Details

analyze467.0ms (11.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
12.5%	87.4%	0.1%	4
18.7%	81.1%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	78%	0.1%	7
27.3%	61.6%	11.1%	8
28.5%	60.5%	11.1%	9
32.6%	53.4%	14%	10
40.2%	38.1%	21.7%	11
41.8%	35.8%	22.4%	12
44.5%	29.2%	26.3%	13
47.1%	21.3%	31.6%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample90.0ms (2.3%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
10.0ms	217×	body	128	invalid

Compiler

Compiled 26 to 18 computations (30.8% saved)

simplify87.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1052×	`fma-def_binary64`
423×	`fabs-mul_binary64`
333×	`distribute-rgt-in_binary64`
319×	`div-sub_binary64`
307×	`*-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	19	12
2	45	12
3	105	12
4	219	12
5	360	12
6	617	12
7	1698	12
8	2037	12
9	2629	12
10	3437	12
11	3909	12
12	4557	12
13	5039	12

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

9.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	9.0b	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (cosh.f64 x) (/.f64 y x))
✓	8.5b	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

series95.0ms (2.4%)

Counts

2 → 60

Calls

2 calls:

63.0ms	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
31.0ms	(*.f64 (cosh.f64 x) (/.f64 y x))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
13×	`associate-r_binary64`
13×	`times-frac_binary64`

Counts

2 → 64

Calls

2 calls:

5.0ms	(*.f64 (cosh.f64 x) (/.f64 y x))
5.0ms	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

simplify92.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

860×	`times-frac_binary64`
530×	`fma-def_binary64`
444×	`associate-l_binary64`
362×	`associate-r_binary64`
348×	`associate-/r/_binary64`

Counts

124 → 120

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	172	2288
1	432	2019
2	1488	2017
3	4433	2011
4	4988	2011

prune82.0ms (2.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	110	10	120
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	110	11	121

Error

0.0b

Counts

121 → 11

Alt Table

Status	Error	Program
✓	9.0b	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
	9.1b	(/.f64 (.f64 (.f64 (cosh.f64 x) y) (/.f64 1 x)) z)
	10.1b	(/.f64 (.f64 (.f64 (cosh.f64 x) (/.f64 1 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))) (/.f64 y (cbrt.f64 x))) z)
	9.8b	(.f64 (/.f64 (cosh.f64 x) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (/.f64 y x) (cbrt.f64 z)))
	9.4b	(/.f64 (cosh.f64 x) (/.f64 z (/.f64 y x)))
▶	7.4b	(.f64 (cosh.f64 x) (/.f64 y (.f64 z x)))
	37.6b	(*.f64 (/.f64 (cosh.f64 x) (sqrt.f64 z)) (/.f64 (/.f64 y x) (sqrt.f64 z)))
	32.4b	(.f64 (sqrt.f64 (.f64 (/.f64 y (.f64 z x)) (cosh.f64 x))) (sqrt.f64 (.f64 (/.f64 y (*.f64 z x)) (cosh.f64 x))))
	33.9b	(.f64 (sqrt.f64 (/.f64 (.f64 (cosh.f64 x) (/.f64 y x)) z)) (sqrt.f64 (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)))
	8.3b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y (.f64 z x)) (cosh.f64 x))) (cbrt.f64 (.f64 (/.f64 y (.f64 z x)) (cosh.f64 x)))) (cbrt.f64 (.f64 (/.f64 y (.f64 z x)) (cosh.f64 x))))
	38.2b	(cbrt.f64 (pow.f64 (.f64 (/.f64 y (.f64 z x)) (cosh.f64 x)) 3))

Compiler

Compiled 2114 to 712 computations (66.3% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cosh.f64 x) (/.f64 y (.f64 z x)))
✓	6.9b	(/.f64 y (*.f64 z x))

series79.0ms (2%)

Counts

2 → 36

Calls

2 calls:

63.0ms	(.f64 (cosh.f64 x) (/.f64 y (.f64 z x)))
15.0ms	(/.f64 y (*.f64 z x))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`

Counts

2 → 54

Calls

2 calls:

8.0ms	(.f64 (cosh.f64 x) (/.f64 y (.f64 z x)))
3.0ms	(/.f64 y (*.f64 z x))

simplify71.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

807×	`times-frac_binary64`
523×	`associate-*r/_binary64`
521×	`associate-*l/_binary64`
483×	`associate-/l*_binary64`
396×	`associate-/r*_binary64`

Counts

90 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	130	1642
1	321	1429
2	1080	1427
3	4803	1427
4	5068	1427

prune59.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	84	5	89
Fresh	7	2	9
Picked	1	0	1
Done	1	0	1
Total	93	7	100

Error

Counts

100 → 7

Alt Table

Status	Error	Program
	7.9b	(.f64 (cosh.f64 x) (.f64 y (/.f64 1 (*.f64 z x))))
	9.1b	(/.f64 (.f64 (.f64 (cosh.f64 x) y) (/.f64 1 x)) z)
▶	7.1b	(*.f64 (cosh.f64 x) (/.f64 (/.f64 y z) x))
	36.0b	(.f64 (cosh.f64 x) (/.f64 (sqrt.f64 y) (/.f64 (.f64 z x) (sqrt.f64 y))))
	9.1b	(.f64 (.f64 (cosh.f64 x) (/.f64 1 z)) (/.f64 y x))
	7.6b	(.f64 (cosh.f64 x) (/.f64 1 (/.f64 (.f64 z x) y)))
	9.8b	(.f64 (/.f64 (cosh.f64 x) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (/.f64 y x) (cbrt.f64 z)))

Compiler

Compiled 1488 to 453 computations (69.6% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cosh.f64 x) (/.f64 (/.f64 y z) x))
✓	7.0b	(/.f64 (/.f64 y z) x)

series123.0ms (3.1%)

Counts

2 → 72

Calls

2 calls:

66.0ms	(/.f64 (/.f64 y z) x)
57.0ms	(*.f64 (cosh.f64 x) (/.f64 (/.f64 y z) x))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64`
89×	`add-sqr-sqrt_binary64`
80×	`*-un-lft-identity_binary64`
80×	`add-cube-cbrt_binary64`
43×	`associate-r_binary64`

Counts

2 → 141

Calls

2 calls:

12.0ms	(*.f64 (cosh.f64 x) (/.f64 (/.f64 y z) x))
4.0ms	(/.f64 (/.f64 y z) x)

simplify137.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

538×	`associate-/r*_binary64`
508×	`fma-def_binary64`
400×	`*-commutative_binary64`
368×	`associate-/r/_binary64`
181×	`associate-*r/_binary64`

Counts

213 → 231

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	264	3615
1	636	3384
2	2143	3382
3	3632	3382
4	4610	3382
5	5003	3382

prune95.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	231	0	231
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	231	7	238

Error

Counts

238 → 7

Alt Table

Status	Error	Program
	7.9b	(.f64 (cosh.f64 x) (.f64 y (/.f64 1 (*.f64 z x))))
	9.1b	(/.f64 (.f64 (.f64 (cosh.f64 x) y) (/.f64 1 x)) z)
✓	7.1b	(*.f64 (cosh.f64 x) (/.f64 (/.f64 y z) x))
	36.0b	(.f64 (cosh.f64 x) (/.f64 (sqrt.f64 y) (/.f64 (.f64 z x) (sqrt.f64 y))))
	9.1b	(.f64 (.f64 (cosh.f64 x) (/.f64 1 z)) (/.f64 y x))
▶	7.6b	(.f64 (cosh.f64 x) (/.f64 1 (/.f64 (.f64 z x) y)))
	9.8b	(.f64 (/.f64 (cosh.f64 x) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (/.f64 y x) (cbrt.f64 z)))

Compiler

Compiled 4220 to 1010 computations (76.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cosh.f64 x) (/.f64 1 (/.f64 (.f64 z x) y)))
✓	0.4b	(/.f64 1 (/.f64 (*.f64 z x) y))
✓	6.9b	(/.f64 (*.f64 z x) y)

series90.0ms (2.3%)

Counts

3 → 72

Calls

3 calls:

60.0ms	(.f64 (cosh.f64 x) (/.f64 1 (/.f64 (.f64 z x) y)))
16.0ms	(/.f64 1 (/.f64 (*.f64 z x) y))
13.0ms	(/.f64 (*.f64 z x) y)

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`times-frac_binary64`
61×	`add-exp-log_binary64`
43×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
36×	`add-cube-cbrt_binary64`

Counts

3 → 142

Calls

3 calls:

10.0ms	(.f64 (cosh.f64 x) (/.f64 1 (/.f64 (.f64 z x) y)))
6.0ms	(/.f64 1 (/.f64 (*.f64 z x) y))
3.0ms	(/.f64 (*.f64 z x) y)

simplify100.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

765×	`associate-/l*_binary64`
551×	`associate-/r/_binary64`
542×	`associate-/r*_binary64`
461×	`fma-def_binary64`
399×	`*-commutative_binary64`

Counts

214 → 211

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	179	3208
1	410	2792
2	1450	2444
3	4112	2444
4	5002	2444

prune106.0ms (2.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	210	1	211
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	211	7	218

Error

Counts

218 → 7

Alt Table

Status	Error	Program
✓	7.1b	(*.f64 (cosh.f64 x) (/.f64 (/.f64 y z) x))
	7.8b	(.f64 y (/.f64 (cosh.f64 x) (.f64 z x)))
	36.0b	(.f64 (cosh.f64 x) (/.f64 (sqrt.f64 y) (/.f64 (.f64 z x) (sqrt.f64 y))))
	9.1b	(.f64 (.f64 (cosh.f64 x) (/.f64 1 z)) (/.f64 y x))
	9.1b	(/.f64 (.f64 (.f64 (cosh.f64 x) y) (/.f64 1 x)) z)
✓	7.6b	(.f64 (cosh.f64 x) (/.f64 1 (/.f64 (.f64 z x) y)))
	9.8b	(.f64 (/.f64 (cosh.f64 x) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (/.f64 y x) (cbrt.f64 z)))

Compiler

Compiled 3600 to 1316 computations (63.4% saved)

regimes854.0ms (21.8%)

Accuracy

Total 0.6b remaining (95.7%)

Threshold costs 0.6b (95.7%)

Counts

76 → 3

Compiler

Compiled 6309 to 3669 computations (41.8% saved)

bsearch29.0ms (0.7%)

Steps

Iters	Range		Point
1	1.2916215955653242e-36	8.482946538406726e-36	3.1993470566798015e-36
7	-5.0729032752555953e-98	-2.6370424511333864e-99	-5.023849266504921e-98

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`if-if-or-not_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	38
1	23	38
2	23	38

end1.0ms (0%)

Compiler: Compiled 28 to 17 computations (39.3% saved)

sample1.1s (29.2%)

Algorithm

1×

intervals

Results

318.0ms	8000×	body	128	valid
289.0ms	7352×	body	128	invalid

Compiler

Compiled 137 to 88 computations (35.8% saved)

Details

analyze467.0ms (11.9%)

sample90.0ms (2.3%)

simplify87.0ms (2.2%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series95.0ms (2.4%)

rewrite13.0ms (0.3%)

simplify92.0ms (2.4%)

prune82.0ms (2.1%)

localize8.0ms (0.2%)

series79.0ms (2%)

rewrite13.0ms (0.3%)

simplify71.0ms (1.8%)

prune59.0ms (1.5%)

localize5.0ms (0.1%)

series123.0ms (3.1%)

rewrite29.0ms (0.7%)

simplify137.0ms (3.5%)

prune95.0ms (2.4%)

localize7.0ms (0.2%)

series90.0ms (2.3%)

rewrite28.0ms (0.7%)

simplify100.0ms (2.6%)

prune106.0ms (2.7%)

regimes854.0ms (21.8%)

bsearch29.0ms (0.7%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.1s (29.2%)

Profiling