Details

analyze2.1s (32.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
3.7%	96.1%	0.2%	13
4.2%	94.5%	1.3%	14

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample1.9s (29.3%)

Results

1.3s	8256×	body	128	valid
570.0ms	2377×	body	128	invalid

Compiler

Compiled 65 to 47 computations (27.7% saved)

simplify102.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-neg_binary64`
614×	`times-frac_binary64`
480×	`neg-mul-1_binary64`
416×	`div-sub_binary64`
394×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	28	23
2	55	23
3	101	21
4	220	21
5	423	21
6	834	20
7	1845	19
8	3893	19
9	4281	19
10	4633	19
11	4956	19
12	4804	19

prune6.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	7.9b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
▶	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

Compiler

Compiled 110 to 79 computations (28.2% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
✓	0.1b	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

series48.0ms (0.7%)

Counts

2 → 72

Calls

2 calls:

33.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
13.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

rewrite55.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

103×	`*-un-lft-identity_binary64`
69×	`times-frac_binary64`
66×	`add-sqr-sqrt_binary64`
66×	`add-cube-cbrt_binary64`
65×	`associate-+r+_binary64`

Counts

2 → 132

Calls

2 calls:

23.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
8.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

simplify166.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

563×	`fma-def_binary64`
447×	`distribute-rgt-in_binary64`
425×	`distribute-lft-in_binary64`
234×	`fma-neg_binary64`
189×	`exp-prod_binary64`

Counts

204 → 177

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	235	4642
1	625	3549
2	1504	3327
3	4434	3327
4	4943	3327

prune234.0ms (3.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	171	6	177
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	172	7	179

Error

Counts

179 → 7

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 2 (.f64 t z)))))))
	23.6b	(+.f64 (/.f64 x y) (-.f64 -2 (cbrt.f64 (.f64 (.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t) (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
	13.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (-.f64 (.f64 -2 -2) (.f64 (/.f64 -2 z) (/.f64 -2 z))) (*.f64 t (-.f64 -2 (/.f64 -2 z))))))
	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
	32.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (sqrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (sqrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

Compiler

Compiled 6442 to 4483 computations (30.4% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 2 (.f64 t z)))))))
✓	0.0b	(+.f64 (/.f64 2 t) (/.f64 2 (*.f64 t z)))
✓	0.5b	(/.f64 2 (*.f64 t z))

series64.0ms (1%)

Counts

3 → 72

Calls

3 calls:

37.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 2 (.f64 t z)))))))
17.0ms	(+.f64 (/.f64 2 t) (/.f64 2 (*.f64 t z)))
10.0ms	(/.f64 2 (*.f64 t z))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`fma-def_binary64`
26×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`

Counts

3 → 89

Calls

3 calls:

7.0ms	(+.f64 (/.f64 2 t) (/.f64 2 (*.f64 t z)))
7.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 2 (.f64 t z)))))))
3.0ms	(/.f64 2 (*.f64 t z))

simplify100.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

548×	`distribute-rgt-in_binary64`
506×	`distribute-lft-in_binary64`
488×	`fma-def_binary64`
221×	`fma-neg_binary64`
210×	`associate-/l*_binary64`

Counts

161 → 141

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	2549
1	425	2403
2	1289	2398
3	4827	2398
4	4950	2398

prune202.0ms (3.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	138	3	141
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	141	7	148

Error

Counts

148 → 7

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))))))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	32.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (sqrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (sqrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 2 (.f64 t z)))))))
	0.2b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (sqrt.f64 2) (/.f64 (.f64 t z) (sqrt.f64 2))))))))
	16.3b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (cbrt.f64 (pow.f64 (/.f64 2 (.f64 z t)) 3)))))))

Compiler

Compiled 4007 to 2581 computations (35.6% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))))))
✓	0.0b	(+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))
✓	0.3b	(/.f64 (/.f64 2 t) z)

series65.0ms (1%)

Counts

3 → 96

Calls

3 calls:

34.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))))))
18.0ms	(+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))
12.0ms	(/.f64 (/.f64 2 t) z)

rewrite54.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`times-frac_binary64`
70×	`*-un-lft-identity_binary64`
60×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`
26×	`fma-def_binary64`

Counts

3 → 138

Calls

3 calls:

25.0ms	(+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))
12.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))))))
5.0ms	(/.f64 (/.f64 2 t) z)

simplify105.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

554×	`distribute-rgt-in_binary64`
513×	`distribute-lft-in_binary64`
485×	`fma-def_binary64`
458×	`times-frac_binary64`
147×	`associate-/l/_binary64`

Counts

234 → 202

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	3705
1	632	3560
2	1752	3552
3	5063	3552

prune287.0ms (4.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	201	1	202
Fresh	1	3	4
Picked	0	1	1
Done	1	1	2
Total	203	6	209

Error

Counts

209 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))))))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	16.3b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (cbrt.f64 (pow.f64 (/.f64 2 (.f64 z t)) 3)))))))
▶	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (/.f64 (fma.f64 2 z 2) (.f64 t z))))))
	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
	0.2b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (sqrt.f64 2) (/.f64 (.f64 t z) (sqrt.f64 2))))))))

Compiler

Compiled 5728 to 3783 computations (34% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (/.f64 (fma.f64 2 z 2) (.f64 t z))))))
✓	7.5b	(/.f64 (fma.f64 2 z 2) (*.f64 t z))

series55.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

36.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (/.f64 (fma.f64 2 z 2) (.f64 t z))))))
19.0ms	(/.f64 (fma.f64 2 z 2) (*.f64 t z))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
13×	`fma-def_binary64`
12×	`times-frac_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`

Counts

2 → 60

Calls

2 calls:

7.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (/.f64 (fma.f64 2 z 2) (.f64 t z))))))
3.0ms	(/.f64 (fma.f64 2 z 2) (*.f64 t z))

simplify93.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

407×	`times-frac_binary64`
317×	`fma-def_binary64`
302×	`distribute-rgt-in_binary64`
289×	`associate-/l*_binary64`
288×	`associate-*r/_binary64`

Counts

132 → 95

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	139	2347
1	362	2169
2	1074	2167
3	4642	2159
4	5493	2159

prune120.0ms (1.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	95	6	101

Error

Counts

101 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))))))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	16.3b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (cbrt.f64 (pow.f64 (/.f64 2 (.f64 z t)) 3)))))))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (/.f64 (fma.f64 2 z 2) (.f64 t z))))))
	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
	0.2b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (sqrt.f64 2) (/.f64 (.f64 t z) (sqrt.f64 2))))))))

Compiler

Compiled 2589 to 1620 computations (37.4% saved)

regimes487.0ms (7.5%)

Accuracy

Total 0.1b remaining (86.4%)

Threshold costs 0.1b (86.4%)

Counts

59 → 1

Compiler

Compiled 8890 to 6878 computations (22.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`cancel-sign-sub-inv_binary64`
7×	`distribute-rgt-neg-in_binary64`
7×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	24
1	34	22
2	51	22
3	66	22
4	78	22
5	82	22
6	76	22

end133.0ms (2%)

Compiler: Compiled 185 to 143 computations (22.7% saved)

Details

analyze2.1s (32.9%)

sample1.9s (29.3%)

simplify102.0ms (1.6%)

prune6.0ms (0.1%)

localize9.0ms (0.1%)

series48.0ms (0.7%)

rewrite55.0ms (0.9%)

simplify166.0ms (2.6%)

prune234.0ms (3.6%)

localize11.0ms (0.2%)

series64.0ms (1%)

rewrite23.0ms (0.3%)

simplify100.0ms (1.5%)

prune202.0ms (3.1%)

localize12.0ms (0.2%)

series65.0ms (1%)

rewrite54.0ms (0.8%)

simplify105.0ms (1.6%)

prune287.0ms (4.4%)

localize11.0ms (0.2%)

series55.0ms (0.9%)

rewrite15.0ms (0.2%)

simplify93.0ms (1.4%)

prune120.0ms (1.8%)

regimes487.0ms (7.5%)

simplify3.0ms (0.1%)

end133.0ms (2%)

Profiling