Details

analyze430.0ms (12.5%)

Algorithm

1×	search
2×	egg-herbie

Rules

805×	`unsub-neg_binary64`
626×	`distribute-rgt-out--_binary64`
462×	`distribute-neg-in_binary64`
449×	`distribute-rgt-out_binary64`
439×	`sub-neg_binary64`
290×	`distribute-rgt-neg-in_binary64`
278×	`distribute-lft-neg-out_binary64`
270×	`+-commutative_binary64`
256×	`neg-sub0_binary64`
214×	`cancel-sign-sub-inv_binary64`
207×	`neg-mul-1_binary64`
206×	`associate-+l+_binary64`
197×	`distribute-lft-out_binary64`
166×	`distribute-neg-out_binary64`
154×	`distribute-lft-neg-in_binary64`
150×	`distribute-rgt1-in_binary64` `*-commutative_binary64`
136×	`associate-+r+_binary64`
134×	`associate--l+_binary64` `associate-+l-_binary64`
127×	`distribute-rgt-neg-out_binary64`
118×	`associate--r+_binary64`
107×	`remove-double-neg_binary64`
102×	`distribute-rgt-in_binary64`
83×	`associate-+r-_binary64`
79×	`associate-l_binary64`
69×	`distribute-lft-out--_binary64`
67×	`distribute-lft-in_binary64`
60×	`distribute-lft1-in_binary64`
52×	`associate--l-_binary64`
44×	`associate--r-_binary64`
42×	`associate-r_binary64`
31×	`*-rgt-identity_binary64`
26×	`sub0-neg_binary64`
23×	`*-lft-identity_binary64`
13×	`mul-1-neg_binary64`
10×	`+-rgt-identity_binary64`
9×	`log-prod_binary64`
6×	`mul0-rgt_binary64` `swap-sqr_binary64`
5×	`mul0-lft_binary64`
4×	`+-lft-identity_binary64` `cancel-sign-sub_binary64`
3×	`sqr-neg_binary64` `--rgt-identity_binary64`
1×	`1-exp_binary64` `+-inverses_binary64` `difference-of-sqr-1_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` `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` `sqr-abs_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `times-frac_binary64` `div-sub_binary64` `/-rgt-identity_binary64` `div0_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-squares_binary64` `unswap-sqr_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `count-2_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64` `associate-l/_binary64` `associate-*r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	17	14
2	21	14
3	36	14
4	57	14
5	94	14
6	185	14
7	360	14
8	1261	14
9	1616	14
10	2338	14
11	2722	14
12	2923	14
13	3093	14
14	3194	14
15	3511	14
16	3955	14
17	4851	14
18	4922	14
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
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample59.0ms (1.7%)

Algorithm

1×

intervals

Results

22.0ms	143×	body	2048	nan
11.0ms	256×	body	128	valid
8.0ms	66×	body	1024	nan
3.0ms	28×	body	512	nan
1.0ms	16×	body	256	nan
1.0ms	16×	body	128	nan

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify148.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

805×	`unsub-neg_binary64`
626×	`distribute-rgt-out--_binary64`
462×	`distribute-neg-in_binary64`
449×	`distribute-rgt-out_binary64`
439×	`sub-neg_binary64`
290×	`distribute-rgt-neg-in_binary64`
278×	`distribute-lft-neg-out_binary64`
270×	`+-commutative_binary64`
256×	`neg-sub0_binary64`
214×	`cancel-sign-sub-inv_binary64`
207×	`neg-mul-1_binary64`
206×	`associate-+l+_binary64`
197×	`distribute-lft-out_binary64`
166×	`distribute-neg-out_binary64`
154×	`distribute-lft-neg-in_binary64`
150×	`distribute-rgt1-in_binary64` `*-commutative_binary64`
136×	`associate-+r+_binary64`
134×	`associate--l+_binary64` `associate-+l-_binary64`
127×	`distribute-rgt-neg-out_binary64`
118×	`associate--r+_binary64`
107×	`remove-double-neg_binary64`
102×	`distribute-rgt-in_binary64`
83×	`associate-+r-_binary64`
79×	`associate-l_binary64`
69×	`distribute-lft-out--_binary64`
67×	`distribute-lft-in_binary64`
60×	`distribute-lft1-in_binary64`
52×	`associate--l-_binary64`
44×	`associate--r-_binary64`
42×	`associate-r_binary64`
31×	`*-rgt-identity_binary64`
26×	`sub0-neg_binary64`
23×	`*-lft-identity_binary64`
13×	`mul-1-neg_binary64`
10×	`+-rgt-identity_binary64`
9×	`log-prod_binary64`
6×	`mul0-rgt_binary64` `swap-sqr_binary64`
5×	`mul0-lft_binary64`
4×	`+-lft-identity_binary64` `cancel-sign-sub_binary64`
3×	`sqr-neg_binary64` `--rgt-identity_binary64`
1×	`1-exp_binary64` `+-inverses_binary64` `difference-of-sqr-1_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` `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` `sqr-abs_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `times-frac_binary64` `div-sub_binary64` `/-rgt-identity_binary64` `div0_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-squares_binary64` `unswap-sqr_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `count-2_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64` `associate-l/_binary64` `associate-*r/_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	17	14
2	21	14
3	36	14
4	57	14
5	94	14
6	185	14
7	360	14
8	1261	14
9	1616	14
10	2338	14
11	2722	14
12	2923	14
13	3093	14
14	3194	14
15	3511	14
16	3955	14
17	4851	14
18	4922	14

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

28.9b

Counts

1 → 1

Compiler

Compiled 9 to 7 computations (22.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
26.9b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite43.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

6×	`sqrt-prod_binary64` `*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64`
2×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64` `difference-of-squares_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3--_binary64` `flip--_binary64` `difference-of-sqr-1_binary64` `rem-sqrt-square_binary64` `sum-log_binary64` `flip3-+_binary64` `flip-+_binary64` `distribute-lft-out_binary64` `+-commutative_binary64`

Counts

2 → 30

Calls

2 calls:

9.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
5.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

Compiler

Compiled 471 to 288 computations (38.9% saved)

series30.0ms (0.9%)

Error

0.0b

Counts

2 → 12

Calls

2 calls:

12.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
9.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

Compiler

Compiled 311 to 264 computations (15.1% saved)

simplify83.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

427×	`neg-mul-1_binary64`
390×	`neg-sub0_binary64`
354×	`sub-neg_binary64`
278×	`associate-l_binary64`
271×	`distribute-rgt-in_binary64`
253×	`times-frac_binary64`
225×	`associate-+l+_binary64`
205×	`distribute-lft-in_binary64`
200×	`unsub-neg_binary64`
199×	`associate-r_binary64`
180×	`associate-+r+_binary64`
164×	`unswap-sqr_binary64`
150×	`distribute-neg-frac_binary64`
135×	`associate-+l-_binary64`
123×	`associate-/r*_binary64`
119×	`distribute-neg-in_binary64`
118×	`distribute-lft-neg-out_binary64`
109×	`distribute-rgt-neg-out_binary64`
105×	`cancel-sign-sub-inv_binary64`
84×	`+-commutative_binary64`
79×	`div-sub_binary64`
76×	`associate--l+_binary64`
70×	`associate--r+_binary64`
68×	`*-commutative_binary64`
65×	`sub0-neg_binary64`
64×	`associate-+r-_binary64`
61×	`cancel-sign-sub_binary64`
51×	`distribute-neg-out_binary64`
43×	`distribute-rgt-out_binary64`
38×	`sqr-pow_binary64`
36×	`associate-*r/_binary64`
35×	`associate-*l/_binary64`
32×	`cube-prod_binary64`
30×	`+-rgt-identity_binary64`
27×	`-rgt-identity_binary64` `-lft-identity_binary64`
22×	`distribute-rgt-neg-in_binary64` `associate-/l*_binary64`
21×	`pow-plus_binary64` `associate--l-_binary64`
20×	`exp-prod_binary64`
17×	`cube-unmult_binary64`
16×	`distribute-lft-neg-in_binary64`
14×	`sqr-neg_binary64` `associate-/l/_binary64`
13×	`distribute-rgt-out--_binary64`
12×	`exp-sum_binary64` `associate--r-_binary64`
11×	`unpow3_binary64` `distribute-rgt1-in_binary64`
10×	`log-prod_binary64` `remove-double-neg_binary64`
9×	`cube-neg_binary64`
8×	`exp-diff_binary64` `difference-of-sqr-1_binary64`
7×	`mul-1-neg_binary64`
5×	`rem-sqrt-square_binary64` `mul0-lft_binary64` `difference-of-sqr--1_binary64`
4×	`cube-mult_binary64` `--rgt-identity_binary64` `mul0-rgt_binary64`
3×	`pow-sqr_binary64` `difference-of-squares_binary64` `distribute-frac-neg_binary64` `distribute-lft1-in_binary64`
2×	`unpow2_binary64` `unpow1/2_binary64` `exp-neg_binary64` `+-inverses_binary64` `remove-double-div_binary64` `swap-sqr_binary64`
1×	`unpow1_binary64` `prod-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `cube-div_binary64` `rem-square-sqrt_binary64` `div0_binary64` `distribute-lft-out--_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-pow_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` `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` `/-rgt-identity_binary64` `+-lft-identity_binary64` `*-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `count-2_binary64` `associate-/r/_binary64`

Counts

42 → 31

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	580
1	187	546
2	428	543
3	1117	540
4	2999	540
5	4398	540
6	5081	540

prune28.0ms (0.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	29	2	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	2	32

Error

Counts

32 → 2

Compiler

Compiled 416 to 275 computations (33.9% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x))))
0.5b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))

rewrite61.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

14×	`add-sqr-sqrt_binary64`
12×	`sqrt-div_binary64` `sqrt-prod_binary64`
10×	`*-un-lft-identity_binary64`
7×	`flip3-+_binary64` `flip-+_binary64` `associate-l_binary64` `associate-r_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-exp-log_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64` `frac-times_binary64` `unswap-sqr_binary64`
3×	`pow-prod-down_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `associate-l/_binary64` `associate-r/_binary64` `distribute-lft-out_binary64`
1×	`prod-exp_binary64` `cbrt-unprod_binary64` `sqrt-unprod_binary64` `*-commutative_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

2 → 51

Calls

2 calls:

12.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))
2.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x))))

Compiler

Compiled 976 to 752 computations (23% saved)

series33.0ms (0.9%)

Error

Counts

2 → 12

Calls

2 calls:

11.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x))))
11.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 -1 x)))

Compiler

Compiled 297 to 254 computations (14.5% saved)

simplify66.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

716×	`distribute-rgt-in_binary64`
592×	`distribute-lft-in_binary64`
253×	`associate-l_binary64`
252×	`distribute-rgt-out_binary64`
233×	`cancel-sign-sub-inv_binary64`
201×	`unsub-neg_binary64`
194×	`associate-r_binary64`
187×	`sub-neg_binary64`
126×	`distribute-lft-neg-out_binary64`
121×	`distribute-rgt-neg-out_binary64`
111×	`distribute-neg-out_binary64`
93×	`distribute-rgt-out--_binary64`
85×	`distribute-rgt-neg-in_binary64`
80×	`*-commutative_binary64`
78×	`associate-+l+_binary64`
75×	`distribute-lft-out_binary64`
63×	`neg-sub0_binary64`
56×	`distribute-neg-in_binary64` `distribute-lft-neg-in_binary64`
52×	`distribute-neg-frac_binary64`
50×	`associate-+r+_binary64`
46×	`associate--r+_binary64`
43×	`sqr-pow_binary64`
42×	`associate-/r*_binary64`
41×	`neg-mul-1_binary64` `unswap-sqr_binary64`
40×	`associate--l+_binary64` `+-commutative_binary64`
36×	`associate-+l-_binary64`
34×	`associate-+r-_binary64`
31×	`times-frac_binary64`
24×	`distribute-rgt1-in_binary64`
21×	`*-rgt-identity_binary64`
20×	`exp-prod_binary64` `*-lft-identity_binary64`
18×	`cube-prod_binary64`
17×	`associate--l-_binary64`
16×	`distribute-lft-out--_binary64`
15×	`sub0-neg_binary64`
12×	`+-rgt-identity_binary64`
11×	`log-prod_binary64`
10×	`difference-of-squares_binary64` `associate-*r/_binary64`
8×	`associate--r-_binary64`
7×	`cube-unmult_binary64` `mul-1-neg_binary64` `cancel-sign-sub_binary64`
6×	`rem-sqrt-square_binary64` `remove-double-neg_binary64` `distribute-lft1-in_binary64`
5×	`unpow3_binary64` `exp-diff_binary64` `pow-sqr_binary64` `swap-sqr_binary64`
4×	`associate-*l/_binary64`
3×	`unpow1/2_binary64` `div-sub_binary64` `--rgt-identity_binary64` `difference-of-sqr-1_binary64`
2×	`exp-sum_binary64` `cube-mult_binary64` `cube-neg_binary64` `rem-square-sqrt_binary64` `+-inverses_binary64` `difference-of-sqr--1_binary64` `distribute-frac-neg_binary64` `associate-/l*_binary64`
1×	`unpow2_binary64` `pow-plus_binary64` `unpow1_binary64` `prod-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `sqr-neg_binary64` `remove-double-div_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` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-div_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_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` `count-2_binary64` `associate-/l/_binary64` `associate-/r/_binary64`

Counts

63 → 33

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	125	1185
1	293	1150
2	731	1135
3	1987	1132
4	4928	1132

prune29.0ms (0.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	33	2	35

Error

Counts

35 → 2

Compiler

Compiled 548 to 396 computations (27.7% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x))))
0.0b	(pow.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))) 3)
26.9b	(sqrt.f64 (+.f64 -1 (*.f64 x x)))
38.1b	(cbrt.f64 (pow.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))) 3))

rewrite86.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

21×	`*-un-lft-identity_binary64`
14×	`cbrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
8×	`unpow-prod-down_binary64` `cube-prod_binary64`
6×	`pow1_binary64` `add-log-exp_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-out_binary64`
4×	`flip3-+_binary64` `cube-div_binary64` `flip-+_binary64`
3×	`sqrt-prod_binary64` `pow-unpow_binary64`
2×	`cbrt-div_binary64` `unpow3_binary64` `cube-mult_binary64` `sqr-pow_binary64` `sqrt-div_binary64`
1×	`pow1/3_binary64` `rem-cbrt-cube_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `pow-pow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `rem-cube-cbrt_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

6.0ms	(cbrt.f64 (pow.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))) 3))
6.0ms	(pow.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))) 3)
5.0ms	(+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x))))
3.0ms	(sqrt.f64 (+.f64 -1 (*.f64 x x)))

Compiler

Compiled 1438 to 957 computations (33.4% saved)

series64.0ms (1.9%)

Error

Counts

4 → 24

Calls

4 calls:

13.0ms	(pow.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))) 3)
10.0ms	(+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x))))
10.0ms	(cbrt.f64 (pow.f64 (+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x)))) 3))
10.0ms	(sqrt.f64 (+.f64 -1 (*.f64 x x)))

Compiler

Compiled 724 to 643 computations (11.2% saved)

simplify118.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

349×	`exp-prod_binary64`
262×	`unswap-sqr_binary64`
261×	`distribute-rgt-in_binary64`
238×	`distribute-lft-in_binary64`
210×	`log-prod_binary64`
201×	`sub-neg_binary64`
197×	`*-commutative_binary64`
184×	`cancel-sign-sub-inv_binary64`
177×	`sqr-pow_binary64`
156×	`distribute-lft-neg-out_binary64`
154×	`distribute-rgt-neg-out_binary64`
135×	`cube-prod_binary64`
130×	`unsub-neg_binary64`
89×	`unpow3_binary64`
87×	`exp-sum_binary64`
84×	`swap-sqr_binary64`
61×	`neg-sub0_binary64` `distribute-neg-out_binary64`
56×	`distribute-neg-frac_binary64` `associate-l_binary64`
55×	`neg-mul-1_binary64`
52×	`associate-r_binary64` `associate-+l+_binary64`
49×	`times-frac_binary64`
45×	`associate--r+_binary64`
43×	`pow-sqr_binary64` `+-commutative_binary64`
41×	`associate-/r*_binary64`
40×	`log-pow_binary64` `distribute-neg-in_binary64`
38×	`associate-+l-_binary64`
36×	`pow-plus_binary64`
35×	`associate--l+_binary64`
31×	`associate-+r-_binary64`
28×	`distribute-rgt-out_binary64` `associate-+r+_binary64`
24×	`cube-mult_binary64` `sub0-neg_binary64` `distribute-rgt-neg-in_binary64`
20×	`distribute-lft-out_binary64`
16×	`cube-unmult_binary64` `distribute-lft-neg-in_binary64`
15×	`rem-sqrt-square_binary64` `associate-*r/_binary64`
13×	`*-lft-identity_binary64` `+-rgt-identity_binary64`
12×	`distribute-rgt-out--_binary64`
11×	`*-rgt-identity_binary64` `associate--l-_binary64`
8×	`rem-cbrt-cube_binary64` `difference-of-squares_binary64`
6×	`mul-1-neg_binary64` `--rgt-identity_binary64` `difference-of-sqr-1_binary64` `cancel-sign-sub_binary64` `associate--r-_binary64`
5×	`sqr-neg_binary64` `difference-of-sqr--1_binary64` `associate-*l/_binary64`
4×	`unpow2_binary64` `pow-base-1_binary64` `exp-diff_binary64` `+-inverses_binary64`
3×	`rem-square-sqrt_binary64` `distribute-rgt1-in_binary64` `count-2_binary64` `associate-/l/_binary64`
2×	`unpow1_binary64` `cube-neg_binary64` `/-rgt-identity_binary64` `remove-double-neg_binary64`
1×	`unpow1/2_binary64` `prod-exp_binary64` `1-exp_binary64` `rem-3cbrt-lft_binary64` `rem-cube-cbrt_binary64` `div-sub_binary64` `distribute-lft1-in_binary64` `distribute-lft-out--_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` `log-rec_binary64` `log-div_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-div_binary64` `rem-3cbrt-rft_binary64` `sqr-abs_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `distribute-frac-neg_binary64`

Counts

103 → 66

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	137	1980
1	314	1825
2	903	1647
3	2784	1647
4	4716	1644
5	4856	1644

prune37.0ms (1.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	66	2	68

Error

Counts

68 → 2

Compiler

Compiled 726 to 516 computations (28.9% saved)

regimes192.0ms (5.6%)

Accuracy

Total 0.0b remaining (17.4%)

Threshold costs 0.0b (17.4%)

Compiler

Compiled 1354 to 1123 computations (17.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
1×	`1-exp_binary64` `sub-neg_binary64` `*-commutative_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `unpow1_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_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	10	19
1	18	19
2	19	19
3	17	19

end1.0ms (0%)

Compiler: Compiled 12 to 10 computations (16.7% saved)

sample1.9s (55.3%)

Algorithm

1×

intervals

Results

664.0ms	4012×	body	2048	nan
341.0ms	8000×	body	128	valid
250.0ms	1978×	body	1024	nan
91.0ms	935×	body	512	nan
28.0ms	459×	body	256	nan
16.0ms	509×	body	128	nan
2.0ms	10×	body	4096	nan

Compiler

Compiled 49 to 45 computations (8.2% saved)

Details

analyze430.0ms (12.5%)

sample59.0ms (1.7%)

simplify148.0ms (4.3%)

prune1.0ms (0%)

localize7.0ms (0.2%)

rewrite43.0ms (1.3%)

series30.0ms (0.9%)

simplify83.0ms (2.4%)

prune28.0ms (0.8%)

localize9.0ms (0.3%)

rewrite61.0ms (1.8%)

series33.0ms (0.9%)

simplify66.0ms (1.9%)

prune29.0ms (0.8%)

localize9.0ms (0.3%)

rewrite86.0ms (2.5%)

series64.0ms (1.9%)

simplify118.0ms (3.4%)

prune37.0ms (1.1%)

regimes192.0ms (5.6%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.9s (55.3%)

Profiling