Details

analyze96.0ms (2.8%)

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 (1.7%)

Algorithm

1×

intervals

Results

35.0ms	117×	body	1024	valid
9.0ms	73×	body	512	valid
3.0ms	36×	body	256	valid
2.0ms	9×	body	2048	valid
1.0ms	21×	body	128	valid

Compiler

Compiled 30 to 16 computations (46.7% saved)

simplify72.0ms (2.1%)

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

57.8b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	57.8b	(/.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 3 expressions with local error:

0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
0.3b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
5.3b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite62.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

47×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
8×	`cosh-undef_binary64` `distribute-lft-out_binary64`

Counts

3 → 89

Calls

3 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)))
4.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Compiler

Compiled 1710 to 265 computations (84.5% saved)

series48.0ms (1.4%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

15.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
10.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
10.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Compiler

Compiled 601 to 382 computations (36.4% saved)

simplify141.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

423×	`prod-exp_binary64`
361×	`cancel-sign-sub-inv_binary64`
247×	`unswap-sqr_binary64`
219×	`div-sub_binary64`
217×	`associate-l_binary64`

Counts

107 → 51

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	166	2671
1	391	2495
2	930	2484
3	2629	2484
4	4279	2484
5	5528	2484

prune32.0ms (1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	4	52

Error

Counts

52 → 4

Alt Table

Status	Error	Program
	1.2b	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 x 5) 2/15))
	57.6b	(-.f64 (/.f64 (exp.f64 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) 1)))
	57.9b	(*.f64 (+.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 (neg.f64 x)))) (/.f64 (-.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 (neg.f64 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
▶	0.3b	(/.f64 (sinh.f64 x) (cosh.f64 x))

Compiler

Compiled 776 to 312 computations (59.8% saved)

localize4.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(cosh.f64 x)
0.0b	(sinh.f64 x)
0.3b	(/.f64 (sinh.f64 x) (cosh.f64 x))

rewrite51.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

11×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
9×	`times-frac_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1_binary64` `add-log-exp_binary64` `associate-/l_binary64` `associate-/r_binary64`
2×	`sinh-def_binary64` `cosh-def_binary64`

Counts

3 → 45

Calls

3 calls:

3.0ms	(/.f64 (sinh.f64 x) (cosh.f64 x))
1.0ms	(cosh.f64 x)
1.0ms	(sinh.f64 x)

Compiler

Compiled 495 to 137 computations (72.3% saved)

series56.0ms (1.7%)

Error

Counts

3 → 18

Calls

3 calls:

21.0ms	(/.f64 (sinh.f64 x) (cosh.f64 x))
11.0ms	(sinh.f64 x)
10.0ms	(cosh.f64 x)

Compiler

Compiled 535 to 374 computations (30.1% saved)

simplify82.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

688×	`associate-/l/_binary64`
536×	`times-frac_binary64`
355×	`associate-/r/_binary64`
268×	`unswap-sqr_binary64`
185×	`sub-neg_binary64`

Counts

63 → 26

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	116	854
1	238	806
2	592	806
3	1553	752
4	4170	752
5	4881	752

prune23.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	26	4	30

Error

Counts

30 → 4

Alt Table

Status	Error	Program
▶	1.2b	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 x 5) 2/15))
	57.6b	(-.f64 (/.f64 (exp.f64 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) 1)))
	57.9b	(*.f64 (+.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 (neg.f64 x)))) (/.f64 (-.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 (neg.f64 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
✓	0.3b	(/.f64 (sinh.f64 x) (cosh.f64 x))

Compiler

Compiled 375 to 215 computations (42.7% 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))

rewrite88.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

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:

6.0ms	(*.f64 1/3 (pow.f64 x 3))
6.0ms	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 x 5) 2/15))
5.0ms	(*.f64 (pow.f64 x 5) 2/15)

Compiler

Compiled 1295 to 1023 computations (21% saved)

series34.0ms (1%)

Error

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))
9.0ms	(*.f64 (pow.f64 x 5) 2/15)
8.0ms	(*.f64 1/3 (pow.f64 x 3))

Compiler

Compiled 295 to 231 computations (21.7% saved)

simplify113.0ms (3.3%)

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

prune42.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	55	4	59

Error

Counts

59 → 4

Alt Table

Status	Error	Program
✓	1.2b	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 x 5) 2/15))
▶	57.6b	(-.f64 (/.f64 (exp.f64 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) 1)))
	57.9b	(*.f64 (+.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 (neg.f64 x)))) (/.f64 (-.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 (neg.f64 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
✓	0.3b	(/.f64 (sinh.f64 x) (cosh.f64 x))

Compiler

Compiled 845 to 630 computations (25.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (exp.f64 x) 2) 1)
0.0b	(/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) 1))
0.0b	(pow.f64 (exp.f64 x) 2)
5.3b	(-.f64 (/.f64 (exp.f64 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) 1)))

rewrite131.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

65×	`*-un-lft-identity_binary64`
41×	`add-sqr-sqrt_binary64`
39×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
18×	`cancel-sign-sub-inv_binary64`

Counts

4 → 112

Calls

4 calls:

33.0ms	(-.f64 (/.f64 (exp.f64 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) 1)))
7.0ms	(/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) 1))
5.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) 1)
3.0ms	(pow.f64 (exp.f64 x) 2)

Compiler

Compiled 2799 to 1422 computations (49.2% saved)

series66.0ms (1.9%)

Error

Counts

4 → 24

Calls

4 calls:

22.0ms	(-.f64 (/.f64 (exp.f64 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) 1)))
14.0ms	(/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) 1))
11.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) 1)
9.0ms	(pow.f64 (exp.f64 x) 2)

Compiler

Compiled 932 to 611 computations (34.4% saved)

simplify182.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

365×	`associate-r_binary64`
364×	`associate-l_binary64`
255×	`exp-prod_binary64`
218×	`times-frac_binary64`
174×	`sub-neg_binary64`

Counts

136 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	181	2674
1	442	2534
2	1065	2517
3	3804	2493
4	4321	2493
5	4947	2493
6	4863	2493

prune47.0ms (1.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	0	1
Picked	0	1	1
Done	1	1	2
Total	115	3	118

Error

Counts

118 → 3

Alt Table

Status	Error	Program
	1.2b	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 x 5) 2/15))
	57.6b	(-.f64 (/.f64 (exp.f64 x) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) 1)))
	57.8b	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) (exp.f64 (neg.f64 x))) (*.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 1 (pow.f64 (exp.f64 x) 2))))

Compiler

Compiled 1656 to 798 computations (51.8% saved)

regimes117.0ms (3.5%)

Accuracy

Total -0.7b remaining (-4717.2%)

Threshold costs -0.7b (-4717.2%)

Compiler

Compiled 1421 to 883 computations (37.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	3	3

end0.0ms (0%)

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

sample1.8s (53.5%)

Algorithm

1×

intervals

Results

1.0s	3888×	body	1024	valid
268.0ms	1978×	body	512	valid
111.0ms	390×	body	2048	valid
76.0ms	959×	body	256	valid
31.0ms	785×	body	128	valid

Compiler

Compiled 75 to 49 computations (34.7% saved)

Details

analyze96.0ms (2.8%)

sample59.0ms (1.7%)

simplify72.0ms (2.1%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite62.0ms (1.8%)

series48.0ms (1.4%)

simplify141.0ms (4.2%)

prune32.0ms (1%)

localize4.0ms (0.1%)

rewrite51.0ms (1.5%)

series56.0ms (1.7%)

simplify82.0ms (2.4%)

prune23.0ms (0.7%)

localize8.0ms (0.2%)

rewrite88.0ms (2.6%)

series34.0ms (1%)

simplify113.0ms (3.3%)

prune42.0ms (1.3%)

localize10.0ms (0.3%)

rewrite131.0ms (3.9%)

series66.0ms (1.9%)

simplify182.0ms (5.4%)

prune47.0ms (1.4%)

regimes117.0ms (3.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.8s (53.5%)

Profiling