Details

analyze1.3s (17.1%)

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
10.1%	89.6%	0.2%	11
15.2%	84.6%	0.2%	12
20.5%	79.3%	0.2%	13
21.6%	77.1%	1.3%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.4s (19.5%)

Results

1.0s	8256×	body	128	valid
327.0ms	2716×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify65.0ms (0.9%)

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

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	6.9b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
▶	5.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 45 computations (40.8% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	0.0b	(*.f64 y (-.f64 z t))
✓	6.7b	(/.f64 (*.f64 y (-.f64 z t)) a)

series55.0ms (0.7%)

Counts

3 → 144

Calls

3 calls:

29.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
20.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
6.0ms	(*.f64 y (-.f64 z t))

rewrite21.0ms (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:

6.0ms	(/.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))

simplify71.0ms (1%)

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

prune118.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	142	6	148
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	143	7	150

Error

0.0b

Counts

150 → 7

Alt Table

Status	Error	Program
	38.2b	(cbrt.f64 (pow.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x) 3))
	6.9b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
▶	3.0b	(+.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
	5.8b	(+.f64 x (-.f64 (/.f64 (.f64 y z) a) (/.f64 (.f64 y t) a)))
	6.2b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
	5.8b	(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
	35.4b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 a)) (/.f64 (-.f64 z t) (sqrt.f64 a))))

Compiler

Compiled 2667 to 793 computations (70.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
✓	0.5b	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
✓	0.5b	(cbrt.f64 a)
✓	4.9b	(.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a)))

series775.0ms (10.5%)

Counts

4 → 96

Calls

4 calls:

654.0ms	(/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
50.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a)))
38.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
33.0ms	(cbrt.f64 a)

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64`
43×	`times-frac_binary64`
40×	`associate-r_binary64`
36×	`cbrt-prod_binary64`

Counts

4 → 151

Calls

4 calls:

17.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a)))
5.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
4.0ms	(/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
1.0ms	(cbrt.f64 a)

simplify123.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

516×	`fma-def_binary64`
334×	`associate-/r/_binary64`
183×	`associate-*r/_binary64`
182×	`associate-/r*_binary64`
179×	`distribute-rgt-in_binary64`

Counts

247 → 234

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	206	4014
1	505	2982
2	2258	2923
3	3938	2868
4	5042	2868

prune196.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	268	2	270
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	268	9	277

Error

0.0b

Counts

277 → 9

Alt Table

Status	Error	Program
	5.8b	(+.f64 x (-.f64 (/.f64 (.f64 y z) a) (/.f64 (.f64 y t) a)))
▶	3.1b	(+.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 (cbrt.f64 a))))))
	38.2b	(cbrt.f64 (pow.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x) 3))
	6.9b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	16.4b	(+.f64 x (.f64 (.f64 y (cbrt.f64 (/.f64 1 (*.f64 a a)))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
✓	3.0b	(+.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
	6.2b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
	5.8b	(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
	35.4b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 a)) (/.f64 (-.f64 z t) (sqrt.f64 a))))

Compiler

Compiled 6259 to 1690 computations (73% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(cbrt.f64 a)
✓	0.5b	(cbrt.f64 (cbrt.f64 a))
✓	0.6b	(cbrt.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))
✓	4.9b	(.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 (cbrt.f64 a)))))

series796.0ms (10.8%)

Counts

3 → 72

Calls

3 calls:

435.0ms

(cbrt.f64 (cbrt.f64 a))

311.0ms

(cbrt.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))

49.0ms

(*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 (cbrt.f64 a)))))

rewrite90.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-exp-log_binary64`
27×	`add-cbrt-cube_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`cbrt-unprod_binary64`
15×	`prod-exp_binary64`

Counts

3 → 77

Calls

3 calls:

13.0ms

(*.f64 (/.f64 y (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 (cbrt.f64 a)))))

3.0ms

(cbrt.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a)))

1.0ms

(cbrt.f64 (cbrt.f64 a))

simplify114.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

719×	`associate-/l/_binary64`
444×	`*-commutative_binary64`
398×	`fma-def_binary64`
191×	`associate-/r/_binary64`
189×	`log-div_binary64`

Counts

149 → 114

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	163	3546
1	389	2803
2	1809	2448
3	4387	2448
4	4974	2448

prune179.0ms (2.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	204	9	213

Error

0.0b

Counts

213 → 9

Alt Table

Status	Error	Program
▶	5.8b	(+.f64 x (-.f64 (/.f64 (.f64 y z) a) (/.f64 (.f64 y t) a)))
✓	3.1b	(+.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 (cbrt.f64 a))))))
	38.2b	(cbrt.f64 (pow.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x) 3))
	6.9b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	16.4b	(+.f64 x (.f64 (.f64 y (cbrt.f64 (/.f64 1 (*.f64 a a)))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
✓	3.0b	(+.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
	6.2b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
	5.8b	(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
	35.4b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 a)) (/.f64 (-.f64 z t) (sqrt.f64 a))))

Compiler

Compiled 6348 to 1370 computations (78.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (-.f64 (/.f64 (.f64 y z) a) (/.f64 (.f64 y t) a)))
✓	0.0b	(-.f64 (/.f64 (.f64 y z) a) (/.f64 (.f64 y t) a))
✓	6.5b	(/.f64 (*.f64 y z) a)
✓	8.1b	(/.f64 (*.f64 y t) a)

series87.0ms (1.2%)

Counts

4 → 90

Calls

4 calls:

34.0ms	(+.f64 x (-.f64 (/.f64 (.f64 y z) a) (/.f64 (.f64 y t) a)))
27.0ms	(-.f64 (/.f64 (.f64 y z) a) (/.f64 (.f64 y t) a))
14.0ms	(/.f64 (*.f64 y t) a)
12.0ms	(/.f64 (*.f64 y z) a)

rewrite51.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

105×	`times-frac_binary64`
98×	`prod-diff_binary64`
80×	`*-un-lft-identity_binary64`
75×	`add-sqr-sqrt_binary64`
73×	`add-cube-cbrt_binary64`

Counts

4 → 207

Calls

4 calls:

14.0ms	(+.f64 x (-.f64 (/.f64 (.f64 y z) a) (/.f64 (.f64 y t) a)))
8.0ms	(-.f64 (/.f64 (.f64 y z) a) (/.f64 (.f64 y t) a))
3.0ms	(/.f64 (*.f64 y t) a)
3.0ms	(/.f64 (*.f64 y z) a)

simplify209.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

925×	`times-frac_binary64`
507×	`fma-neg_binary64`
195×	`cancel-sign-sub-inv_binary64`
182×	`exp-prod_binary64`
174×	`distribute-rgt-neg-in_binary64`

Counts

297 → 320

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	287	5726
1	623	4778
2	1992	4266
3	4193	4266
4	4886	4266

prune258.0ms (3.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	318	2	320
Fresh	3	3	6
Picked	0	1	1
Done	1	1	2
Total	322	7	329

Error

0.0b

Counts

329 → 7

Alt Table

Status	Error	Program
✓	5.8b	(+.f64 x (-.f64 (/.f64 (.f64 y z) a) (/.f64 (.f64 y t) a)))
✓	3.1b	(+.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 z t) (.f64 (cbrt.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 (cbrt.f64 a))))))
	38.2b	(cbrt.f64 (pow.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x) 3))
	16.4b	(+.f64 x (.f64 (.f64 y (cbrt.f64 (/.f64 1 (*.f64 a a)))) (/.f64 (-.f64 z t) (cbrt.f64 a))))
	2.7b	(+.f64 x (*.f64 (/.f64 y a) (-.f64 z t)))
	6.2b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
	6.9b	(+.f64 (+.f64 (.f64 (/.f64 z a) y) x) (.f64 (neg.f64 (/.f64 y 1)) (/.f64 t a)))

Compiler

Compiled 9314 to 1650 computations (82.3% saved)

regimes1.2s (16.7%)

Accuracy

Total 1.3b remaining (98.9%)

Threshold costs 0b (0%)

Counts

85 → 3

Compiler

Compiled 13653 to 8850 computations (35.2% saved)

bsearch46.0ms (0.6%)

Steps

Iters	Range		Point
5	1.9562311358258616e-88	7.777938587842933e-88	6.996154411165649e-88
8	-3.876135808164779e+30	-2.274666984782897e+27	-1.681862728285677e+28

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
10×	`*-commutative_binary64`
8×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	78
1	55	78
2	73	78
3	88	78
4	94	78
5	95	78
6	94	78

end109.0ms (1.5%)

Compiler: Compiled 248 to 148 computations (40.3% saved)

Details

analyze1.3s (17.1%)

sample1.4s (19.5%)

simplify65.0ms (0.9%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series55.0ms (0.7%)

rewrite21.0ms (0.3%)

simplify71.0ms (1%)

prune118.0ms (1.6%)

localize10.0ms (0.1%)

series775.0ms (10.5%)

rewrite39.0ms (0.5%)

simplify123.0ms (1.7%)

prune196.0ms (2.6%)

localize15.0ms (0.2%)

series796.0ms (10.8%)

rewrite90.0ms (1.2%)

simplify114.0ms (1.5%)

prune179.0ms (2.4%)

localize9.0ms (0.1%)

series87.0ms (1.2%)

rewrite51.0ms (0.7%)

simplify209.0ms (2.8%)

prune258.0ms (3.5%)

regimes1.2s (16.7%)

bsearch46.0ms (0.6%)

simplify5.0ms (0.1%)

end109.0ms (1.5%)

Profiling