Details

analyze154.0ms (2%)

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
25%	74.9%	0.1%	4
37.4%	62.4%	0.1%	5
37.4%	62.4%	0.1%	6
56.2%	43.7%	0.1%	7
65.5%	34.3%	0.1%	8
65.5%	34.3%	0.1%	9
76.5%	23.4%	0.1%	10
81.9%	17.9%	0.1%	11
81.9%	17.9%	0.1%	12
87.8%	12.1%	0.1%	13
90.7%	9.2%	0.1%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample724.0ms (9.4%)

Infinites

64% of outputs are infinite.

Results

646.0ms

8256×

body

128

valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify86.0ms (1.1%)

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

10.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	10.6b	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.1b	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
✓	6.9b	(*.f64 (cosh.f64 x) (/.f64 y x))

series85.0ms (1.1%)

Counts

2 → 60

Calls

2 calls:

57.0ms	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
28.0ms	(*.f64 (cosh.f64 x) (/.f64 y x))

rewrite15.0ms (0.2%)

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:

7.0ms	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
5.0ms	(*.f64 (cosh.f64 x) (/.f64 y x))

simplify80.0ms (1%)

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 → 122

Iterations

Useful iterations: 3 (0.0ms)

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

prune102.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	114	8	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	8	123

Error

0.0b

Counts

123 → 8

Alt Table

Status	Error	Program
	15.8b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y (.f64 x z)) (cosh.f64 x))) (cbrt.f64 (.f64 (/.f64 y (.f64 x z)) (cosh.f64 x)))) (cbrt.f64 (.f64 (/.f64 y (.f64 x z)) (cosh.f64 x))))
	3.1b	(/.f64 (.f64 (.f64 (cosh.f64 x) y) (/.f64 1 x)) z)
	5.7b	(/.f64 (.f64 (.f64 (cosh.f64 x) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 y) x)) z)
	5.2b	(/.f64 (.f64 (.f64 (cosh.f64 x) (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (/.f64 (cbrt.f64 y) (cbrt.f64 x))) z)
	10.6b	(.f64 (.f64 (cosh.f64 x) (/.f64 y x)) (/.f64 1 z))
▶	3.1b	(/.f64 (/.f64 (*.f64 (cosh.f64 x) y) x) z)
	15.5b	(.f64 (cosh.f64 x) (/.f64 y (.f64 x z)))
	39.0b	(*.f64 (/.f64 (cosh.f64 x) (sqrt.f64 z)) (/.f64 (/.f64 y x) (sqrt.f64 z)))

Compiler

Compiled 2036 to 672 computations (67% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (*.f64 (cosh.f64 x) y) x)
✓	0.0b	(*.f64 (cosh.f64 x) y)
✓	3.1b	(/.f64 (/.f64 (*.f64 (cosh.f64 x) y) x) z)

series110.0ms (1.4%)

Counts

3 → 84

Calls

3 calls:

57.0ms	(/.f64 (/.f64 (*.f64 (cosh.f64 x) y) x) z)
32.0ms	(/.f64 (*.f64 (cosh.f64 x) y) x)
21.0ms	(*.f64 (cosh.f64 x) y)

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
25×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
19×	`add-cbrt-cube_binary64`

Counts

3 → 95

Calls

3 calls:

5.0ms	(/.f64 (/.f64 (*.f64 (cosh.f64 x) y) x) z)
5.0ms	(/.f64 (*.f64 (cosh.f64 x) y) x)
3.0ms	(*.f64 (cosh.f64 x) y)

simplify99.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

848×	`fma-def_binary64`
583×	`associate-/r*_binary64`
536×	`associate-l_binary64`
506×	`associate-*r/_binary64`
475×	`associate-/r/_binary64`

Counts

179 → 183

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	220	3252
1	531	2935
2	1703	2930
3	4933	2918
4	5486	2918

prune159.0ms (2.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	179	4	183
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	182	9	191

Error

Counts

191 → 9

Alt Table

Status	Error	Program
	3.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (cosh.f64 x) y) x)) (cbrt.f64 (/.f64 (.f64 (cosh.f64 x) y) x))) 1) (/.f64 (cbrt.f64 (/.f64 (*.f64 (cosh.f64 x) y) x)) z))
	10.6b	(.f64 (.f64 (cosh.f64 x) (/.f64 y x)) (/.f64 1 z))
✓	3.1b	(/.f64 (/.f64 (*.f64 (cosh.f64 x) y) x) z)
	12.4b	(.f64 (/.f64 (.f64 (cosh.f64 x) y) 1) (/.f64 (/.f64 1 x) z))
	15.8b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y (.f64 x z)) (cosh.f64 x))) (cbrt.f64 (.f64 (/.f64 y (.f64 x z)) (cosh.f64 x)))) (cbrt.f64 (.f64 (/.f64 y (.f64 x z)) (cosh.f64 x))))
	14.1b	(/.f64 (cbrt.f64 (.f64 (.f64 (/.f64 (.f64 (cosh.f64 x) y) x) (/.f64 (.f64 (cosh.f64 x) y) x)) (/.f64 (*.f64 (cosh.f64 x) y) x))) z)
▶	3.1b	(/.f64 (.f64 (.f64 (cosh.f64 x) y) (/.f64 1 x)) z)
	36.3b	(/.f64 (/.f64 (cosh.f64 x) (sqrt.f64 x)) (/.f64 z (/.f64 y (sqrt.f64 x))))
	15.5b	(.f64 (cosh.f64 x) (/.f64 y (.f64 x z)))

Compiler

Compiled 3075 to 950 computations (69.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (cosh.f64 x) y)
✓	0.1b	(.f64 (.f64 (cosh.f64 x) y) (/.f64 1 x))
✓	3.1b	(/.f64 (.f64 (.f64 (cosh.f64 x) y) (/.f64 1 x)) z)

series89.0ms (1.2%)

Counts

2 → 60

Calls

2 calls:

60.0ms	(/.f64 (.f64 (.f64 (cosh.f64 x) y) (/.f64 1 x)) z)
29.0ms	(.f64 (.f64 (cosh.f64 x) y) (/.f64 1 x))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`add-exp-log_binary64`
32×	`add-cbrt-cube_binary64`
24×	`prod-exp_binary64`
17×	`div-exp_binary64`
13×	`associate-r_binary64`

Counts

2 → 79

Calls

2 calls:

7.0ms	(.f64 (.f64 (cosh.f64 x) y) (/.f64 1 x))
7.0ms	(/.f64 (.f64 (.f64 (cosh.f64 x) y) (/.f64 1 x)) z)

simplify96.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

825×	`fma-def_binary64`
494×	`associate-/r/_binary64`
479×	`associate-/r*_binary64`
389×	`*-commutative_binary64`
178×	`associate-/l*_binary64`

Counts

139 → 139

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	177	2507
1	452	2148
2	1547	2148
3	3399	2141
4	4734	2139
5	4982	2139

prune162.0ms (2.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	181	9	190

Error

Counts

190 → 9

Alt Table

Status	Error	Program
▶	3.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (cosh.f64 x) y) x)) (cbrt.f64 (/.f64 (.f64 (cosh.f64 x) y) x))) 1) (/.f64 (cbrt.f64 (/.f64 (*.f64 (cosh.f64 x) y) x)) z))
	10.6b	(.f64 (.f64 (cosh.f64 x) (/.f64 y x)) (/.f64 1 z))
✓	3.1b	(/.f64 (/.f64 (*.f64 (cosh.f64 x) y) x) z)
	12.4b	(.f64 (/.f64 (.f64 (cosh.f64 x) y) 1) (/.f64 (/.f64 1 x) z))
	15.8b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y (.f64 x z)) (cosh.f64 x))) (cbrt.f64 (.f64 (/.f64 y (.f64 x z)) (cosh.f64 x)))) (cbrt.f64 (.f64 (/.f64 y (.f64 x z)) (cosh.f64 x))))
	14.1b	(/.f64 (cbrt.f64 (.f64 (.f64 (/.f64 (.f64 (cosh.f64 x) y) x) (/.f64 (.f64 (cosh.f64 x) y) x)) (/.f64 (*.f64 (cosh.f64 x) y) x))) z)
✓	3.1b	(/.f64 (.f64 (.f64 (cosh.f64 x) y) (/.f64 1 x)) z)
	36.3b	(/.f64 (/.f64 (cosh.f64 x) (sqrt.f64 x)) (/.f64 z (/.f64 y (sqrt.f64 x))))
	15.5b	(.f64 (cosh.f64 x) (/.f64 y (.f64 x z)))

Compiler

Compiled 3203 to 1381 computations (56.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (cbrt.f64 (/.f64 (*.f64 (cosh.f64 x) y) x)) z)
✓	0.2b	(.f64 (cbrt.f64 (/.f64 (.f64 (cosh.f64 x) y) x)) (cbrt.f64 (/.f64 (*.f64 (cosh.f64 x) y) x)))
✓	0.3b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (cosh.f64 x) y) x)) (cbrt.f64 (/.f64 (.f64 (cosh.f64 x) y) x))) 1) (/.f64 (cbrt.f64 (/.f64 (*.f64 (cosh.f64 x) y) x)) z))
✓	8.1b	(cbrt.f64 (/.f64 (*.f64 (cosh.f64 x) y) x))

series4.1s (53.2%)

Counts

4 → 120

Calls

4 calls:

1.6s	(.f64 (cbrt.f64 (/.f64 (.f64 (cosh.f64 x) y) x)) (cbrt.f64 (/.f64 (*.f64 (cosh.f64 x) y) x)))
1.5s	(/.f64 (cbrt.f64 (/.f64 (*.f64 (cosh.f64 x) y) x)) z)
863.0ms	(cbrt.f64 (/.f64 (*.f64 (cosh.f64 x) y) x))
84.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (cosh.f64 x) y) x)) (cbrt.f64 (/.f64 (.f64 (cosh.f64 x) y) x))) 1) (/.f64 (cbrt.f64 (/.f64 (*.f64 (cosh.f64 x) y) x)) z))

rewrite53.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

111×	`times-frac_binary64`
92×	`add-sqr-sqrt_binary64`
91×	`cbrt-prod_binary64`
66×	`*-un-lft-identity_binary64`
63×	`add-cube-cbrt_binary64`

Counts

4 → 213

Calls

4 calls:

15.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (cosh.f64 x) y) x)) (cbrt.f64 (/.f64 (.f64 (cosh.f64 x) y) x))) 1) (/.f64 (cbrt.f64 (/.f64 (*.f64 (cosh.f64 x) y) x)) z))
7.0ms	(.f64 (cbrt.f64 (/.f64 (.f64 (cosh.f64 x) y) x)) (cbrt.f64 (/.f64 (*.f64 (cosh.f64 x) y) x)))
5.0ms	(/.f64 (cbrt.f64 (/.f64 (*.f64 (cosh.f64 x) y) x)) z)
2.0ms	(cbrt.f64 (/.f64 (*.f64 (cosh.f64 x) y) x))

simplify234.0ms (3%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-def_binary64`
271×	`associate-l_binary64`
268×	`associate-r_binary64`
259×	`associate-/l*_binary64`
174×	`associate-*l/_binary64`

Counts

333 → 409

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	420	10058
1	934	9263
2	3218	8403
3	4640	8379
4	4927	8379

prune481.0ms (6.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	503	0	503
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	503	9	512

Error

Counts

512 → 9

Alt Table

Status	Error	Program
✓	3.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 (.f64 (cosh.f64 x) y) x)) (cbrt.f64 (/.f64 (.f64 (cosh.f64 x) y) x))) 1) (/.f64 (cbrt.f64 (/.f64 (*.f64 (cosh.f64 x) y) x)) z))
	10.6b	(.f64 (.f64 (cosh.f64 x) (/.f64 y x)) (/.f64 1 z))
✓	3.1b	(/.f64 (/.f64 (*.f64 (cosh.f64 x) y) x) z)
	12.4b	(.f64 (/.f64 (.f64 (cosh.f64 x) y) 1) (/.f64 (/.f64 1 x) z))
	15.8b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y (.f64 x z)) (cosh.f64 x))) (cbrt.f64 (.f64 (/.f64 y (.f64 x z)) (cosh.f64 x)))) (cbrt.f64 (.f64 (/.f64 y (.f64 x z)) (cosh.f64 x))))
	14.1b	(/.f64 (cbrt.f64 (.f64 (.f64 (/.f64 (.f64 (cosh.f64 x) y) x) (/.f64 (.f64 (cosh.f64 x) y) x)) (/.f64 (*.f64 (cosh.f64 x) y) x))) z)
✓	3.1b	(/.f64 (.f64 (.f64 (cosh.f64 x) y) (/.f64 1 x)) z)
	36.3b	(/.f64 (/.f64 (cosh.f64 x) (sqrt.f64 x)) (/.f64 z (/.f64 y (sqrt.f64 x))))
	15.5b	(.f64 (cosh.f64 x) (/.f64 y (.f64 x z)))

Compiler

Compiled 18128 to 4064 computations (77.6% saved)

regimes687.0ms (8.9%)

Accuracy

Total 2.2b remaining (98.9%)

Threshold costs 0b (0%)

Counts

99 → 3

Compiler

Compiled 8988 to 5310 computations (40.9% saved)

bsearch29.0ms (0.4%)

Steps

Iters	Range		Point
6	6.9277346961878965e-25	1.056242507861308e-23	7.30782984999272e-25
10	6.511457214736032e-292	2.0627809027092624e-277	2.71211154208478e-288

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`if-if-or-not_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	64
1	38	64
2	37	64

end109.0ms (1.4%)

Compiler: Compiled 254 to 140 computations (44.9% saved)

Details

analyze154.0ms (2%)

sample724.0ms (9.4%)

simplify86.0ms (1.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series85.0ms (1.1%)

rewrite15.0ms (0.2%)

simplify80.0ms (1%)

prune102.0ms (1.3%)

localize5.0ms (0.1%)

series110.0ms (1.4%)

rewrite18.0ms (0.2%)

simplify99.0ms (1.3%)

prune159.0ms (2.1%)

localize6.0ms (0.1%)

series89.0ms (1.2%)

rewrite20.0ms (0.3%)

simplify96.0ms (1.2%)

prune162.0ms (2.1%)

localize10.0ms (0.1%)

series4.1s (53.2%)

rewrite53.0ms (0.7%)

simplify234.0ms (3%)

prune481.0ms (6.2%)

regimes687.0ms (8.9%)

bsearch29.0ms (0.4%)

simplify3.0ms (0%)

end109.0ms (1.4%)

Profiling