`
4×	`log-pow_binary64` `rem-sqrt-square_binary64` `associate-/l*_binary64`
3×	`cube-unmult_binary64` `cube-mult_binary64` `fabs-mul_binary64`
2×	`prod-exp_binary64` `distribute-lft-out_binary64` `count-2_binary64` `associate-/l/_binary64` `associate-*r/_binary64`
1×	`unpow2_binary64` `unpow1_binary64` `1-exp_binary64` `exp-1-e_binary64` `fabs-sqr_binary64` `distribute-lft-out--_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-rec_binary64` `log-div_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-div_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `fabs-div_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-square-sqrt_binary64` `times-frac_binary64` `div-sub_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `remove-double-neg_binary64` `--rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `associate-/r/_binary64` `associate-/r_binary64` `associate-*l/_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

97 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	1270
1	315	1147
2	1058	1141
3	3490	1141
4	4317	1141
5	4986	1141
6	4891	1141

prune247.0ms (10.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	71	3	74

Error

Counts

74 → 3

Compiler

Compiled 1066 to 822 computations (22.9% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (exp.f64 x))
0.0b	(sqrt.f64 (exp.f64 x))
0.0b	(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (/.f64 (+.f64 -1 (sqrt.f64 (exp.f64 x))) x))
4.9b	(+.f64 -1 (sqrt.f64 (exp.f64 x)))

rewrite80.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

28×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64`
16×	`associate-r_binary64`
13×	`times-frac_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64` `sqrt-pow1_binary64`
7×	`sqrt-prod_binary64`
6×	`add-log-exp_binary64` `distribute-lft-out_binary64` `exp-prod_binary64`
5×	`associate-l_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`prod-exp_binary64` `cbrt-unprod_binary64` `frac-times_binary64` `unswap-sqr_binary64` `associate-*l/_binary64` `pow1/2_binary64` `rem-sqrt-square_binary64`
1×	`sum-log_binary64` `+-commutative_binary64` `pow-prod-down_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 85

Calls

4 calls:

14.0ms	(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (/.f64 (+.f64 -1 (sqrt.f64 (exp.f64 x))) x))
5.0ms	(+.f64 -1 (sqrt.f64 (exp.f64 x)))
2.0ms	(sqrt.f64 (exp.f64 x))
2.0ms	(sqrt.f64 (exp.f64 x))

Compiler

Compiled 1634 to 819 computations (49.9% saved)

series61.0ms (2.6%)

Error

Counts

4 → 24

Calls

4 calls:

17.0ms	(*.f64 (+.f64 1 (sqrt.f64 (exp.f64 x))) (/.f64 (+.f64 -1 (sqrt.f64 (exp.f64 x))) x))
11.0ms	(+.f64 -1 (sqrt.f64 (exp.f64 x)))
9.0ms	(sqrt.f64 (exp.f64 x))
9.0ms	(sqrt.f64 (exp.f64 x))

Compiler

Compiled 748 to 567 computations (24.2% saved)

simplify92.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

639×	`div-sub_binary64`
448×	`associate-l_binary64`
419×	`distribute-rgt-in_binary64`
400×	`distribute-lft-in_binary64`
379×	`associate-r_binary64`
234×	`associate-*r/_binary64`
220×	`associate-*l/_binary64`
204×	`associate-/l*_binary64`
182×	`times-frac_binary64`
139×	`*-commutative_binary64`
110×	`associate-+l+_binary64`
95×	`associate-/r*_binary64`
81×	`associate-+r+_binary64`
60×	`associate-/l/_binary64`
54×	`exp-prod_binary64` `+-commutative_binary64`
52×	`associate-/r/_binary64`
46×	`log-prod_binary64`
38×	`distribute-lft-neg-out_binary64`
36×	`distribute-rgt-neg-out_binary64`
34×	`cube-prod_binary64`
26×	`sub-neg_binary64`
24×	`associate-+l-_binary64`
23×	`distribute-rgt-out_binary64` `associate-+r-_binary64`
22×	`-rgt-identity_binary64` `-lft-identity_binary64` `sqr-pow_binary64`
18×	`log-div_binary64` `exp-diff_binary64` `distribute-lft-out_binary64`
17×	`cube-div_binary64`
16×	`exp-sum_binary64`
15×	`mul-1-neg_binary64`
12×	`neg-sub0_binary64`
10×	`cancel-sign-sub-inv_binary64`
9×	`unsub-neg_binary64`
7×	`unpow3_binary64` `cube-unmult_binary64` `sqr-neg_binary64` `distribute-rgt1-in_binary64`
5×	`pow-plus_binary64` `neg-mul-1_binary64` `/-rgt-identity_binary64` `associate--r-_binary64` `associate--r+_binary64`
4×	`exp-neg_binary64` `cube-mult_binary64` `cube-neg_binary64` `unswap-sqr_binary64` `swap-sqr_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-in_binary64`
3×	`unpow1/2_binary64` `fabs-mul_binary64` `rem-sqrt-square_binary64` `distribute-neg-frac_binary64` `distribute-rgt-out--_binary64`
2×	`log-pow_binary64` `log-rec_binary64` `prod-exp_binary64` `fabs-sub_binary64` `difference-of-sqr--1_binary64` `distribute-frac-neg_binary64` `distribute-lft-neg-in_binary64` `associate--l-_binary64`
1×	`unpow2_binary64` `unpow1_binary64` `1-exp_binary64` `exp-1-e_binary64` `fabs-neg_binary64` `sqr-abs_binary64` `rem-square-sqrt_binary64` `remove-double-neg_binary64` `pow-sqr_binary64` `difference-of-sqr-1_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` `rec-exp_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` `fabs-div_binary64` `fabs-sqr_binary64` `fabs-fabs_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` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-neg-out_binary64` `distribute-lft-out--_binary64` `count-2_binary64`

Counts

109 → 65

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	1719
1	370	1405
2	1120	1378
3	3767	1378
4	5337	1378

prune36.0ms (1.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	65	3	68

Error

Counts

68 → 3

Compiler

Compiled 1037 to 567 computations (45.3% saved)

regimes157.0ms (6.7%)

Accuracy

Total 0.2b remaining (91.6%)

Threshold costs 0.2b (91.6%)

Compiler

Compiled 1048 to 857 computations (18.2% saved)

bsearch14.0ms (0.6%)

Steps

Iters	Range		Point
8	-1.623566671865002	-0.00014290349280612102	-0.0014209620453650323

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`
1×	`unpow1_binary64` `1-exp_binary64` `sub-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` `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` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_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` `neg-mul-1_binary64` `neg-sub0_binary64` `unsub-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `cancel-sign-sub-inv_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	34
1	31	34
2	32	34
3	30	34

end1.0ms (0.1%)

Compiler: Compiled 23 to 18 computations (21.7% saved)

sample1.1s (45.1%)

Algorithm

1×

intervals

Results

433.0ms	2741×	body	1024	valid
114.0ms	1303×	body	512	valid
80.0ms	3024×	body	128	valid
50.0ms	281×	body	2048	valid
35.0ms	651×	body	256	valid

Compiler

Compiled 87 to 71 computations (18.4% saved)

Iter	Nodes	Cost
0	6	9
1	14	9
2	17	9
3	21	9
4	28	9
5	35	9
6	52	9
7	78	9
8	97	9
9	131	9
10	183	9
11	192	9
12	207	9
13	205	9
14	168	9
0	1	1
1	1	1

Iter	Nodes	Cost
0	6	9
1	14	9
2	17	9
3	21	9
4	28	9
5	35	9
6	52	9
7	78	9
8	97	9
9	131	9
10	183	9
11	192	9
12	207	9
13	205	9
14	168	9

Iter	Nodes	Cost
0	6	9
1	14	9
2	17	9
3	21	9
4	28	9
5	35	9
6	52	9
7	78	9
8	97	9
9	131	9
10	183	9
11	192	9
12	207	9
13	205	9
14	168	9
0	1	1
1	1	1

Iter	Nodes	Cost
0	6	9
1	14	9
2	17	9
3	21	9
4	28	9
5	35	9
6	52	9
7	78	9
8	97	9
9	131	9
10	183	9
11	192	9
12	207	9
13	205	9
14	168	9

Details

analyze32.0ms (1.4%)

sample30.0ms (1.3%)

simplify17.0ms (0.7%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

rewrite89.0ms (3.8%)

series30.0ms (1.3%)

simplify90.0ms (3.8%)

prune23.0ms (1%)

localize8.0ms (0.3%)

rewrite80.0ms (3.4%)

series68.0ms (2.9%)

simplify115.0ms (4.9%)

prune247.0ms (10.6%)

localize8.0ms (0.3%)

rewrite80.0ms (3.4%)

series61.0ms (2.6%)

simplify92.0ms (3.9%)

prune36.0ms (1.5%)

regimes157.0ms (6.7%)

bsearch14.0ms (0.6%)

simplify3.0ms (0.1%)

end1.0ms (0.1%)

sample1.1s (45.1%)

Profiling

Iter	Nodes	Cost
0	6	9
1	14	9
2	17	9
3	21	9
4	28	9
5	35	9
6	52	9
7	78	9
8	97	9
9	131	9
10	183	9
11	192	9
12	207	9
13	205	9
14	168	9
0	1	1
1	1	1

Iter	Nodes	Cost
0	6	9
1	14	9
2	17	9
3	21	9
4	28	9
5	35	9
6	52	9
7	78	9
8	97	9
9	131	9
10	183	9
11	192	9
12	207	9
13	205	9
14	168	9