Details

analyze13.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample221.0ms (2.8%)

Algorithm

1×

intervals

Results

210.0ms

256×

body

128

valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify288.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

527×	`distribute-rgt-in_binary64`
476×	`distribute-rgt-out_binary64`
437×	`cube-prod_binary64`
434×	`associate-*l/_binary64`
352×	`associate-/l*_binary64`
343×	`cube-div_binary64`
311×	`distribute-lft-in_binary64`
270×	`associate-*r/_binary64`
249×	`*-commutative_binary64`
185×	`associate-/r/_binary64`
168×	`associate-/l/_binary64`
148×	`sqr-pow_binary64` `associate-/r*_binary64`
142×	`swap-sqr_binary64` `associate-l_binary64`
121×	`unswap-sqr_binary64`
102×	`distribute-lft-out_binary64`
85×	`associate-r_binary64`
70×	`pow-sqr_binary64`
64×	`times-frac_binary64`
63×	`unpow3_binary64`
61×	`cube-mult_binary64` `*-lft-identity_binary64`
53×	`*-rgt-identity_binary64`
34×	`pow-plus_binary64`
28×	`associate-+l+_binary64`
27×	`exp-prod_binary64` `associate-+r+_binary64`
24×	`distribute-rgt1-in_binary64`
20×	`remove-double-div_binary64`
17×	`count-2_binary64`
16×	`div-exp_binary64` `prod-exp_binary64`
11×	`distribute-lft1-in_binary64`
10×	`cube-unmult_binary64`
8×	`+-commutative_binary64`
6×	`/-rgt-identity_binary64`
5×	`sub-neg_binary64`
4×	`pow-base-1_binary64` `rec-exp_binary64` `distribute-rgt-out--_binary64`
3×	`neg-mul-1_binary64` `neg-sub0_binary64`
2×	`exp-sum_binary64` `+-inverses_binary64` `cancel-sign-sub-inv_binary64` `distribute-lft-neg-in_binary64`
1×	`unpow2_binary64` `unpow1_binary64` `exp-lft-sqr_binary64` `exp-sqrt_binary64` `1-exp_binary64` `--rgt-identity_binary64` `*-inverses_binary64` `rgt-mult-inverse_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` `unpow1/2_binary64` `exp-to-pow_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `exp-diff_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-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` `div-sub_binary64` `unsub-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` `lft-mult-inverse_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-neg-in_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-out--_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+l-_binary64` `associate-+r-_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	11	9
2	26	9
3	44	9
4	143	9
5	518	9
6	2320	9
7	4108	9

prune8.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

30.1b

Counts

3 → 1

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

28.9b

(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

14.7b

Rules

4×	`pow1_binary64`
2×	`sqrt-pow1_binary64` `associate-*r/_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `flip-+_binary64` `sqrt-prod_binary64` `*-un-lft-identity_binary64`

Counts

1 → 13

Calls

1 calls:

7.0ms

(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 161 to 50 computations (68.9% saved)

series51.0ms (0.6%)

Error

0.2b

Counts

1 → 3

Calls

1 calls:

47.0ms

(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 42 to 40 computations (4.8% saved)

simplify436.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

674×	`distribute-rgt-out--_binary64`
546×	`exp-diff_binary64`
402×	`cancel-sign-sub-inv_binary64`
290×	`associate-+l-_binary64`
254×	`associate--r-_binary64`
211×	`associate--l-_binary64`
210×	`associate-+r-_binary64`
206×	`distribute-lft-out_binary64`
201×	`exp-sum_binary64`
131×	`distribute-neg-in_binary64`
127×	`exp-prod_binary64`
107×	`*-commutative_binary64`
92×	`times-frac_binary64`
84×	`distribute-rgt-in_binary64`
80×	`associate-r_binary64`
78×	`+-commutative_binary64`
74×	`div-exp_binary64`
71×	`associate-/l*_binary64`
67×	`distribute-lft-in_binary64`
63×	`distribute-lft-neg-in_binary64`
58×	`sub-neg_binary64`
54×	`distribute-rgt-neg-in_binary64`
52×	`associate-l_binary64`
51×	`distribute-lft-out--_binary64`
49×	`distribute-rgt1-in_binary64`
47×	`swap-sqr_binary64`
34×	`pow-plus_binary64`
29×	`distribute-lft-neg-out_binary64`
28×	`sqr-pow_binary64`
27×	`associate--l+_binary64`
26×	`distribute-rgt-neg-out_binary64`
24×	`unsub-neg_binary64` `associate-+l+_binary64`
23×	`associate--r+_binary64`
19×	`unswap-sqr_binary64`
18×	`exp-lft-sqr_binary64` `neg-sub0_binary64`
17×	`associate-+r+_binary64`
15×	`div-sub_binary64` `distribute-rgt-out_binary64`
14×	`neg-mul-1_binary64` `associate-/l/_binary64`
13×	`count-2_binary64`
8×	`mul0-rgt_binary64` `pow-sqr_binary64`
7×	`distribute-lft1-in_binary64` `associate-/r*_binary64`
6×	`+-lft-identity_binary64` `difference-of-squares_binary64` `associate-*r/_binary64`
5×	`mul0-lft_binary64` `associate-/r/_binary64`
4×	`pow-base-1_binary64` `+-inverses_binary64`
3×	`rec-exp_binary64` `exp-neg_binary64` `cube-unmult_binary64` `+-rgt-identity_binary64`
2×	`unpow3_binary64` `rem-sqrt-square_binary64`
1×	`exp-sqrt_binary64` `1-exp_binary64` `cube-mult_binary64` `cube-prod_binary64` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `remove-double-neg_binary64` `div0_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` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow2_binary64` `unpow1/2_binary64` `exp-to-pow_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `prod-exp_binary64` `e-exp-1_binary64` `exp-1-e_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` `sqr-abs_binary64` `sqr-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `sub0-neg_binary64` `--rgt-identity_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-neg-frac_binary64` `distribute-frac-neg_binary64`

Counts

16 → 28

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	161
1	65	152
2	168	149
3	855	149
4	4381	149

prune35.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	23	5	28
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	23	6	29

Error

15.5b

Counts

29 → 6

Compiler

Compiled 431 to 243 computations (43.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))))
28.9b	(sqrt.f64 (*.f64 x (+.f64 x x)))
28.9b	(sqrt.f64 (.f64 2 (.f64 x x)))

rewrite139.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

15.4b

Rules

42×	`pow1_binary64`
39×	`sqrt-pow1_binary64`
24×	`pow-prod-down_binary64`
21×	`sqrt-prod_binary64`
18×	`add-sqr-sqrt_binary64`
10×	`sqrt-div_binary64`
9×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
8×	`pow1/2_binary64`
7×	`associate-l_binary64` `associate-r_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-*r/_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`associate-*l/_binary64`
1×	`prod-exp_binary64` `cbrt-unprod_binary64` `sqrt-unprod_binary64` `*-commutative_binary64` `rem-sqrt-square_binary64`

Counts

4 → 85

Calls

4 calls:

17.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))))
6.0ms	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
4.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 1929 to 779 computations (59.6% saved)

series175.0ms (2.2%)

Error

0.2b

Counts

4 → 12

Calls

4 calls:

46.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))))
45.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
38.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
34.0ms	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))

Compiler

Compiled 437 to 348 computations (20.4% saved)

simplify558.0ms (7%)

Algorithm

1×	egg-herbie

Rules

554×	`distribute-rgt-out--_binary64`
443×	`cancel-sign-sub-inv_binary64`
368×	`times-frac_binary64`
322×	`associate-l_binary64`
287×	`associate-r_binary64`
205×	`exp-prod_binary64`
199×	`exp-sum_binary64`
131×	`distribute-neg-in_binary64`
113×	`distribute-rgt-in_binary64`
102×	`swap-sqr_binary64`
93×	`distribute-lft-in_binary64`
89×	`unswap-sqr_binary64`
88×	`distribute-lft-neg-in_binary64`
80×	`distribute-rgt-neg-in_binary64`
68×	`distribute-lft-out--_binary64`
58×	`sub-neg_binary64`
57×	`exp-diff_binary64`
54×	`associate-r/_binary64` `-commutative_binary64`
49×	`associate-*l/_binary64`
48×	`sqr-pow_binary64` `distribute-rgt1-in_binary64`
47×	`log-prod_binary64`
34×	`cube-prod_binary64`
33×	`distribute-lft-neg-out_binary64`
30×	`distribute-rgt-neg-out_binary64`
27×	`associate--l+_binary64`
25×	`unsub-neg_binary64` `associate-+l+_binary64`
24×	`associate--r+_binary64`
22×	`log-div_binary64`
21×	`pow-sqr_binary64` `distribute-rgt-out_binary64`
18×	`neg-sub0_binary64` `associate-+r+_binary64`
17×	`log-pow_binary64` `pow-plus_binary64`
16×	`*-rgt-identity_binary64`
15×	`div-sub_binary64` `associate--r-_binary64` `associate-+l-_binary64`
14×	`cube-div_binary64` `neg-mul-1_binary64` `*-lft-identity_binary64`
13×	`distribute-lft-out_binary64` `associate-+r-_binary64`
12×	`mul0-rgt_binary64`
10×	`rem-sqrt-square_binary64`
9×	`associate--l-_binary64`
8×	`exp-to-pow_binary64` `distribute-lft1-in_binary64` `count-2_binary64`
7×	`exp-lft-sqr_binary64` `mul0-lft_binary64` `associate-/l*_binary64`
6×	`prod-exp_binary64` `+-lft-identity_binary64` `difference-of-squares_binary64` `associate-/l/_binary64` `+-commutative_binary64`
5×	`cube-unmult_binary64` `rem-square-sqrt_binary64`
4×	`+-inverses_binary64` `distribute-neg-frac_binary64`
3×	`exp-neg_binary64` `+-rgt-identity_binary64`
2×	`log-rec_binary64` `unpow3_binary64` `rem-log-exp_binary64`
1×	`pow-base-1_binary64` `1-exp_binary64` `exp-1-e_binary64` `cube-mult_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `remove-double-neg_binary64` `div0_binary64` `distribute-neg-out_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow2_binary64` `unpow1/2_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `e-exp-1_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` `sqr-abs_binary64` `sqr-neg_binary64` `sub0-neg_binary64` `--rgt-identity_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` `associate-/r/_binary64` `associate-/r_binary64`

Counts

97 → 130

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	1293
1	139	1234
2	384	1194
3	1815	1194

prune142.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	126	4	130
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	129	7	136

Error

15.4b

Counts

136 → 7

Compiler

Compiled 2624 to 1088 computations (58.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (.f64 (fabs.f64 (cbrt.f64 (sqrt.f64 (.f64 x (+.f64 x x))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))))) (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))))
28.9b	(sqrt.f64 (*.f64 x (+.f64 x x)))
28.9b	(sqrt.f64 (*.f64 x (+.f64 x x)))
28.9b	(sqrt.f64 (.f64 2 (.f64 x x)))

rewrite122.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

15.4b

Rules

21×	`pow1_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow-prod-down_binary64` `sqrt-prod_binary64` `associate-*r/_binary64` `sqrt-div_binary64`
7×	`sqrt-pow1_binary64` `associate-r_binary64`
6×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`pow1/2_binary64` `flip3-+_binary64` `flip-+_binary64` `prod-exp_binary64` `cbrt-unprod_binary64`
2×	`cbrt-div_binary64` `associate-*l/_binary64`
1×	`associate-l_binary64` `*-commutative_binary64`

Counts

4 → 62

Calls

4 calls:

13.0ms	(.f64 (.f64 (fabs.f64 (cbrt.f64 (sqrt.f64 (.f64 x (+.f64 x x))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))))) (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))))
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
4.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 2131 to 651 computations (69.5% saved)

series443.0ms (5.6%)

Error

1.9b

Counts

4 → 12

Calls

4 calls:

277.0ms	(.f64 (.f64 (fabs.f64 (cbrt.f64 (sqrt.f64 (.f64 x (+.f64 x x))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))))) (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))))
50.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
49.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
49.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 846 to 597 computations (29.4% saved)

simplify945.0ms (11.9%)

Algorithm

1×	egg-herbie

Rules

680×	`times-frac_binary64`
419×	`unswap-sqr_binary64`
266×	`exp-sum_binary64`
240×	`exp-prod_binary64`
199×	`*-commutative_binary64`
137×	`associate-l_binary64`
129×	`sqr-pow_binary64`
112×	`sub-neg_binary64`
106×	`associate-r_binary64`
104×	`distribute-rgt-in_binary64`
91×	`log-prod_binary64`
87×	`distribute-lft-in_binary64`
69×	`exp-diff_binary64` `difference-of-squares_binary64`
67×	`log-div_binary64` `associate-*r/_binary64`
64×	`associate-*l/_binary64`
63×	`cube-prod_binary64`
57×	`pow-sqr_binary64` `associate--l+_binary64`
52×	`unsub-neg_binary64`
49×	`cube-div_binary64`
45×	`associate-+l+_binary64`
39×	`div-sub_binary64`
32×	`associate-+r+_binary64`
31×	`neg-mul-1_binary64` `neg-sub0_binary64`
26×	`swap-sqr_binary64`
25×	`log-pow_binary64` `cancel-sign-sub-inv_binary64` `associate--r+_binary64`
23×	`associate-+l-_binary64`
21×	`pow-plus_binary64` `rem-sqrt-square_binary64`
18×	`exp-to-pow_binary64` `exp-sqrt_binary64` `associate-+r-_binary64`
17×	`distribute-lft-out_binary64` `associate--r-_binary64` `associate--l-_binary64`
16×	`distribute-rgt-out_binary64` `+-commutative_binary64`
14×	`exp-lft-sqr_binary64`
12×	`*-rgt-identity_binary64`
11×	`distribute-rgt-neg-in_binary64`
10×	`distribute-lft-neg-out_binary64`
9×	`distribute-lft-out--_binary64` `associate-/r*_binary64`
8×	`cube-unmult_binary64` `-lft-identity_binary64` `mul0-rgt_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-in_binary64` `associate-/l/_binary64` `associate-/l_binary64`
7×	`unpow1/3_binary64` `unpow3_binary64` `exp-neg_binary64` `distribute-neg-in_binary64` `count-2_binary64`
6×	`prod-exp_binary64` `+-lft-identity_binary64` `mul0-lft_binary64`
5×	`rem-log-exp_binary64` `cube-mult_binary64` `rem-square-sqrt_binary64` `distribute-rgt-out--_binary64`
4×	`remove-double-neg_binary64` `+-rgt-identity_binary64` `+-inverses_binary64` `distribute-rgt1-in_binary64`
3×	`log-rec_binary64`
2×	`sub0-neg_binary64` `*-inverses_binary64`
1×	`unpow2_binary64` `pow-base-1_binary64` `unpow1_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-exp-log_binary64` `rem-3cbrt-lft_binary64` `sqr-abs_binary64` `mul-1-neg_binary64` `--rgt-identity_binary64` `div0_binary64` `rgt-mult-inverse_binary64` `difference-of-sqr--1_binary64` `cancel-sign-sub_binary64` `distribute-lft1-in_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` `unpow1/2_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `div-exp_binary64` `rec-exp_binary64` `e-exp-1_binary64` `exp-0_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-neg_binary64` `/-rgt-identity_binary64` `lft-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr-1_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `associate-/r/_binary64`

Counts

74 → 148

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	121	1681
1	262	1503
2	722	1476
3	2201	1361

prune276.0ms (3.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	144	4	148
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	146	9	155

Error

0.2b

Counts

155 → 9

Compiler

Compiled 5266 to 2188 computations (58.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 x (sqrt.f64 2))
0.4b	(*.f64 x (sqrt.f64 2))
0.5b	(cbrt.f64 (fabs.f64 (*.f64 x (sqrt.f64 2))))
0.5b	(cbrt.f64 (fabs.f64 (*.f64 x (sqrt.f64 2))))

rewrite160.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

20×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64` `-un-lft-identity_binary64` `associate-r*_binary64`
8×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
6×	`cbrt-prod_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
2×	`pow1/3_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `*-commutative_binary64`

Counts

4 → 66

Calls

4 calls:

7.0ms	(*.f64 x (sqrt.f64 2))
5.0ms	(*.f64 x (sqrt.f64 2))
1.0ms	(cbrt.f64 (fabs.f64 (*.f64 x (sqrt.f64 2))))
1.0ms	(cbrt.f64 (fabs.f64 (*.f64 x (sqrt.f64 2))))

Compiler

Compiled 1976 to 1719 computations (13% saved)

series430.0ms (5.4%)

Error

0.2b

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt.f64 (fabs.f64 (*.f64 x (sqrt.f64 2))))
149.0ms	(cbrt.f64 (fabs.f64 (*.f64 x (sqrt.f64 2))))
54.0ms	(*.f64 x (sqrt.f64 2))
49.0ms	(*.f64 x (sqrt.f64 2))

Compiler

Compiled 882 to 799 computations (9.4% saved)

simplify236.0ms (3%)

Algorithm

1×	egg-herbie

Rules

506×	`distribute-rgt-out_binary64`
434×	`log-prod_binary64`
420×	`times-frac_binary64`
270×	`distribute-lft-out_binary64`
263×	`distribute-rgt-in_binary64`
256×	`distribute-lft-in_binary64`
223×	`unswap-sqr_binary64`
190×	`associate-l_binary64`
165×	`exp-prod_binary64`
155×	`associate-*l/_binary64`
137×	`sqr-pow_binary64`
124×	`associate-/l*_binary64`
116×	`associate-*r/_binary64`
106×	`associate-r_binary64`
97×	`associate-+l+_binary64`
95×	`*-commutative_binary64`
93×	`associate-+r+_binary64`
92×	`log-pow_binary64`
90×	`associate-/r*_binary64`
82×	`pow-sqr_binary64`
70×	`log-div_binary64`
66×	`associate-/l/_binary64`
64×	`count-2_binary64`
62×	`cube-div_binary64`
58×	`distribute-rgt1-in_binary64`
52×	`cube-prod_binary64`
51×	`pow-plus_binary64`
40×	`+-commutative_binary64`
28×	`swap-sqr_binary64`
26×	`exp-to-pow_binary64`
25×	`unpow3_binary64`
23×	`exp-sum_binary64`
21×	`-rgt-identity_binary64` `-lft-identity_binary64`
18×	`cube-mult_binary64` `/-rgt-identity_binary64`
17×	`distribute-lft1-in_binary64`
16×	`exp-diff_binary64` `rem-sqrt-square_binary64`
12×	`cube-unmult_binary64`
11×	`associate-/r/_binary64`
10×	`distribute-rgt-out--_binary64`
8×	`log-rec_binary64` `remove-double-div_binary64`
7×	`exp-lft-sqr_binary64`
6×	`exp-sqrt_binary64`
5×	`pow-base-1_binary64` `prod-exp_binary64`
4×	`associate-+l-_binary64`
3×	`cancel-sign-sub-inv_binary64` `distribute-lft-neg-in_binary64` `distribute-lft-out--_binary64`
2×	`rem-log-exp_binary64` `distribute-rgt-neg-in_binary64` `associate-+r-_binary64`
1×	`unpow1/3_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-exp-log_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-square-sqrt_binary64` `neg-mul-1_binary64` `*-inverses_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` `unpow2_binary64` `unpow1/2_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `div-exp_binary64` `rec-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `div-sub_binary64` `neg-sub0_binary64` `unsub-neg_binary64` `sub-neg_binary64` `mul-1-neg_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` `lft-mult-inverse_binary64` `rgt-mult-inverse_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-neg-in_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64`

Counts

78 → 34

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	53	850
1	89	810
2	229	810
3	354	810
4	827	806
5	2776	806
6	4388	806

prune70.0ms (0.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	29	5	34
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	32	11	43

Error

0.1b

Counts

43 → 11

Compiler

Compiled 948 to 816 computations (13.9% saved)

regimes672.0ms (8.5%)

Accuracy

Total 0.8b remaining (95.8%)

Threshold costs 0.8b (95.8%)

Compiler

Compiled 7322 to 5686 computations (22.3% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`unpow1_binary64` `1-exp_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `unsub-neg_binary64` `sub-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `cancel-sign-sub-inv_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64` `+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	47
1	26	47

Proof

(=> (pow f64 (* f64 (sqrt f64 (cbrt f64 (fabs f64 (* f64 h0 (sqrt f64 2))))) (* f64 (sqrt f64 (fabs f64 (* f64 h0 (sqrt f64 2)))) (fabs f64 (cbrt f64 (fabs f64 (* f64 (* f64 h0 (sqrt f64 (sqrt f64 2))) (sqrt f64 (sqrt f64 2)))))))) 1))
unpow1_binary64 =>
(* f64 (sqrt f64 (cbrt f64 (fabs f64 (* f64 h0 (sqrt f64 2))))) (* f64 (sqrt f64 (fabs f64 (* f64 h0 (sqrt f64 2)))) (fabs f64 (cbrt f64 (fabs f64 (=> (* f64 (* f64 h0 (sqrt f64 (sqrt f64 2))) (sqrt f64 (sqrt f64 2)))))))))
*-commutative_binary64 =>
(* f64 (sqrt f64 (cbrt f64 (fabs f64 (* f64 h0 (sqrt f64 2))))) (* f64 (sqrt f64 (fabs f64 (* f64 h0 (sqrt f64 2)))) (fabs f64 (cbrt f64 (fabs f64 (* f64 (sqrt f64 (sqrt f64 2)) (* f64 h0 (sqrt f64 (sqrt f64 2)))))))))

end0.0ms (0%)

sample2.4s (30.6%)

Algorithm

1×

intervals

Results

354.0ms	8000×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 1857 to 1447 computations (22.1% saved)

Details

analyze13.0ms (0.2%)

sample221.0ms (2.8%)

simplify288.0ms (3.6%)

prune8.0ms (0.1%)

localize5.0ms (0.1%)

rewrite32.0ms (0.4%)

series51.0ms (0.6%)

simplify436.0ms (5.5%)

prune35.0ms (0.4%)

localize11.0ms (0.1%)

rewrite139.0ms (1.8%)

series175.0ms (2.2%)

simplify558.0ms (7%)

prune142.0ms (1.8%)

localize14.0ms (0.2%)

rewrite122.0ms (1.5%)

series443.0ms (5.6%)

simplify945.0ms (11.9%)

prune276.0ms (3.5%)

localize12.0ms (0.2%)

rewrite160.0ms (2%)

series430.0ms (5.4%)

simplify236.0ms (3%)

prune70.0ms (0.9%)

regimes672.0ms (8.5%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.4s (30.6%)

Profiling