Details

analyze2.0s (21.6%)

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
13.2%	86.5%	0.2%	11
16.8%	83%	0.2%	12
22.7%	77.1%	0.2%	13
24.1%	74.7%	1.3%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample63.0ms (0.7%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
9.0ms	66×	body	128	invalid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify105.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

946×	`fma-def_binary64`
719×	`fma-neg_binary64`
235×	`cancel-sign-sub-inv_binary64`
163×	`distribute-rgt-in_binary64`
116×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	16	13
2	31	11
3	62	11
4	130	11
5	231	11
6	390	11
7	639	11
8	955	11
9	1272	11
10	1381	11
11	1449	11
12	1474	11
13	1471	11
14	1471	11
15	1398	11

prune7.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	7.9b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
▶	7.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 45 computations (40.8% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 z t))
✓	0.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	8.3b	(/.f64 (*.f64 y (-.f64 z t)) a)

series97.0ms (1.1%)

Counts

3 → 144

Calls

3 calls:

50.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
39.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
7.0ms	(*.f64 y (-.f64 z t))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 92

Calls

3 calls:

9.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
5.0ms	(*.f64 y (-.f64 z t))
4.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

simplify82.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

599×	`times-frac_binary64`
517×	`distribute-rgt-in_binary64`
492×	`distribute-lft-in_binary64`
448×	`fma-def_binary64`
124×	`associate-l_binary64`

Counts

236 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	2898
1	425	2525
2	1558	2355
3	5186	2355

prune207.0ms (2.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	140	8	148
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	142	8	150

Error

0.0b

Counts

150 → 8

Alt Table

Status	Error	Program
	18.5b	(fma.f64 (/.f64 y a) z x)
	29.3b	(+.f64 x (/.f64 (.f64 (sqrt.f64 (.f64 y (-.f64 z t))) (sqrt.f64 (*.f64 y (-.f64 z t)))) a))
	7.2b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
▶	7.0b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
	7.0b	(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
	7.9b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) a)))
	7.4b	(+.f64 x (/.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (-.f64 z t))) a))
	31.9b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 a)) (/.f64 (-.f64 z t) (sqrt.f64 a))))

Compiler

Compiled 2699 to 809 computations (70% saved)

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (-.f64 z t))
✓	0.0b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
✓	8.3b	(.f64 (.f64 y (-.f64 z t)) (/.f64 1 a))

series97.0ms (1.1%)

Counts

2 → 108

Calls

2 calls:

58.0ms	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
39.0ms	(.f64 (.f64 y (-.f64 z t)) (/.f64 1 a))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
13×	`associate-r_binary64`
12×	`prod-exp_binary64`
10×	`*-un-lft-identity_binary64`

Counts

2 → 60

Calls

2 calls:

15.0ms	(.f64 (.f64 y (-.f64 z t)) (/.f64 1 a))
6.0ms	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))

simplify155.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

627×	`distribute-rgt-in_binary64`
613×	`distribute-lft-in_binary64`
359×	`fma-def_binary64`
140×	`associate-l_binary64`
136×	`fma-neg_binary64`

Counts

168 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	134	2264
1	362	1850
2	1278	1848
3	4946	1848
4	4985	1848

prune248.0ms (2.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	176	8	184

Error

0.0b

Counts

184 → 8

Alt Table

Status	Error	Program
	18.5b	(fma.f64 (/.f64 y a) z x)
	29.3b	(+.f64 x (/.f64 (.f64 (sqrt.f64 (.f64 y (-.f64 z t))) (sqrt.f64 (*.f64 y (-.f64 z t)))) a))
	7.2b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
✓	7.0b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
▶	7.0b	(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
	7.9b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) a)))
	7.4b	(+.f64 x (/.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (-.f64 z t))) a))
	31.9b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 a)) (/.f64 (-.f64 z t) (sqrt.f64 a))))

Compiler

Compiled 3470 to 1340 computations (61.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (-.f64 z t))
✓	0.0b	(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
✓	0.8b	(/.f64 1 (/.f64 a (*.f64 y (-.f64 z t))))
✓	8.1b	(/.f64 a (*.f64 y (-.f64 z t)))

series164.0ms (1.8%)

Counts

3 → 156

Calls

3 calls:

64.0ms	(/.f64 a (*.f64 y (-.f64 z t)))
61.0ms	(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
39.0ms	(/.f64 1 (/.f64 a (*.f64 y (-.f64 z t))))

rewrite69.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`times-frac_binary64`
29×	`add-exp-log_binary64`
27×	`*-un-lft-identity_binary64`
24×	`add-sqr-sqrt_binary64`
24×	`add-cube-cbrt_binary64`

Counts

3 → 109

Calls

3 calls:

24.0ms	(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
15.0ms	(/.f64 a (*.f64 y (-.f64 z t)))
13.0ms	(/.f64 1 (/.f64 a (*.f64 y (-.f64 z t))))

simplify245.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

476×	`fma-def_binary64`
446×	`distribute-rgt-in_binary64`
412×	`distribute-lft-in_binary64`
290×	`associate-/l/_binary64`
179×	`fma-neg_binary64`

Counts

265 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	197	4358
1	493	3727
2	1854	3499
3	4842	3499
4	4981	3499

prune280.0ms (3.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	254	3	257
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	257	8	265

Error

0.0b

Counts

265 → 8

Alt Table

Status	Error	Program
	7.3b	(+.f64 x (/.f64 1 (*.f64 (/.f64 1 y) (/.f64 a (-.f64 z t)))))
▶	7.2b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
✓	7.0b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
✓	7.0b	(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
	7.9b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) a)))
	7.4b	(+.f64 x (/.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (-.f64 z t))) a))
	34.1b	(/.f64 (-.f64 (.f64 x x) (.f64 (/.f64 1 (/.f64 a (.f64 y (-.f64 z t)))) (/.f64 1 (/.f64 a (.f64 y (-.f64 z t)))))) (-.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t))))))
	31.9b	(+.f64 x (/.f64 (/.f64 y (sqrt.f64 a)) (/.f64 (sqrt.f64 a) (-.f64 z t))))

Compiler

Compiled 5085 to 1853 computations (63.6% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (-.f64 z t))
✓	0.0b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
✓	7.4b	(/.f64 y (/.f64 a (-.f64 z t)))

series132.0ms (1.5%)

Counts

3 → 132

Calls

3 calls:

59.0ms	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
40.0ms	(/.f64 y (/.f64 a (-.f64 z t)))
33.0ms	(/.f64 a (-.f64 z t))

rewrite231.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
106×	`*-un-lft-identity_binary64`
104×	`add-sqr-sqrt_binary64`
72×	`add-cube-cbrt_binary64`
26×	`associate-/r*_binary64`

Counts

3 → 160

Calls

3 calls:

168.0ms	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
13.0ms	(/.f64 y (/.f64 a (-.f64 z t)))
8.0ms	(/.f64 a (-.f64 z t))

simplify208.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

526×	`times-frac_binary64`
444×	`fma-def_binary64`
427×	`distribute-rgt-in_binary64`
403×	`distribute-lft-in_binary64`
202×	`associate-/r/_binary64`

Counts

292 → 250

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	298	5248
1	687	4778
2	2318	4647
3	5032	4647

prune320.0ms (3.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	248	2	250
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	251	7	258

Error

0.0b

Counts

258 → 7

Alt Table

Status	Error	Program
	31.9b	(+.f64 x (/.f64 (/.f64 y (sqrt.f64 a)) (/.f64 (sqrt.f64 a) (-.f64 z t))))
	33.7b	(/.f64 (-.f64 (.f64 x x) (.f64 (/.f64 y (/.f64 a (-.f64 z t))) (/.f64 y (/.f64 a (-.f64 z t))))) (-.f64 x (/.f64 y (/.f64 a (-.f64 z t)))))
	7.3b	(+.f64 x (/.f64 1 (*.f64 (/.f64 1 y) (/.f64 a (-.f64 z t)))))
✓	7.0b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
✓	7.0b	(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
	7.9b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) a)))
	3.3b	(+.f64 x (/.f64 (/.f64 y a) (/.f64 1 (-.f64 z t))))

Compiler

Compiled 4730 to 1190 computations (74.8% saved)

regimes2.4s (26.7%)

Accuracy

Total 0.7b remaining (98.3%)

Threshold costs 0.7b (98.3%)

Counts

98 → 3

Compiler

Compiled 16190 to 10122 computations (37.5% saved)

bsearch63.0ms (0.7%)

Steps

Iters	Range		Point
4	6.696402572781159e-38	5.680795044156463e-23	1.706055111709416e-29
11	-1.0618791638913521e+58	-4.015989318026583e+37	-9.764712075529109e+47

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	57
1	37	57
2	41	57
3	43	57
4	44	57
5	43	57

end1.0ms (0%)

Compiler: Compiled 44 to 25 computations (43.2% saved)

sample1.8s (19.9%)

Algorithm

1×

intervals

Results

543.0ms	8000×	body	128	valid
295.0ms	2534×	body	128	invalid

Compiler

Compiled 196 to 119 computations (39.3% saved)

Details

analyze2.0s (21.6%)

sample63.0ms (0.7%)

simplify105.0ms (1.2%)

prune7.0ms (0.1%)

localize13.0ms (0.1%)

series97.0ms (1.1%)

rewrite25.0ms (0.3%)

simplify82.0ms (0.9%)

prune207.0ms (2.3%)

localize15.0ms (0.2%)

series97.0ms (1.1%)

rewrite28.0ms (0.3%)

simplify155.0ms (1.7%)

prune248.0ms (2.7%)

localize16.0ms (0.2%)

series164.0ms (1.8%)

rewrite69.0ms (0.8%)

simplify245.0ms (2.7%)

prune280.0ms (3.1%)

localize13.0ms (0.1%)

series132.0ms (1.5%)

rewrite231.0ms (2.5%)

simplify208.0ms (2.3%)

prune320.0ms (3.5%)

regimes2.4s (26.7%)

bsearch63.0ms (0.7%)

simplify9.0ms (0.1%)

end1.0ms (0%)

sample1.8s (19.9%)

Profiling