Details

analyze722.0ms (13.1%)

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
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
6.2%	79.6%	14.2%	8
7.8%	75.7%	16.5%	9
11.7%	68.6%	19.6%	10
20.3%	49.3%	30.4%	11
22.2%	44.4%	33.4%	12
25.2%	37.3%	37.5%	13
28%	27.3%	44.7%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.5s (28%)

Results

903.0ms	8256×	body	128	valid
555.0ms	4443×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify85.0ms (1.6%)

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

8.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	8.9b	(/.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(cosh.f64 x)
✓	0.0b	(*.f64 (cosh.f64 x) (/.f64 y x))
✓	8.4b	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

series97.0ms (1.8%)

Counts

3 → 72

Calls

3 calls:

58.0ms	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
30.0ms	(*.f64 (cosh.f64 x) (/.f64 y x))
9.0ms	(cosh.f64 x)

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
13×	`associate-r_binary64`
13×	`*-un-lft-identity_binary64`

Counts

3 → 74

Calls

3 calls:

6.0ms	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
5.0ms	(*.f64 (cosh.f64 x) (/.f64 y x))
1.0ms	(cosh.f64 x)

simplify88.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

935×	`times-frac_binary64`
578×	`fma-def_binary64`
493×	`associate-l_binary64`
378×	`associate-/r*_binary64`
349×	`associate-/r/_binary64`

Counts

146 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	190	2514
1	472	2226
2	1591	2222
3	4481	2216
4	4965	2216

prune150.0ms (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	133	7	140
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	7	141

Error

0.0b

Counts

141 → 7

Alt Table

Status	Error	Program
	7.9b	(.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))))
▶	7.1b	(/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (.f64 1/2 (/.f64 y (exp.f64 x)))) (.f64 z x))
	8.9b	(/.f64 (/.f64 (fma.f64 y (exp.f64 x) (/.f64 y (exp.f64 x))) (*.f64 x 2)) z)
	9.4b	(/.f64 1 (/.f64 z (*.f64 (cosh.f64 x) (/.f64 y x))))
	9.0b	(.f64 (.f64 (cosh.f64 x) (/.f64 y x)) (/.f64 1 z))
	37.2b	(/.f64 (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) (sqrt.f64 z)) (sqrt.f64 z))
	9.9b	(/.f64 (.f64 (/.f64 (cosh.f64 x) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y x)) (cbrt.f64 z))

Compiler

Compiled 2277 to 784 computations (65.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (exp.f64 x))
✓	0.0b	(+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x))))
✓	0.0b	(*.f64 (exp.f64 x) y)
✓	6.7b	(/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (.f64 1/2 (/.f64 y (exp.f64 x)))) (.f64 z x))

series111.0ms (2%)

Counts

4 → 64

Calls

4 calls:

63.0ms	(/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (.f64 1/2 (/.f64 y (exp.f64 x)))) (.f64 z x))
28.0ms	(+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x))))
14.0ms	(/.f64 y (exp.f64 x))
6.0ms	(*.f64 (exp.f64 x) y)

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
13×	`times-frac_binary64`
13×	`add-cbrt-cube_binary64`

Counts

4 → 91

Calls

4 calls:

7.0ms	(/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (.f64 1/2 (/.f64 y (exp.f64 x)))) (.f64 z x))
5.0ms	(+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x))))
4.0ms	(*.f64 (exp.f64 x) y)
3.0ms	(/.f64 y (exp.f64 x))

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

734×	`associate-/l*_binary64`
620×	`fma-def_binary64`
230×	`distribute-rgt-in_binary64`
206×	`distribute-lft-in_binary64`
196×	`associate-/l/_binary64`

Counts

155 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	2868
1	531	2628
2	1818	2609
3	5244	2609

prune165.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	159	4	163
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	163	7	170

Error

0.0b

Counts

170 → 7

Alt Table

Status	Error	Program
	8.6b	(/.f64 1 (*.f64 (/.f64 z 1/2) (/.f64 x (fma.f64 y (exp.f64 x) (/.f64 y (exp.f64 x))))))
	7.9b	(.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))))
	9.1b	(.f64 (/.f64 1 z) (.f64 (/.f64 1/2 x) (fma.f64 y (exp.f64 x) (/.f64 y (exp.f64 x)))))
✓	7.1b	(/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (.f64 1/2 (/.f64 y (exp.f64 x)))) (.f64 z x))
	8.9b	(/.f64 (/.f64 (fma.f64 y (exp.f64 x) (/.f64 y (exp.f64 x))) (*.f64 x 2)) z)
▶	6.9b	(/.f64 (/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) z) x)
	7.8b	(.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (.f64 1/2 (/.f64 y (exp.f64 x)))) (/.f64 1 (*.f64 z x)))

Compiler

Compiled 4251 to 1813 computations (57.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) z)
	0.0b	(+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x))))
	0.0b	(*.f64 (exp.f64 x) y)
✓	6.9b	(/.f64 (/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) z) x)

series114.0ms (2.1%)

Counts

2 → 64

Calls

2 calls:

63.0ms	(/.f64 (/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) z) x)
51.0ms	(/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) z)

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64`
60×	`*-un-lft-identity_binary64`
60×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`
20×	`associate-/l*_binary64`

Counts

2 → 119

Calls

2 calls:

8.0ms	(/.f64 (/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) z) x)
8.0ms	(/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) z)

simplify145.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

705×	`associate-/l*_binary64`
563×	`associate-/r*_binary64`
543×	`associate-/l/_binary64`
307×	`fma-def_binary64`
265×	`associate-/r/_binary64`

Counts

183 → 238

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	256	5498
1	621	5280
2	1699	5270
3	5044	5270

prune242.0ms (4.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	305	3	308
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	307	8	315

Error

Counts

315 → 8

Alt Table

Status	Error	Program
▶	7.8b	(.f64 (.f64 y (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x)))) (/.f64 1 (*.f64 z x)))
✓	7.1b	(/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (.f64 1/2 (/.f64 y (exp.f64 x)))) (.f64 z x))
	33.6b	(.f64 (sqrt.f64 (.f64 (/.f64 y z) (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))))) (/.f64 (sqrt.f64 (*.f64 (/.f64 y z) (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))))) x))
	8.9b	(/.f64 (/.f64 (fma.f64 y (exp.f64 x) (/.f64 y (exp.f64 x))) (*.f64 x 2)) z)
	8.6b	(/.f64 1 (*.f64 (/.f64 z 1/2) (/.f64 x (fma.f64 y (exp.f64 x) (/.f64 y (exp.f64 x))))))
	9.1b	(.f64 (/.f64 1 z) (.f64 (/.f64 1/2 x) (fma.f64 y (exp.f64 x) (/.f64 y (exp.f64 x)))))
✓	6.9b	(/.f64 (/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) z) x)
	7.9b	(/.f64 (/.f64 1/2 (/.f64 z (fma.f64 y (exp.f64 x) (/.f64 y (exp.f64 x))))) x)

Compiler

Compiled 9039 to 3966 computations (56.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))))
✓	0.0b	(/.f64 1/2 (exp.f64 x))
✓	0.3b	(/.f64 1 (*.f64 z x))
✓	7.2b	(.f64 (.f64 y (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x)))) (/.f64 1 (*.f64 z x)))

series95.0ms (1.7%)

Counts

4 → 64

Calls

4 calls:

59.0ms	(.f64 (.f64 y (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x)))) (/.f64 1 (*.f64 z x)))
22.0ms	(*.f64 y (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))))
8.0ms	(/.f64 1 (*.f64 z x))
6.0ms	(/.f64 1/2 (exp.f64 x))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-exp-log_binary64`
34×	`add-cbrt-cube_binary64`
31×	`prod-exp_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`

Counts

4 → 123

Calls

4 calls:

8.0ms	(.f64 (.f64 y (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x)))) (/.f64 1 (*.f64 z x)))
3.0ms	(/.f64 1 (*.f64 z x))
3.0ms	(/.f64 1/2 (exp.f64 x))
3.0ms	(*.f64 y (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))))

simplify80.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

505×	`distribute-rgt-in_binary64`
501×	`distribute-lft-in_binary64`
463×	`associate-/l*_binary64`
291×	`fma-def_binary64`
256×	`associate-l_binary64`

Counts

187 → 179

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	3501
1	479	3054
2	1686	3046
3	5116	3046

prune149.0ms (2.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	179	8	187

Error

Counts

187 → 8

Alt Table

Status	Error	Program
✓	7.8b	(.f64 (.f64 y (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x)))) (/.f64 1 (*.f64 z x)))
✓	7.1b	(/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (.f64 1/2 (/.f64 y (exp.f64 x)))) (.f64 z x))
	33.6b	(.f64 (sqrt.f64 (.f64 (/.f64 y z) (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))))) (/.f64 (sqrt.f64 (*.f64 (/.f64 y z) (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))))) x))
	8.9b	(/.f64 (/.f64 (fma.f64 y (exp.f64 x) (/.f64 y (exp.f64 x))) (*.f64 x 2)) z)
	8.6b	(/.f64 1 (*.f64 (/.f64 z 1/2) (/.f64 x (fma.f64 y (exp.f64 x) (/.f64 y (exp.f64 x))))))
	9.1b	(.f64 (/.f64 1 z) (.f64 (/.f64 1/2 x) (fma.f64 y (exp.f64 x) (/.f64 y (exp.f64 x)))))
✓	6.9b	(/.f64 (/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) z) x)
	7.9b	(/.f64 (/.f64 1/2 (/.f64 z (fma.f64 y (exp.f64 x) (/.f64 y (exp.f64 x))))) x)

Compiler

Compiled 4115 to 2218 computations (46.1% saved)

regimes1.4s (25.1%)

Accuracy

Total 0.5b remaining (86.8%)

Threshold costs 0.5b (86.8%)

Counts

151 → 3

Compiler

Compiled 14115 to 8678 computations (38.5% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	102
1	44	102
2	46	102
3	47	102
4	46	102

end118.0ms (2.2%)

Compiler: Compiled 303 to 170 computations (43.9% saved)

Details

analyze722.0ms (13.1%)

sample1.5s (28%)

simplify85.0ms (1.6%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series97.0ms (1.8%)

rewrite15.0ms (0.3%)

simplify88.0ms (1.6%)

prune150.0ms (2.7%)

localize12.0ms (0.2%)

series111.0ms (2%)

rewrite24.0ms (0.4%)

simplify80.0ms (1.4%)

prune165.0ms (3%)

localize10.0ms (0.2%)

series114.0ms (2.1%)

rewrite29.0ms (0.5%)

simplify145.0ms (2.6%)

prune242.0ms (4.4%)

localize10.0ms (0.2%)

series95.0ms (1.7%)

rewrite24.0ms (0.4%)

simplify80.0ms (1.5%)

prune149.0ms (2.7%)

regimes1.4s (25.1%)

bsearch4.0ms (0.1%)

simplify4.0ms (0.1%)

end118.0ms (2.2%)

Profiling