Details

analyze595.0ms (13.5%)

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)

sample1.4s (31.6%)

Results

847.0ms	8256×	body	128	valid
473.0ms	4521×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify82.0ms (1.9%)

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

8.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	8.2b	(/.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
✓	0.0b	(*.f64 (cosh.f64 x) (/.f64 y x))
✓	7.8b	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

series81.0ms (1.8%)

Counts

2 → 60

Calls

2 calls:

54.0ms	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
27.0ms	(*.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 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
5.0ms	(*.f64 (cosh.f64 x) (/.f64 y x))

simplify79.0ms (1.8%)

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

prune86.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	110	10	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	10	121

Error

0.0b

Counts

121 → 10

Alt Table

Status	Error	Program
	9.1b	(/.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cosh.f64 x) (/.f64 y x))) (cbrt.f64 (.f64 (cosh.f64 x) (/.f64 y x)))) (cbrt.f64 (*.f64 (cosh.f64 x) (/.f64 y x)))) z)
	8.2b	(/.f64 (/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) x) z)
	8.3b	(/.f64 (.f64 (.f64 (cosh.f64 x) y) (/.f64 1 x)) z)
	6.5b	(.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))))
	37.1b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 (/.f64 y x) (cosh.f64 x)) 3)) z)
	9.4b	(/.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)
▶	6.1b	(fma.f64 1/2 (/.f64 (.f64 y x) z) (/.f64 y (.f64 z x)))
	33.4b	(.f64 (sqrt.f64 (.f64 (/.f64 y (.f64 z x)) (cosh.f64 x))) (sqrt.f64 (.f64 (/.f64 y (*.f64 z x)) (cosh.f64 x))))
	36.2b	(cbrt.f64 (pow.f64 (.f64 (/.f64 y (.f64 z x)) (cosh.f64 x)) 3))
	8.4b	(/.f64 (cosh.f64 x) (/.f64 z (/.f64 y x)))

Compiler

Compiled 2135 to 721 computations (66.2% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (/.f64 (.f64 y x) z) (/.f64 y (.f64 z x)))
✓	3.9b	(/.f64 (*.f64 y x) z)
✓	5.2b	(/.f64 y (*.f64 z x))

series54.0ms (1.2%)

Counts

3 → 36

Calls

3 calls:

26.0ms	(fma.f64 1/2 (/.f64 (.f64 y x) z) (/.f64 y (.f64 z x)))
16.0ms	(/.f64 y (*.f64 z x))
11.0ms	(/.f64 (*.f64 y x) z)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 56

Calls

3 calls:

3.0ms	(/.f64 (*.f64 y x) z)
3.0ms	(/.f64 y (*.f64 z x))
0.0ms	(fma.f64 1/2 (/.f64 (.f64 y x) z) (/.f64 y (.f64 z x)))

simplify73.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-def_binary64`
594×	`associate-/l*_binary64`
546×	`times-frac_binary64`
404×	`distribute-rgt-in_binary64`
298×	`associate-/l/_binary64`

Counts

92 → 96

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	106	1316
1	242	1191
2	783	1191
3	2978	1160
4	3649	1098
5	5060	1098

prune62.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	100	6	106

Error

0.0b

Counts

106 → 6

Alt Table

Status	Error	Program
	8.2b	(/.f64 (/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) x) z)
	37.1b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 (/.f64 y x) (cosh.f64 x)) 3)) z)
✓	6.1b	(fma.f64 1/2 (/.f64 (.f64 y x) z) (/.f64 y (.f64 z x)))
	33.4b	(.f64 (sqrt.f64 (.f64 (/.f64 y (.f64 z x)) (cosh.f64 x))) (sqrt.f64 (.f64 (/.f64 y (*.f64 z x)) (cosh.f64 x))))
▶	7.8b	(fma.f64 1/2 (/.f64 (*.f64 y x) z) (/.f64 (/.f64 y z) x))
	8.4b	(/.f64 (cosh.f64 x) (/.f64 z (/.f64 y x)))

Compiler

Compiled 1749 to 590 computations (66.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (/.f64 (*.f64 y x) z) (/.f64 (/.f64 y z) x))
	3.9b	(/.f64 (*.f64 y x) z)
✓	7.2b	(/.f64 (/.f64 y z) x)

series42.0ms (1%)

Counts

2 → 72

Calls

2 calls:

27.0ms	(fma.f64 1/2 (/.f64 (*.f64 y x) z) (/.f64 (/.f64 y z) x))
15.0ms	(/.f64 (/.f64 y z) x)

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
44×	`*-un-lft-identity_binary64`
44×	`add-sqr-sqrt_binary64`
44×	`add-cube-cbrt_binary64`
13×	`associate-/l*_binary64`

Counts

2 → 82

Calls

2 calls:

4.0ms	(/.f64 (/.f64 y z) x)
0.0ms	(fma.f64 1/2 (/.f64 (*.f64 y x) z) (/.f64 (/.f64 y z) x))

simplify109.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

597×	`fma-def_binary64`
390×	`associate-/l/_binary64`
384×	`*-commutative_binary64`
292×	`distribute-lft-in_binary64`
292×	`distribute-rgt-in_binary64`

Counts

154 → 125

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	176	2298
1	369	2218
2	843	2218
3	2102	2187
4	2752	2125
5	4516	2125
6	4965	2125

prune84.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	159	7	166

Error

Counts

166 → 7

Alt Table

Status	Error	Program
	38.9b	(fma.f64 1/2 (/.f64 (*.f64 y x) z) (/.f64 (/.f64 (/.f64 y z) (sqrt.f64 x)) (sqrt.f64 x)))
✓	7.8b	(fma.f64 1/2 (/.f64 (*.f64 y x) z) (/.f64 (/.f64 y z) x))
▶	8.2b	(/.f64 (/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) x) z)
	36.2b	(fma.f64 1/2 (/.f64 (.f64 y x) z) (.f64 (sqrt.f64 (/.f64 y z)) (/.f64 (sqrt.f64 (/.f64 y z)) x)))
✓	6.1b	(fma.f64 1/2 (/.f64 (.f64 y x) z) (/.f64 y (.f64 z x)))
	33.4b	(.f64 (sqrt.f64 (.f64 (/.f64 y (.f64 z x)) (cosh.f64 x))) (sqrt.f64 (.f64 (/.f64 y (*.f64 z x)) (cosh.f64 x))))
	8.4b	(/.f64 (cosh.f64 x) (/.f64 z (/.f64 y x)))

Compiler

Compiled 3251 to 980 computations (69.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (exp.f64 x) y)
✓	0.0b	(+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x))))
✓	0.0b	(/.f64 y (exp.f64 x))
✓	7.8b	(/.f64 (/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) x) z)

series100.0ms (2.3%)

Counts

4 → 68

Calls

4 calls:

60.0ms	(/.f64 (/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) x) z)
21.0ms	(+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x))))
12.0ms	(/.f64 y (exp.f64 x))
6.0ms	(*.f64 (exp.f64 x) y)

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

105×	`times-frac_binary64`
65×	`add-sqr-sqrt_binary64`
63×	`*-un-lft-identity_binary64`
63×	`add-cube-cbrt_binary64`
19×	`associate-/l*_binary64`

Counts

4 → 148

Calls

4 calls:

8.0ms	(/.f64 (/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) x) z)
6.0ms	(+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x))))
3.0ms	(*.f64 (exp.f64 x) y)
3.0ms	(/.f64 y (exp.f64 x))

simplify123.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

623×	`associate-/r*_binary64`
612×	`fma-def_binary64`
254×	`associate-/r/_binary64`
202×	`associate-/l/_binary64`
172×	`cancel-sign-sub-inv_binary64`

Counts

216 → 272

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	319	5292
1	780	5057
2	2242	5042
3	5003	5042

prune170.0ms (3.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	272	0	272
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	272	7	279

Error

Counts

279 → 7

Alt Table

Status	Error	Program
	38.9b	(fma.f64 1/2 (/.f64 (*.f64 y x) z) (/.f64 (/.f64 (/.f64 y z) (sqrt.f64 x)) (sqrt.f64 x)))
✓	7.8b	(fma.f64 1/2 (/.f64 (*.f64 y x) z) (/.f64 (/.f64 y z) x))
✓	8.2b	(/.f64 (/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x)))) x) z)
	36.2b	(fma.f64 1/2 (/.f64 (.f64 y x) z) (.f64 (sqrt.f64 (/.f64 y z)) (/.f64 (sqrt.f64 (/.f64 y z)) x)))
✓	6.1b	(fma.f64 1/2 (/.f64 (.f64 y x) z) (/.f64 y (.f64 z x)))
	33.4b	(.f64 (sqrt.f64 (.f64 (/.f64 y (.f64 z x)) (cosh.f64 x))) (sqrt.f64 (.f64 (/.f64 y (*.f64 z x)) (cosh.f64 x))))
	8.4b	(/.f64 (cosh.f64 x) (/.f64 z (/.f64 y x)))

Compiler

Compiled 7755 to 3288 computations (57.6% saved)

regimes1.0s (22.7%)

Accuracy

Total 0.6b remaining (87.3%)

Threshold costs 0.6b (87.3%)

Counts

111 → 3

Compiler

Compiled 9856 to 5869 computations (40.5% saved)

bsearch83.0ms (1.9%)

Steps

Iters	Range		Point
8	5.091406886650036e+47	1.8181697477523267e+50	5.152424174613172e+47
7	-3.4967812219886254e-84	-3.006164823680938e-86	-3.441851333323831e-84

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	66
1	29	66
2	29	66

end93.0ms (2.1%)

Compiler: Compiled 217 to 115 computations (47% saved)

Details

analyze595.0ms (13.5%)

sample1.4s (31.6%)

simplify82.0ms (1.9%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series81.0ms (1.8%)

rewrite13.0ms (0.3%)

simplify79.0ms (1.8%)

prune86.0ms (1.9%)

localize9.0ms (0.2%)

series54.0ms (1.2%)

rewrite8.0ms (0.2%)

simplify73.0ms (1.6%)

prune62.0ms (1.4%)

localize8.0ms (0.2%)

series42.0ms (1%)

rewrite11.0ms (0.2%)

simplify109.0ms (2.5%)

prune84.0ms (1.9%)

localize10.0ms (0.2%)

series100.0ms (2.3%)

rewrite32.0ms (0.7%)

simplify123.0ms (2.8%)

prune170.0ms (3.8%)

regimes1.0s (22.7%)

bsearch83.0ms (1.9%)

simplify3.0ms (0.1%)

end93.0ms (2.1%)

Profiling