Details

analyze90.0ms (2.7%)

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)

sample65.0ms (1.9%)

Algorithm

1×

intervals

Results

39.0ms	139×	body	1024	valid
12.0ms	60×	body	512	valid
3.0ms	32×	body	256	valid
3.0ms	10×	body	2048	valid
1.0ms	15×	body	128	valid

Compiler

Compiled 30 to 16 computations (46.7% saved)

simplify67.0ms (2%)

Algorithm

1×	egg-herbie

Rules

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

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

58.6b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	58.6b	(/.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)

localize7.0ms (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))))
4.6b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite44.0ms (1.3%)

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×	`distribute-lft-out_binary64`

Counts

3 → 89

Calls

3 calls:

8.0ms	(/.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)

series37.0ms (1.1%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

12.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
7.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
6.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Compiler

Compiled 601 to 382 computations (36.4% saved)

simplify126.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

423×	`prod-exp_binary64`
377×	`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	165	2671
1	389	2495
2	930	2484
3	2633	2484
4	4318	2484
5	5566	2484

prune26.0ms (0.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	46	5	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	5	52

Error

0.2b

Counts

52 → 5

Alt Table

Status	Error	Program
	58.6b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 3))
	58.6b	(/.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (exp.f64 x) -2)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
	1.0b	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 x 5) 2/15))
▶	0.3b	(/.f64 (sinh.f64 x) (cosh.f64 x))
	58.6b	(/.f64 (-.f64 (.f64 (exp.f64 x) (exp.f64 x)) (.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x)))) (+.f64 (pow.f64 (exp.f64 x) -2) (+.f64 (pow.f64 (exp.f64 x) 2) 2)))

Compiler

Compiled 822 to 338 computations (58.9% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite19.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 37

Calls

2 calls:

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

Compiler

Compiled 420 to 117 computations (72.1% saved)

series29.0ms (0.9%)

Error

0.2b

Counts

2 → 12

Calls

2 calls:

15.0ms	(/.f64 (sinh.f64 x) (cosh.f64 x))
8.0ms	(sinh.f64 x)

Compiler

Compiled 354 to 241 computations (31.9% saved)

simplify97.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

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

Counts

49 → 19

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	97	714
1	192	673
2	494	673
3	1283	627
4	4076	615
5	4762	615
6	5000	615
7	4871	615

prune15.0ms (0.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	18	1	19
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	19	5	24

Error

0.2b

Counts

24 → 5

Alt Table

Status	Error	Program
	58.6b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 3))
	58.6b	(/.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (exp.f64 x) -2)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	1.0b	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 x 5) 2/15))
	42.2b	(cbrt.f64 (pow.f64 (/.f64 (sinh.f64 x) (cosh.f64 x)) 3))
	58.6b	(/.f64 (-.f64 (.f64 (exp.f64 x) (exp.f64 x)) (.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x)))) (+.f64 (pow.f64 (exp.f64 x) -2) (+.f64 (pow.f64 (exp.f64 x) 2) 2)))

Compiler

Compiled 355 to 210 computations (40.8% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite76.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

23×	`add-sqr-sqrt_binary64`
15×	`associate-r_binary64`
14×	`add-exp-log_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

4 → 83

Calls

4 calls:

5.0ms	(*.f64 1/3 (pow.f64 x 3))
4.0ms	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 x 5) 2/15))
4.0ms	(*.f64 (pow.f64 x 5) 2/15)
2.0ms	(-.f64 x (*.f64 1/3 (pow.f64 x 3)))

Compiler

Compiled 1554 to 1223 computations (21.3% saved)

series36.0ms (1.1%)

Error

0.2b

Counts

4 → 17

Calls

4 calls:

10.0ms	(-.f64 x (*.f64 1/3 (pow.f64 x 3)))
8.0ms	(*.f64 (pow.f64 x 5) 2/15)
7.0ms	(+.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))

Compiler

Compiled 429 to 337 computations (21.4% saved)

simplify95.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

486×	`cancel-sign-sub-inv_binary64`
483×	`unswap-sqr_binary64`
326×	`*-commutative_binary64`
282×	`exp-prod_binary64`
249×	`log-prod_binary64`

Counts

100 → 63

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	145	1335
1	317	1268
2	972	1228
3	2471	1228
4	4319	1219
5	4902	1219

prune36.0ms (1.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	62	6	68

Error

0.2b

Counts

68 → 6

Alt Table

Status	Error	Program
	58.6b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) 3))
	58.6b	(/.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (exp.f64 x) -2)) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	1.0b	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 x 5) 2/15))
▶	42.2b	(cbrt.f64 (pow.f64 (/.f64 (sinh.f64 x) (cosh.f64 x)) 3))
	60.7b	(+.f64 (.f64 (pow.f64 x 3) -1/3) (.f64 (pow.f64 x 5) 2/15))
	58.6b	(/.f64 (-.f64 (.f64 (exp.f64 x) (exp.f64 x)) (.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x)))) (+.f64 (pow.f64 (exp.f64 x) -2) (+.f64 (pow.f64 (exp.f64 x) 2) 2)))

Compiler

Compiled 1036 to 770 computations (25.7% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (/.f64 (sinh.f64 x) (cosh.f64 x)) 3)
0.0b	(sinh.f64 x)
0.3b	(/.f64 (sinh.f64 x) (cosh.f64 x))
41.9b	(cbrt.f64 (pow.f64 (/.f64 (sinh.f64 x) (cosh.f64 x)) 3))

rewrite67.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

45×	`times-frac_binary64`
42×	`*-un-lft-identity_binary64`
42×	`add-sqr-sqrt_binary64`
42×	`add-cube-cbrt_binary64`
34×	`cbrt-prod_binary64`

Counts

4 → 129

Calls

4 calls:

4.0ms	(cbrt.f64 (pow.f64 (/.f64 (sinh.f64 x) (cosh.f64 x)) 3))
4.0ms	(pow.f64 (/.f64 (sinh.f64 x) (cosh.f64 x)) 3)
3.0ms	(/.f64 (sinh.f64 x) (cosh.f64 x))
1.0ms	(sinh.f64 x)

Compiler

Compiled 1562 to 631 computations (59.6% saved)

series77.0ms (2.3%)

Error

0.2b

Counts

4 → 24

Calls

4 calls:

24.0ms	(pow.f64 (/.f64 (sinh.f64 x) (cosh.f64 x)) 3)
16.0ms	(/.f64 (sinh.f64 x) (cosh.f64 x))
15.0ms	(cbrt.f64 (pow.f64 (/.f64 (sinh.f64 x) (cosh.f64 x)) 3))
10.0ms	(sinh.f64 x)

Compiler

Compiled 820 to 583 computations (28.9% saved)

simplify116.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

911×	`times-frac_binary64`
388×	`associate-/l/_binary64`
345×	`log-div_binary64`
330×	`unswap-sqr_binary64`
124×	`sqr-pow_binary64`

Counts

153 → 103

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	193	2619
1	447	2410
2	1435	2394
3	4822	2394
4	5198	2394

prune31.0ms (0.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	103	6	109

Error

0.2b

Counts

109 → 6

Alt Table

Status	Error	Program
	58.6b	(/.f64 (-.f64 (.f64 (exp.f64 x) (exp.f64 x)) (.f64 (exp.f64 (neg.f64 x)) (exp.f64 (neg.f64 x)))) (+.f64 (pow.f64 (exp.f64 x) -2) (+.f64 (pow.f64 (exp.f64 x) 2) 2)))
	42.9b	(cbrt.f64 (+.f64 (-.f64 (pow.f64 x 3) (pow.f64 x 5)) (*.f64 (pow.f64 x 7) 11/15)))
	1.0b	(+.f64 (-.f64 x (.f64 1/3 (pow.f64 x 3))) (.f64 (pow.f64 x 5) 2/15))
	42.2b	(cbrt.f64 (pow.f64 (/.f64 (sinh.f64 x) (cosh.f64 x)) 3))
	30.4b	(.f64 (cbrt.f64 (.f64 (sinh.f64 x) (sinh.f64 x))) (/.f64 (cbrt.f64 (sinh.f64 x)) (cosh.f64 x)))
	42.1b	(cbrt.f64 (*.f64 (pow.f64 (/.f64 (sinh.f64 x) (cosh.f64 x)) 2) (/.f64 (sinh.f64 x) (cosh.f64 x))))

Compiler

Compiled 846 to 393 computations (53.5% saved)

regimes159.0ms (4.7%)

Accuracy

Total -1.2b remaining (-10116.3%)

Threshold costs -1.2b (-10116.3%)

Compiler

Compiled 2629 to 1830 computations (30.4% 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)

sample2.0s (60%)

Algorithm

1×

intervals

Results

1.1s	3888×	body	1024	valid
313.0ms	1981×	body	512	valid
121.0ms	392×	body	2048	valid
93.0ms	984×	body	256	valid
38.0ms	755×	body	128	valid
0.0ms	1×	body	128	overflowed

Compiler

Compiled 112 to 72 computations (35.7% saved)

Details

analyze90.0ms (2.7%)

sample65.0ms (1.9%)

simplify67.0ms (2%)

prune1.0ms (0%)

localize7.0ms (0.2%)

rewrite44.0ms (1.3%)

series37.0ms (1.1%)

simplify126.0ms (3.8%)

prune26.0ms (0.8%)

localize3.0ms (0.1%)

rewrite19.0ms (0.6%)

series29.0ms (0.9%)

simplify97.0ms (2.9%)

prune15.0ms (0.5%)

localize9.0ms (0.3%)

rewrite76.0ms (2.3%)

series36.0ms (1.1%)

simplify95.0ms (2.8%)

prune36.0ms (1.1%)

localize7.0ms (0.2%)

rewrite67.0ms (2%)

series77.0ms (2.3%)

simplify116.0ms (3.5%)

prune31.0ms (0.9%)

regimes159.0ms (4.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.0s (60%)

Profiling