Details

analyze93.0ms (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)

sample55.0ms (1.7%)

Algorithm

1×

intervals

Results

31.0ms	122×	body	1024	valid
8.0ms	65×	body	512	valid
4.0ms	13×	body	2048	valid
3.0ms	33×	body	256	valid
1.0ms	23×	body	128	valid

Compiler

Compiled 30 to 16 computations (46.7% saved)

simplify74.0ms (2.2%)

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

57.7b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	57.7b	(/.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)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
0.5b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
5.9b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite64.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

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:

12.0ms	(/.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)

series50.0ms (1.5%)

Error

0.4b

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))))
9.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
8.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Compiler

Compiled 601 to 382 computations (36.4% saved)

simplify140.0ms (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	2634	2484
4	4287	2484
5	5538	2484

prune31.0ms (0.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	3	52

Error

0.2b

Counts

52 → 3

Alt Table

Status	Error	Program
	0.7b	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 x 5) 2/15))
▶	0.5b	(/.f64 (sinh.f64 x) (cosh.f64 x))
	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)))

Compiler

Compiled 726 to 290 computations (60.1% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sinh.f64 x)
0.5b	(/.f64 (sinh.f64 x) (cosh.f64 x))

rewrite34.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

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

Counts

2 → 37

Calls

2 calls:

4.0ms	(/.f64 (sinh.f64 x) (cosh.f64 x))
1.0ms	(sinh.f64 x)

Compiler

Compiled 420 to 117 computations (72.1% saved)

series45.0ms (1.4%)

Error

0.2b

Counts

2 → 12

Calls

2 calls:

25.0ms	(/.f64 (sinh.f64 x) (cosh.f64 x))
11.0ms	(sinh.f64 x)

Compiler

Compiled 354 to 241 computations (31.9% saved)

simplify90.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

687×	`associate-/l/_binary64`
536×	`times-frac_binary64`
430×	`associate-/l*_binary64`
354×	`associate-/r/_binary64`
248×	`cancel-sign-sub-inv_binary64`

Counts

49 → 19

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	98	714
1	194	673
2	494	673
3	1285	627
4	4051	615
5	4735	615
6	4874	615

prune18.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	18	1	19
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	19	3	22

Error

0.2b

Counts

22 → 3

Alt Table

Status	Error	Program
	39.6b	(cbrt.f64 (pow.f64 (/.f64 (sinh.f64 x) (cosh.f64 x)) 3))
▶	0.7b	(+.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)))

Compiler

Compiled 259 to 162 computations (37.5% 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))

rewrite91.0ms (2.7%)

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:

7.0ms	(*.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

0.2b

Counts

3 → 11

Calls

3 calls:

13.0ms	(+.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 (3.4%)

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	2058	997
4	3917	991
5	4904	991
6	4954	991

prune45.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	54	4	58

Error

0.2b

Counts

58 → 4

Alt Table

Status	Error	Program
	39.6b	(cbrt.f64 (pow.f64 (/.f64 (sinh.f64 x) (cosh.f64 x)) 3))
▶	36.3b	(exp.f64 (log.f64 (+.f64 (.f64 2/15 (pow.f64 x 5)) (-.f64 x (.f64 1/3 (pow.f64 x 3))))))
✓	0.7b	(+.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)))

Compiler

Compiled 839 to 644 computations (23.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 2/15 (pow.f64 x 5)) (-.f64 x (.f64 1/3 (pow.f64 x 3))))
0.1b	(*.f64 2/15 (pow.f64 x 5))
0.1b	(*.f64 1/3 (pow.f64 x 3))
2.7b	(exp.f64 (log.f64 (+.f64 (.f64 2/15 (pow.f64 x 5)) (-.f64 x (.f64 1/3 (pow.f64 x 3))))))

rewrite112.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

25×	`add-sqr-sqrt_binary64`
19×	`associate-r_binary64`
14×	`add-exp-log_binary64`
13×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
9×	`add-log-exp_binary64`

Counts

4 → 88

Calls

4 calls:

10.0ms	(+.f64 (.f64 2/15 (pow.f64 x 5)) (-.f64 x (.f64 1/3 (pow.f64 x 3))))
8.0ms	(*.f64 1/3 (pow.f64 x 3))
8.0ms	(exp.f64 (log.f64 (+.f64 (.f64 2/15 (pow.f64 x 5)) (-.f64 x (.f64 1/3 (pow.f64 x 3))))))
6.0ms	(*.f64 2/15 (pow.f64 x 5))

Compiler

Compiled 1921 to 1556 computations (19% saved)

series86.0ms (2.6%)

Error

0.2b

Counts

4 → 20

Calls

4 calls:

31.0ms	(+.f64 (.f64 2/15 (pow.f64 x 5)) (-.f64 x (.f64 1/3 (pow.f64 x 3))))
29.0ms	(exp.f64 (log.f64 (+.f64 (.f64 2/15 (pow.f64 x 5)) (-.f64 x (.f64 1/3 (pow.f64 x 3))))))
10.0ms	(*.f64 2/15 (pow.f64 x 5))
9.0ms	(*.f64 1/3 (pow.f64 x 3))

Compiler

Compiled 609 to 482 computations (20.9% saved)

simplify111.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

465×	`exp-prod_binary64`
359×	`log-prod_binary64`
329×	`*-commutative_binary64`
316×	`cancel-sign-sub-inv_binary64`
275×	`distribute-rgt-in_binary64`

Counts

108 → 79

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	182	1807
1	364	1585
2	938	1551
3	2592	1515
4	4402	1506
5	4900	1506

prune49.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	79	4	83

Error

0.2b

Counts

83 → 4

Alt Table

Status	Error	Program
	39.6b	(cbrt.f64 (pow.f64 (/.f64 (sinh.f64 x) (cosh.f64 x)) 3))
	36.6b	(pow.f64 E.f64 (log.f64 (+.f64 (.f64 2/15 (pow.f64 x 5)) (-.f64 x (.f64 1/3 (pow.f64 x 3))))))
	0.7b	(+.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)))

Compiler

Compiled 1128 to 902 computations (20% saved)

regimes122.0ms (3.7%)

Accuracy

Total -0.5b remaining (-3582.6%)

Threshold costs -0.5b (-3582.6%)

Compiler

Compiled 1392 to 990 computations (28.9% saved)

simplify2.0ms (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 (55.1%)

Algorithm

1×

intervals

Results

1.0s	3918×	body	1024	valid
253.0ms	1907×	body	512	valid
117.0ms	424×	body	2048	valid
79.0ms	992×	body	256	valid
34.0ms	759×	body	128	valid
0.0ms	1×	body	128	overflowed

Compiler

Compiled 78 to 56 computations (28.2% saved)

Details

analyze93.0ms (2.8%)

sample55.0ms (1.7%)

simplify74.0ms (2.2%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite64.0ms (1.9%)

series50.0ms (1.5%)

simplify140.0ms (4.2%)

prune31.0ms (0.9%)

localize4.0ms (0.1%)

rewrite34.0ms (1%)

series45.0ms (1.4%)

simplify90.0ms (2.7%)

prune18.0ms (0.6%)

localize8.0ms (0.2%)

rewrite91.0ms (2.7%)

series34.0ms (1%)

simplify113.0ms (3.4%)

prune45.0ms (1.4%)

localize11.0ms (0.3%)

rewrite112.0ms (3.4%)

series86.0ms (2.6%)

simplify111.0ms (3.3%)

prune49.0ms (1.5%)

regimes122.0ms (3.7%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample1.8s (55.1%)

Profiling