Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.3s (29.4%)

Results

560.0ms	2039×	body	1024	valid
363.0ms	4375×	body	128	valid
228.0ms	1065×	body	512	valid
81.0ms	546×	body	256	valid
78.0ms	231×	body	2048	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`rules-21_binary64`
1×	`rules-53-rev_binary64`
1×	`1-exp_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	11	11

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

30.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.3b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(cbrt.f64 (+.f64 x 1))
✓	0.6b	(cbrt.f64 x)
✓	3.9b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

series46.0ms (1%)

Counts

3 → 36

Calls

3 calls:

34.0ms	(cbrt.f64 x)
8.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
4.0ms	(cbrt.f64 (+.f64 x 1))

rewrite62.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

702×	`prod-diff_binary64`
684×	`log1p-expm1-u_binary64`
684×	`expm1-log1p-u_binary64`
148×	`egg-rr`
67×	`add-sqr-sqrt_binary64`

Counts

3 → 148

Calls

3 calls:

59.0ms	(cbrt.f64 (+.f64 x 1))
59.0ms	(cbrt.f64 x)
59.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	161	20
2	1954	20
3	5659	20
0	0	0
1	0	0

simplify96.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

345×	`fma-neg_binary64`
331×	`rules-21_binary64`
243×	`rules-4_binary64`
241×	`rules-11_binary64`
170×	`rules-20_binary64`

Counts

184 → 195

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	851
1	234	825
2	881	663
3	4262	560
4	4892	560
5	4978	560
6	4950	560

prune175.0ms (3.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	189	6	195
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	190	6	196

Error

13.7b

Counts

196 → 6

Alt Table

Status	Error	Program
	51.0b	(+.f64 (fma.f64 (pow.f64 (+.f64 x 1) 1/6) (pow.f64 (+.f64 x 1) 1/6) (neg.f64 (.f64 (cbrt.f64 (cbrt.f64 x)) (pow.f64 (pow.f64 x 2/3) 1/3)))) (fma.f64 (neg.f64 (cbrt.f64 (cbrt.f64 x))) (pow.f64 (pow.f64 x 2/3) 1/3) (.f64 (cbrt.f64 (cbrt.f64 x)) (pow.f64 (pow.f64 x 2/3) 1/3))))
	45.4b	(fma.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x))) (fma.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9)))
	30.4b	(-.f64 (cbrt.f64 (+.f64 x 1)) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3))
	30.5b	(-.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 3) (cbrt.f64 x))
	51.2b	(/.f64 (-.f64 (+.f64 x 1) x) (+.f64 (pow.f64 (+.f64 x 1) 2/3) (+.f64 (pow.f64 x 2/3) (cbrt.f64 (*.f64 (+.f64 x 1) x)))))
▶	30.3b	(*.f64 (cbrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))) (pow.f64 (cbrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))) 2))

Compiler

Compiled 3813 to 2624 computations (31.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cbrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))
	0.3b	(cbrt.f64 (+.f64 x 1))
	0.6b	(cbrt.f64 x)
	3.9b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

series36.0ms (0.8%)

Counts

1 → 12

Calls

1 calls:

36.0ms

(cbrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))

rewrite54.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

749×	`log1p-expm1-u_binary64`
749×	`expm1-log1p-u_binary64`
722×	`prod-diff_binary64`
74×	`add-sqr-sqrt_binary64`
70×	`add-cbrt-cube_binary64`

Counts

1 → 32

Calls

1 calls:

53.0ms

(cbrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	180	13
2	2155	13
3	6141	13
0	0	0
1	0	0

simplify44.0ms (1%)

Algorithm

1×	egg-herbie

Rules

771×	`fma-def_binary64`
514×	`fma-neg_binary64`
495×	`rules-13_binary64`
377×	`rules-20_binary64`
219×	`rules-14-rev_binary64`

Counts

44 → 56

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	1285
1	365	1255
2	1526	1037
3	5116	1037

prune523.0ms (11.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	502	0	502
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	502	6	508

Error

13.7b

Counts

508 → 6

Alt Table

Status	Error	Program
	51.0b	(+.f64 (fma.f64 (pow.f64 (+.f64 x 1) 1/6) (pow.f64 (+.f64 x 1) 1/6) (neg.f64 (.f64 (cbrt.f64 (cbrt.f64 x)) (pow.f64 (pow.f64 x 2/3) 1/3)))) (fma.f64 (neg.f64 (cbrt.f64 (cbrt.f64 x))) (pow.f64 (pow.f64 x 2/3) 1/3) (.f64 (cbrt.f64 (cbrt.f64 x)) (pow.f64 (pow.f64 x 2/3) 1/3))))
	45.4b	(fma.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x))) (fma.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9)))
▶	30.4b	(-.f64 (cbrt.f64 (+.f64 x 1)) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3))
	30.5b	(-.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 3) (cbrt.f64 x))
	51.2b	(/.f64 (-.f64 (+.f64 x 1) x) (+.f64 (pow.f64 (+.f64 x 1) 2/3) (+.f64 (pow.f64 x 2/3) (cbrt.f64 (*.f64 (+.f64 x 1) x)))))
✓	30.3b	(*.f64 (cbrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))) (pow.f64 (cbrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))) 2))

Compiler

Compiled 17249 to 12541 computations (27.3% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (cbrt.f64 x))
	0.6b	(cbrt.f64 x)
✓	0.7b	(pow.f64 (cbrt.f64 (cbrt.f64 x)) 3)
✓	20.6b	(-.f64 (cbrt.f64 (+.f64 x 1)) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3))

series589.0ms (12.9%)

Counts

3 → 36

Calls

3 calls:

308.0ms	(cbrt.f64 (cbrt.f64 x))
270.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 x)) 3)
11.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3))

rewrite81.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

837×	`prod-diff_binary64`
822×	`expm1-log1p-u_binary64`
207×	`egg-rr`
82×	`add-sqr-sqrt_binary64`
81×	`log1p-expm1-u_binary64`

Counts

3 → 207

Calls

3 calls:

76.0ms	(cbrt.f64 (cbrt.f64 x))
76.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 x)) 3)
76.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	208	18
2	2370	18
3	5298	18
0	0	0
1	0	0

simplify89.0ms (2%)

Algorithm

1×	egg-herbie

Rules

802×	`rules-20_binary64`
791×	`fma-def_binary64`
268×	`rules-21_binary64`
240×	`fma-neg_binary64`
179×	`rules-4_binary64`

Counts

243 → 236

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	606
1	197	584
2	703	499
3	3326	444
4	4967	444
5	4977	444

prune276.0ms (6.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	267	3	270
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	268	8	276

Error

13.7b

Counts

276 → 8

Alt Table

Status	Error	Program
	45.4b	(fma.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x))) (fma.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9)))
✓	30.4b	(-.f64 (cbrt.f64 (+.f64 x 1)) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3))
	51.4b	(+.f64 (fma.f64 (pow.f64 (+.f64 x 1) 1/6) (pow.f64 (+.f64 x 1) 1/6) (neg.f64 (.f64 (pow.f64 x 1/9) (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2/3)) 3)))) (fma.f64 (neg.f64 (pow.f64 x 1/9)) (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2/3)) 3) (.f64 (pow.f64 x 1/9) (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2/3)) 3))))
	51.2b	(/.f64 (-.f64 (+.f64 x 1) x) (+.f64 (pow.f64 (+.f64 x 1) 2/3) (+.f64 (pow.f64 x 2/3) (cbrt.f64 (*.f64 (+.f64 x 1) x)))))
	51.4b	(+.f64 (fma.f64 (pow.f64 (+.f64 x 1) 1/6) (pow.f64 (+.f64 x 1) 1/6) (neg.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 x) 2/3) (pow.f64 (cbrt.f64 x) 1/6)) (pow.f64 (cbrt.f64 x) 1/6)))) (fma.f64 (neg.f64 (.f64 (pow.f64 (cbrt.f64 x) 2/3) (pow.f64 (cbrt.f64 x) 1/6))) (pow.f64 (cbrt.f64 x) 1/6) (.f64 (*.f64 (pow.f64 (cbrt.f64 x) 2/3) (pow.f64 (cbrt.f64 x) 1/6)) (pow.f64 (cbrt.f64 x) 1/6))))
✓	30.3b	(*.f64 (cbrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))) (pow.f64 (cbrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))) 2))
	51.3b	(+.f64 (fma.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/3) (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/3) (neg.f64 (cbrt.f64 x))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 x) 2/3)) (pow.f64 x 1/9) (cbrt.f64 x)))
▶	30.5b	(-.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 3) (cbrt.f64 x))

Compiler

Compiled 6767 to 4770 computations (29.5% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(cbrt.f64 (+.f64 x 1))
✓	0.4b	(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 3)
	0.6b	(cbrt.f64 x)
✓	20.9b	(-.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 3) (cbrt.f64 x))

series18.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

11.0ms	(-.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 3) (cbrt.f64 x))
8.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 3)

rewrite103.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

816×	`expm1-log1p-u_binary64`
813×	`prod-diff_binary64`
171×	`egg-rr`
82×	`add-sqr-sqrt_binary64`
81×	`log1p-expm1-u_binary64`

Counts

2 → 171

Calls

2 calls:

99.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 3)
99.0ms	(-.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 3) (cbrt.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	208	17
2	2361	17
3	5238	17
0	0	0
1	0	0

simplify61.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

420×	`fma-neg_binary64`
298×	`rules-11_binary64`
247×	`rules-20_binary64`
225×	`fma-def_binary64`
175×	`rules-13_binary64`

Counts

195 → 218

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	832
1	282	804
2	1134	638
3	4974	638
4	5083	638

prune280.0ms (6.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	301	3	304
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	303	9	312

Error

13.7b

Counts

312 → 9

Alt Table

Status	Error	Program
	45.4b	(fma.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x))) (fma.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9)))
✓	30.4b	(-.f64 (cbrt.f64 (+.f64 x 1)) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3))
	51.4b	(+.f64 (fma.f64 (pow.f64 (+.f64 x 1) 1/6) (pow.f64 (+.f64 x 1) 1/6) (neg.f64 (.f64 (pow.f64 x 1/9) (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2/3)) 3)))) (fma.f64 (neg.f64 (pow.f64 x 1/9)) (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2/3)) 3) (.f64 (pow.f64 x 1/9) (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2/3)) 3))))
	51.2b	(/.f64 (-.f64 (+.f64 x 1) x) (+.f64 (pow.f64 (+.f64 x 1) 2/3) (+.f64 (pow.f64 x 2/3) (cbrt.f64 (*.f64 (+.f64 x 1) x)))))
	51.1b	(+.f64 (fma.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2/3)) (*.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 1/9)) (pow.f64 (cbrt.f64 (+.f64 x 1)) 2/3)) (neg.f64 (cbrt.f64 x))) (fma.f64 (neg.f64 (pow.f64 x 1/6)) (pow.f64 x 1/6) (cbrt.f64 x)))
	51.1b	(+.f64 (fma.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 1/9)) (*.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2/3) (cbrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2/3))) (neg.f64 (cbrt.f64 x))) (fma.f64 (neg.f64 (pow.f64 x 1/6)) (pow.f64 x 1/6) (cbrt.f64 x)))
	51.3b	(+.f64 (fma.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/3) (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/3) (neg.f64 (cbrt.f64 x))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 x) 2/3)) (pow.f64 x 1/9) (cbrt.f64 x)))
✓	30.3b	(*.f64 (cbrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))) (pow.f64 (cbrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))) 2))
	30.5b	(-.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 3)) 3) (cbrt.f64 x))

Compiler

Compiled 7010 to 5056 computations (27.9% saved)

regimes322.0ms (7.1%)

Accuracy

Total 0.1b remaining (0.6%)

Threshold costs 0.1b (0.6%)

Counts

121 → 3

Compiler

Compiled 4205 to 3226 computations (23.3% saved)

bsearch39.0ms (0.9%)

Steps

Iters	Range		Point
10	258.5703696741409	428556599157938050.0	79786.94334344249
10	-33273678.46348828	-0.0005681719633583311	-4620.5717379085545

Compiler

Compiled 2 to 1 computations (50% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	92
1	40	92
2	39	92

end283.0ms (6.2%)

Compiler: Compiled 364 to 287 computations (21.2% saved)

Details

analyze1.0ms (0%)

sample1.3s (29.4%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series46.0ms (1%)

rewrite62.0ms (1.4%)

simplify96.0ms (2.1%)

prune175.0ms (3.8%)

localize8.0ms (0.2%)

series36.0ms (0.8%)

rewrite54.0ms (1.2%)

simplify44.0ms (1%)

prune523.0ms (11.5%)

localize7.0ms (0.2%)

series589.0ms (12.9%)

rewrite81.0ms (1.8%)

simplify89.0ms (2%)

prune276.0ms (6.1%)

localize7.0ms (0.2%)

series18.0ms (0.4%)

rewrite103.0ms (2.3%)

simplify61.0ms (1.3%)

prune280.0ms (6.1%)

regimes322.0ms (7.1%)

bsearch39.0ms (0.9%)

simplify2.0ms (0%)

end283.0ms (6.2%)

Profiling