Details

analyze1.3s (13%)

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
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
14%	83.4%	2.5%	11
18.7%	78.2%	3.1%	12
28.1%	65.5%	6.4%	13
30.7%	59.4%	9.9%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample2.1s (20.1%)

Results

1.1s	8256×	body	128	valid
843.0ms	6068×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify80.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1010×	`fma-neg_binary64`
443×	`fma-def_binary64`
399×	`rules-40_binary64`
399×	`rules-41_binary64`
399×	`rules-42_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	78	20
2	301	20
3	1431	20
4	4336	20
5	4926	20
6	4919	20

prune4.0ms (0%)

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

32.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	32.0b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z z) (*.f64 t t)))
	36.6b	(+.f64 (/.f64 (.f64 x x) (.f64 y y)) (/.f64 (.f64 z z) (.f64 t t)))

Compiler

Compiled 107 to 55 computations (48.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	4.2b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z z) (*.f64 t t)))
✓	12.1b	(/.f64 x (*.f64 y y))
✓	22.0b	(/.f64 (.f64 z z) (.f64 t t))

series176.0ms (1.7%)

Counts

3 → 96

Calls

3 calls:

119.0ms	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z z) (*.f64 t t)))
29.0ms	(/.f64 x (*.f64 y y))
28.0ms	(/.f64 (.f64 z z) (.f64 t t))

rewrite85.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

851×	`fma-neg_binary64`
340×	`prod-diff_binary64`
191×	`expm1-udef_binary64`
191×	`log1p-udef_binary64`
110×	`add-sqr-sqrt_binary64`

Counts

3 → 106

Calls

3 calls:

83.0ms	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z z) (*.f64 t t)))
83.0ms	(/.f64 x (*.f64 y y))
83.0ms	(/.f64 (.f64 z z) (.f64 t t))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	256	31
2	3071	31
3	5096	31
0	0	0
1	0	0

simplify87.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

395×	`fma-neg_binary64`
274×	`rules-40_binary64`
274×	`rules-41_binary64`
274×	`rules-42_binary64`
274×	`rules-43_binary64`

Counts

202 → 111

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	960
1	80	960
2	248	960
3	999	960
4	3996	960
5	9	960

prune119.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	99	12	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	101	12	113

Error

10.5b

Counts

113 → 12

Alt Table

Status	Error	Program
▶	15.6b	(pow.f64 (sqrt.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2))) 2)
	17.3b	(fma.f64 x (/.f64 x (*.f64 y y)) (exp.f64 (log.f64 (pow.f64 (/.f64 z t) 2))))
	16.1b	(pow.f64 (cbrt.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2))) 3)
	31.5b	(fma.f64 x (/.f64 x (*.f64 y y)) (cbrt.f64 (pow.f64 (pow.f64 (/.f64 z t) 2) 3)))
	25.2b	(fma.f64 x (/.f64 x (.f64 y y)) (.f64 z (/.f64 z (*.f64 t t))))
	42.9b	(/.f64 (pow.f64 x 2) (pow.f64 y 2))
	41.8b	(fma.f64 x (pow.f64 (/.f64 (sqrt.f64 x) y) 2) (/.f64 (.f64 z z) (.f64 t t)))
	32.3b	(fma.f64 x (.f64 x (/.f64 1 (.f64 y y))) (/.f64 (.f64 z z) (.f64 t t)))
	27.2b	(fma.f64 x (/.f64 x (*.f64 y y)) (sqrt.f64 (pow.f64 (pow.f64 (/.f64 z t) 2) 2)))
	24.4b	(/.f64 (+.f64 (.f64 z (/.f64 z t)) (.f64 (.f64 x (/.f64 x (.f64 y y))) t)) t)
	32.0b	(fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (pow.f64 (pow.f64 (/.f64 z t) 2) 3) 1/3))
	49.7b	(/.f64 (pow.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2)) 3) (+.f64 (pow.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2)) 2) (+.f64 0 (.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2)) 0))))

Compiler

Compiled 2464 to 945 computations (61.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(pow.f64 (sqrt.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2))) 2)
✓	4.2b	(fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2))
✓	5.2b	(sqrt.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2)))
	12.1b	(/.f64 x (*.f64 y y))

series480.0ms (4.7%)

Counts

3 → 144

Calls

3 calls:

340.0ms

(pow.f64 (sqrt.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2))) 2)

75.0ms

(fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2))

65.0ms

(sqrt.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2)))

rewrite102.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

833×	`fma-neg_binary64`
276×	`prod-diff_binary64`
202×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`
174×	`egg-rr`

Counts

3 → 174

Calls

3 calls:

97.0ms

(pow.f64 (sqrt.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2))) 2)

97.0ms

(fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2))

97.0ms

(sqrt.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	53
1	281	53
2	3176	53
3	5079	53
0	0	0
1	0	0

simplify158.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

672×	`rules-40_binary64`
672×	`rules-41_binary64`
672×	`rules-42_binary64`
672×	`rules-43_binary64`
670×	`rules-21_binary64`

Counts

318 → 161

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	81	3730
1	553	3658
2	2414	3658
3	4652	3658
4	4971	3658

prune195.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	192	4	196
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	198	10	208

Error

0.1b

Counts

208 → 10

Alt Table

Status	Error	Program
	16.1b	(pow.f64 (cbrt.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2))) 3)
	31.5b	(fma.f64 x (/.f64 x (*.f64 y y)) (cbrt.f64 (pow.f64 (pow.f64 (/.f64 z t) 2) 3)))
	25.3b	(pow.f64 (/.f64 x y) 2)
	24.4b	(/.f64 (+.f64 (.f64 z (/.f64 z t)) (.f64 (.f64 x (/.f64 x (.f64 y y))) t)) t)
	25.2b	(fma.f64 x (/.f64 x (.f64 y y)) (.f64 z (/.f64 z (*.f64 t t))))
	42.9b	(/.f64 (pow.f64 x 2) (pow.f64 y 2))
▶	15.6b	(fma.f64 (pow.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2)) 1/4) (.f64 (sqrt.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2))) (pow.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2)) 1/4)) 0)
	41.8b	(fma.f64 x (pow.f64 (/.f64 (sqrt.f64 x) y) 2) (/.f64 (.f64 z z) (.f64 t t)))
	15.8b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 z t)) 2) (.f64 (cbrt.f64 (/.f64 z t)) (/.f64 z t)) (neg.f64 (-.f64 0 (.f64 x (/.f64 x (*.f64 y y))))))
	29.5b	(pow.f64 (/.f64 z t) 2)

Compiler

Compiled 6050 to 2840 computations (53.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.2b	(fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2))
	5.2b	(sqrt.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2)))
✓	7.2b	(pow.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2)) 1/4)
	12.1b	(/.f64 x (*.f64 y y))

series165.0ms (1.6%)

Counts

1 → 48

Calls

1 calls:

164.0ms

(pow.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2)) 1/4)

rewrite82.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

862×	`fma-neg_binary64`
274×	`prod-diff_binary64`
219×	`expm1-udef_binary64`
219×	`log1p-udef_binary64`
125×	`add-sqr-sqrt_binary64`

Counts

1 → 32

Calls

1 calls:

81.0ms

(pow.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2)) 1/4)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	302	20
2	3395	20
3	5340	20
0	0	0
1	0	0

simplify73.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

574×	`fma-neg_binary64`
455×	`rules-20_binary64`
404×	`rules-41_binary64`
404×	`rules-43_binary64`
402×	`rules-40_binary64`

Counts

80 → 94

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	225	3500
1	1660	3456
2	5120	3456

prune773.0ms (7.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	538	2	540
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	539	11	550

Error

0.1b

Counts

550 → 11

Alt Table

Status	Error	Program
▶	15.7b	(fma.f64 (pow.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2)) 1/4) (.f64 (sqrt.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2))) (.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2))) 2) 1/4) (pow.f64 (cbrt.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2))) 1/4))) 0)
✓	15.6b	(fma.f64 (pow.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2)) 1/4) (.f64 (sqrt.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2))) (pow.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2)) 1/4)) 0)
	38.6b	(fma.f64 (pow.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2)) 1/4) (.f64 (/.f64 (pow.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2)) 3/2) (+.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2)) (-.f64 0 (.f64 (sqrt.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2))) 0)))) (pow.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2)) 1/4)) 0)
	25.3b	(pow.f64 (/.f64 x y) 2)
	24.4b	(/.f64 (+.f64 (.f64 z (/.f64 z t)) (.f64 (.f64 x (/.f64 x (.f64 y y))) t)) t)
	25.2b	(fma.f64 x (/.f64 x (.f64 y y)) (.f64 z (/.f64 z (*.f64 t t))))
	42.9b	(/.f64 (pow.f64 x 2) (pow.f64 y 2))
	41.8b	(fma.f64 x (pow.f64 (/.f64 (sqrt.f64 x) y) 2) (/.f64 (.f64 z z) (.f64 t t)))
	15.8b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 z t)) 2) (.f64 (cbrt.f64 (/.f64 z t)) (/.f64 z t)) (neg.f64 (-.f64 0 (.f64 x (/.f64 x (*.f64 y y))))))
	16.1b	(pow.f64 (cbrt.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2))) 3)
	29.5b	(pow.f64 (/.f64 z t) 2)

Compiler

Compiled 35091 to 16691 computations (52.4% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.2b	(sqrt.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2)))
	7.2b	(pow.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2)) 1/4)
✓	7.6b	(cbrt.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2)))
	12.1b	(/.f64 x (*.f64 y y))

series166.0ms (1.6%)

Counts

1 → 48

Calls

1 calls:

166.0ms

(cbrt.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2)))

rewrite70.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

829×	`fma-neg_binary64`
276×	`prod-diff_binary64`
202×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`
116×	`add-sqr-sqrt_binary64`

Counts

1 → 36

Calls

1 calls:

68.0ms

(cbrt.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	273	19
2	3164	19
3	5072	19
0	0	0
1	0	0

simplify109.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

567×	`fma-neg_binary64`
450×	`rules-20_binary64`
410×	`rules-41_binary64`
410×	`rules-43_binary64`
408×	`rules-40_binary64`

Counts

84 → 100

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	218	3640
1	1598	3600
2	5082	3600

prune860.0ms (8.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	500	1	501
Fresh	1	8	9
Picked	0	1	1
Done	1	0	1
Total	502	10	512

Error

0.1b

Counts

512 → 10

Alt Table

Status	Error	Program
	25.3b	(pow.f64 (/.f64 x y) 2)
	24.4b	(/.f64 (+.f64 (.f64 z (/.f64 z t)) (.f64 (.f64 x (/.f64 x (.f64 y y))) t)) t)
	25.2b	(fma.f64 x (/.f64 x (.f64 y y)) (.f64 z (/.f64 z (*.f64 t t))))
	42.9b	(/.f64 (pow.f64 x 2) (pow.f64 y 2))
✓	15.7b	(fma.f64 (pow.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2)) 1/4) (.f64 (sqrt.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2))) (.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2))) 2) 1/4) (pow.f64 (cbrt.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2))) 1/4))) 0)
	41.8b	(fma.f64 x (pow.f64 (/.f64 (sqrt.f64 x) y) 2) (/.f64 (.f64 z z) (.f64 t t)))
	15.8b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 z t)) 2) (.f64 (cbrt.f64 (/.f64 z t)) (/.f64 z t)) (neg.f64 (-.f64 0 (.f64 x (/.f64 x (*.f64 y y))))))
	15.8b	(fma.f64 (pow.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2)) 1/4) (.f64 (sqrt.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2))) (.f64 (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2)))) 3) 2) 1/4) (pow.f64 (cbrt.f64 (fma.f64 x (/.f64 x (.f64 y y)) (pow.f64 (/.f64 z t) 2))) 1/4))) 0)
	16.1b	(pow.f64 (cbrt.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2))) 3)
	29.5b	(pow.f64 (/.f64 z t) 2)

Compiler

Compiled 42343 to 21888 computations (48.3% saved)

regimes2.8s (27.2%)

Accuracy

Total 5.6b remaining (94.5%)

Threshold costs 0b (0%)

Counts

94 → 2

Compiler

Compiled 41268 to 23138 computations (43.9% saved)

bsearch5.0ms (0%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	42
1	23	42
2	22	42

end194.0ms (1.9%)

Compiler: Compiled 338 to 197 computations (41.7% saved)

Details

analyze1.3s (13%)

sample2.1s (20.1%)

simplify80.0ms (0.8%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series176.0ms (1.7%)

rewrite85.0ms (0.8%)

simplify87.0ms (0.9%)

prune119.0ms (1.2%)

localize11.0ms (0.1%)

series480.0ms (4.7%)

rewrite102.0ms (1%)

simplify158.0ms (1.5%)

prune195.0ms (1.9%)

localize15.0ms (0.1%)

series165.0ms (1.6%)

rewrite82.0ms (0.8%)

simplify73.0ms (0.7%)

prune773.0ms (7.6%)

localize29.0ms (0.3%)

series166.0ms (1.6%)

rewrite70.0ms (0.7%)

simplify109.0ms (1.1%)

prune860.0ms (8.4%)

regimes2.8s (27.2%)

bsearch5.0ms (0%)

simplify5.0ms (0.1%)

end194.0ms (1.9%)

Profiling