Details

analyze95.0ms (3.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	1.6%	48.5%	9
50.4%	1.2%	48.5%	10
50.4%	1.2%	48.5%	11
50.4%	1.1%	48.6%	12
50.4%	1%	48.6%	13
50.5%	0.9%	48.6%	14

Compiler

Compiled 15 to 8 computations (46.7% saved)

sample59.0ms (1.9%)

Algorithm

1×

intervals

Results

30.0ms	118×	body	1024	valid
14.0ms	71×	body	512	valid
4.0ms	11×	body	2048	valid
2.0ms	30×	body	256	valid
1.0ms	26×	body	128	valid

Compiler

Compiled 30 to 16 computations (46.7% saved)

simplify82.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

464×	`times-frac_binary64`
407×	`neg-mul-1_binary64`
388×	`neg-sub0_binary64` `associate-/r/_binary64`
311×	`associate-/l/_binary64`
286×	`unswap-sqr_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	20	22
2	34	22
3	57	22
4	116	22
5	263	22
6	561	22
7	1419	22
8	3334	22
9	4405	22
10	4797	22

prune2.0ms (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

57.6b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	57.6b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 28 to 14 computations (50% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.7b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
6.0b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite53.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

44×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64` `times-frac_binary64`
16×	`add-cube-cbrt_binary64`
7×	`sinh-undef_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `cosh-undef_binary64` `distribute-lft-out_binary64`
6×	`associate-/l*_binary64`

Counts

2 → 76

Calls

2 calls:

11.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
5.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Compiler

Compiled 1465 to 231 computations (84.2% saved)

series40.0ms (1.3%)

Error

0.7b

Counts

2 → 12

Calls

2 calls:

14.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
9.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Compiler

Compiled 401 to 259 computations (35.4% saved)

simplify130.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

756×	`div-sub_binary64`
320×	`cancel-sign-sub-inv_binary64`
201×	`unswap-sqr_binary64`
195×	`exp-prod_binary64`
186×	`cube-prod_binary64`

Counts

88 → 48

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	148	2388
1	346	2245
2	826	2236
3	2336	2236
4	3876	2223
5	5288	2223

prune28.0ms (0.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	3	49

Error

0.2b

Counts

49 → 3

Alt Table

Status	Error	Program
	1.9b	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 x 5) 2/15))
	57.1b	(-.f64 (/.f64 (exp.f64 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) 1)))
▶	0.8b	(/.f64 (sinh.f64 x) (cosh.f64 x))

Compiler

Compiled 734 to 286 computations (61% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.7b	(/.f64 (sinh.f64 x) (cosh.f64 x))

rewrite22.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

9×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `times-frac_binary64` `*-un-lft-identity_binary64`
3×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64` `associate-/r_binary64`
1×	`pow1_binary64` `div-exp_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64` `sinh-def_binary64` `associate-/l/_binary64` `cosh-def_binary64` `associate-/r/_binary64`

Counts

1 → 29

Calls

1 calls:

3.0ms

(/.f64 (sinh.f64 x) (cosh.f64 x))

Compiler

Compiled 345 to 97 computations (71.9% saved)

series23.0ms (0.7%)

Error

0.2b

Counts

1 → 6

Calls

1 calls:

19.0ms

(/.f64 (sinh.f64 x) (cosh.f64 x))

Compiler

Compiled 173 to 116 computations (32.9% saved)

simplify82.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

687×	`associate-/l/_binary64`
536×	`times-frac_binary64`
430×	`associate-/l*_binary64`
405×	`associate-*l/_binary64`
354×	`associate-/r/_binary64`

Counts

35 → 12

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	570
1	166	536
2	415	536
3	1142	490
4	4115	490
5	4692	490
6	4904	490

prune11.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	12	0	12
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	12	3	15

Error

0.2b

Counts

15 → 3

Alt Table

Status	Error	Program
▶	1.9b	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 x 5) 2/15))
	57.1b	(-.f64 (/.f64 (exp.f64 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) 1)))
✓	0.8b	(/.f64 (sinh.f64 x) (cosh.f64 x))

Compiler

Compiled 173 to 105 computations (39.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 x 5) 2/15))
0.1b	(*.f64 (pow.f64 x 5) 2/15)
0.1b	(*.f64 1/3 (pow.f64 x 3))

rewrite90.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

22×	`add-sqr-sqrt_binary64`
15×	`associate-r_binary64`
13×	`add-exp-log_binary64`
10×	`add-cube-cbrt_binary64` `-un-lft-identity_binary64` `associate-l*_binary64`
8×	`add-log-exp_binary64` `unpow-prod-down_binary64`

Counts

3 → 71

Calls

3 calls:

8.0ms	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 x 5) 2/15))
6.0ms	(*.f64 1/3 (pow.f64 x 3))
6.0ms	(*.f64 (pow.f64 x 5) 2/15)

Compiler

Compiled 1295 to 1023 computations (21% saved)

series35.0ms (1.1%)

Error

0.2b

Counts

3 → 11

Calls

3 calls:

11.0ms	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 x 5) 2/15))
10.0ms	(*.f64 1/3 (pow.f64 x 3))
10.0ms	(*.f64 (pow.f64 x 5) 2/15)

Compiler

Compiled 295 to 231 computations (21.7% saved)

simplify113.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

478×	`unswap-sqr_binary64`
475×	`log-prod_binary64`
401×	`exp-prod_binary64`
337×	`cancel-sign-sub-inv_binary64`
314×	`*-commutative_binary64`

Counts

82 → 55

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	133	1113
1	288	1034
2	848	997
3	2055	997
4	3911	991
5	4898	991
6	4947	991

prune45.0ms (1.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	55	3	58

Error

0.2b

Counts

58 → 3

Alt Table

Status	Error	Program
	57.1b	(-.f64 (/.f64 (exp.f64 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) 1)))
✓	0.8b	(/.f64 (sinh.f64 x) (cosh.f64 x))
▶	1.9b	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 5) (.f64 2/15 (pow.f64 (cbrt.f64 x) 5))))

Compiler

Compiled 827 to 629 computations (23.9% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.7b	(pow.f64 (cbrt.f64 x) 5)
0.7b	(cbrt.f64 x)
0.7b	(cbrt.f64 x)
0.7b	(cbrt.f64 x)

rewrite69.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

12×	`cbrt-prod_binary64`
10×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
6×	`unpow-prod-down_binary64`
5×	`pow1_binary64` `add-exp-log_binary64`
4×	`pow1/3_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64`

Counts

4 → 54

Calls

4 calls:

2.0ms	(pow.f64 (cbrt.f64 x) 5)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

Compiler

Compiled 1391 to 817 computations (41.3% saved)

series91.0ms (2.9%)

Error

0.2b

Counts

4 → 12

Calls

4 calls:

29.0ms	(pow.f64 (cbrt.f64 x) 5)
18.0ms	(cbrt.f64 x)
17.0ms	(cbrt.f64 x)
16.0ms	(cbrt.f64 x)

Compiler

Compiled 827 to 625 computations (24.4% saved)

simplify77.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

763×	`associate-l_binary64`
657×	`distribute-rgt-in_binary64`
551×	`log-prod_binary64`
524×	`associate-r_binary64`
358×	`exp-prod_binary64`

Counts

66 → 43

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	57	497
1	113	476
2	266	470
3	652	470
4	2301	442
5	4274	428
6	4981	428

prune31.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	43	3	46

Error

0.2b

Counts

46 → 3

Alt Table

Status	Error	Program
	34.6b	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 5) (.f64 2/15 (exp.f64 (*.f64 5/3 (log.f64 x))))))
	57.1b	(-.f64 (/.f64 (exp.f64 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) 1)))
	0.8b	(/.f64 (sinh.f64 x) (cosh.f64 x))

Compiler

Compiled 640 to 425 computations (33.6% saved)

regimes73.0ms (2.4%)

Accuracy

Total -0.5b remaining (-4189.9%)

Threshold costs -0.5b (-4189.9%)

Compiler

Compiled 1002 to 728 computations (27.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	3	3

end1.0ms (0%)

Compiler: Compiled 3 to 2 computations (33.3% saved)

sample1.8s (58.4%)

Algorithm

1×

intervals

Results

1.0s	3884×	body	1024	valid
265.0ms	1967×	body	512	valid
117.0ms	419×	body	2048	valid
80.0ms	971×	body	256	valid
31.0ms	759×	body	128	valid
0.0ms	1×	body	128	overflowed

Compiler

Compiled 68 to 46 computations (32.4% saved)

Details

analyze95.0ms (3.1%)

sample59.0ms (1.9%)

simplify82.0ms (2.7%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite53.0ms (1.7%)

series40.0ms (1.3%)

simplify130.0ms (4.2%)

prune28.0ms (0.9%)

localize4.0ms (0.1%)

rewrite22.0ms (0.7%)

series23.0ms (0.7%)

simplify82.0ms (2.7%)

prune11.0ms (0.4%)

localize8.0ms (0.2%)

rewrite90.0ms (2.9%)

series35.0ms (1.1%)

simplify113.0ms (3.6%)

prune45.0ms (1.5%)

localize13.0ms (0.4%)

rewrite69.0ms (2.2%)

series91.0ms (2.9%)

simplify77.0ms (2.5%)

prune31.0ms (1%)

regimes73.0ms (2.4%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.8s (58.4%)

Profiling