Details

analyze934.0ms (14.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
14%	85.8%	0.1%	7
22.6%	77.2%	0.1%	8
23.8%	74.5%	1.7%	9
40%	56%	4%	10
47.3%	48.7%	4%	11
48.4%	45.8%	5.8%	12
58.6%	32.4%	9%	13
63.4%	27.5%	9%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample28.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	31×	body	128	invalid

Compiler

Compiled 24 to 16 computations (33.3% saved)

simplify243.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

907×	`associate-/l*_binary64`
740×	`associate-/l/_binary64`
677×	`fma-def_binary64`
607×	`associate-/r/_binary64`
557×	`associate-*l/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	17	10
2	23	10
3	36	10
4	41	10
5	47	10
6	51	8
7	61	8
8	228	8
9	761	8
10	851	8
11	964	8
12	975	8
13	980	8
14	985	8
15	2231	8
16	2288	8
17	2637	8
18	2689	8
19	2901	8
20	3031	8
21	3278	8
22	3700	8
23	4109	8
24	4157	8
25	4872	8
26	4997	8
27	4889	8

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.1b	(fma.f64 x (/.f64 y z) x)
	11.8b	(/.f64 (*.f64 x (+.f64 y z)) z)

Compiler

Compiled 54 to 30 computations (44.4% saved)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.9b	(fma.f64 x (/.f64 y z) x)

series27.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

27.0ms

(fma.f64 x (/.f64 y z) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma.f64 x (/.f64 y z) x)

simplify134.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

635×	`fma-def_binary64`
449×	`associate-/l/_binary64`
410×	`distribute-rgt-in_binary64`
404×	`distribute-rgt-out_binary64`
400×	`unswap-sqr_binary64`

Counts

46 → 24

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	451
1	32	374
2	63	374
3	171	374
4	650	374
5	2482	374
6	3613	374
7	3881	374
8	4329	374
9	5248	374

prune27.0ms (0.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	20	4	24
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	21	5	26

Error

0.0b

Counts

26 → 5

Alt Table

Status	Error	Program
▶	3.1b	(+.f64 (*.f64 x (/.f64 y z)) x)
	4.1b	(+.f64 (/.f64 (*.f64 y x) z) x)
	11.8b	(/.f64 (*.f64 x (+.f64 y z)) z)
	32.1b	(*.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x)) (sqrt.f64 (fma.f64 x (/.f64 y z) x)))
	4.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))

Compiler

Compiled 382 to 118 computations (69.1% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 x (/.f64 y z)) x)
✓	7.0b	(*.f64 x (/.f64 y z))

series30.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

17.0ms	(*.f64 x (/.f64 y z))
13.0ms	(+.f64 (*.f64 x (/.f64 y z)) x)

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

2 → 48

Calls

2 calls:

16.0ms	(+.f64 (*.f64 x (/.f64 y z)) x)
6.0ms	(*.f64 x (/.f64 y z))

simplify161.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

407×	`associate-/l/_binary64`
352×	`associate-/r*_binary64`
337×	`associate-l_binary64`
324×	`associate-/r/_binary64`
269×	`fma-neg_binary64`

Counts

120 → 76

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	1126
1	235	1047
2	773	1042
3	2269	1039
4	4322	1039
5	4960	1039

prune100.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	72	4	76
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	75	6	81

Error

0.0b

Counts

81 → 6

Alt Table

Status	Error	Program
▶	2.6b	(+.f64 (.f64 (.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 y) z)) x)
	11.8b	(/.f64 (*.f64 x (+.f64 y z)) z)
✓	3.1b	(+.f64 (*.f64 x (/.f64 y z)) x)
	4.2b	(+.f64 (.f64 (.f64 x y) (/.f64 1 z)) x)
	3.7b	(+.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z))) x)
	3.5b	(+.f64 (.f64 (.f64 x (*.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z)))) (cbrt.f64 (/.f64 y z))) x)

Compiler

Compiled 1146 to 368 computations (67.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 x (.f64 (cbrt.f64 y) (cbrt.f64 y)))
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.7b	(cbrt.f64 y)
✓	3.8b	(.f64 (.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 y) z))

series796.0ms (12.2%)

Counts

4 → 84

Calls

4 calls:

627.0ms	(.f64 x (.f64 (cbrt.f64 y) (cbrt.f64 y)))
73.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
49.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 y) z))
46.0ms	(cbrt.f64 y)

rewrite127.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
32×	`add-exp-log_binary64`
29×	`associate-r_binary64`
28×	`cbrt-prod_binary64`
27×	`*-un-lft-identity_binary64`

Counts

4 → 125

Calls

4 calls:

89.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 y) z))
13.0ms	(.f64 x (.f64 (cbrt.f64 y) (cbrt.f64 y)))
8.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify170.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

621×	`unswap-sqr_binary64`
589×	`associate-*l/_binary64`
440×	`times-frac_binary64`
320×	`associate-l_binary64`
266×	`associate-r_binary64`

Counts

209 → 185

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	159	2293
1	364	1911
2	1572	1798
3	3571	1744
4	4823	1744
5	4951	1744

prune301.0ms (4.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	220	1	221
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	221	6	227

Error

0.0b

Counts

227 → 6

Alt Table

Status	Error	Program
✓	3.1b	(+.f64 (*.f64 x (/.f64 y z)) x)
	4.2b	(+.f64 (.f64 (.f64 x y) (/.f64 1 z)) x)
▶	2.7b	(+.f64 (.f64 (.f64 x (.f64 (cbrt.f64 y) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y))))) (/.f64 (cbrt.f64 y) z)) x)
	3.7b	(+.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z))) x)
	11.8b	(/.f64 (*.f64 x (+.f64 y z)) z)
	3.5b	(+.f64 (.f64 (.f64 x (*.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z)))) (cbrt.f64 (/.f64 y z))) x)

Compiler

Compiled 4376 to 1310 computations (70.1% saved)

localize30.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)))
	0.7b	(cbrt.f64 y)
✓	0.7b	(cbrt.f64 (cbrt.f64 y))
✓	3.8b	(.f64 (.f64 x (.f64 (cbrt.f64 y) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y))))) (/.f64 (cbrt.f64 y) z))

series957.0ms (14.7%)

Counts

3 → 60

Calls

3 calls:

492.0ms

(cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)))

431.0ms

(cbrt.f64 (cbrt.f64 y))

33.0ms

(*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y))))) (/.f64 (cbrt.f64 y) z))

rewrite55.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-exp-log_binary64`
23×	`add-cbrt-cube_binary64`
22×	`associate-r_binary64`
20×	`cbrt-unprod_binary64`
20×	`prod-exp_binary64`

Counts

3 → 81

Calls

3 calls:

28.0ms

(*.f64 (*.f64 x (*.f64 (cbrt.f64 y) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y))))) (/.f64 (cbrt.f64 y) z))

5.0ms

(cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)))

2.0ms

(cbrt.f64 (cbrt.f64 y))

simplify261.0ms (4%)

Algorithm

1×	egg-herbie

Rules

619×	`associate-*l/_binary64`
480×	`times-frac_binary64`
428×	`associate-l_binary64`
318×	`associate-r_binary64`
268×	`associate-/r*_binary64`

Counts

141 → 118

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	154	3153
1	397	2301
2	1691	1448
3	3660	1412
4	4406	1352
5	4855	1352
6	4925	1352

prune249.0ms (3.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	208	6	214

Error

0.0b

Counts

214 → 6

Alt Table

Status	Error	Program
✓	3.1b	(+.f64 (*.f64 x (/.f64 y z)) x)
	4.2b	(+.f64 (.f64 (.f64 x y) (/.f64 1 z)) x)
✓	2.7b	(+.f64 (.f64 (.f64 x (.f64 (cbrt.f64 y) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y))))) (/.f64 (cbrt.f64 y) z)) x)
	3.7b	(+.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z))) x)
	11.8b	(/.f64 (*.f64 x (+.f64 y z)) z)
	3.5b	(+.f64 (.f64 (.f64 x (*.f64 (cbrt.f64 (/.f64 y z)) (cbrt.f64 (/.f64 y z)))) (cbrt.f64 (/.f64 y z))) x)

Compiler

Compiled 5658 to 1376 computations (75.7% saved)

regimes716.0ms (11%)

Accuracy

Total 2.3b remaining (98.9%)

Threshold costs 0b (0%)

Counts

69 → 2

Compiler

Compiled 5152 to 2866 computations (44.4% saved)

bsearch45.0ms (0.7%)

Steps

Iters	Range		Point
9	7.593352039700157e-286	8.141788655894956e-281	7.661779887729346e-286

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	57
1	27	57
2	27	57

end1.0ms (0%)

Compiler: Compiled 39 to 20 computations (48.7% saved)

sample1.1s (16.2%)

Algorithm

1×

intervals

Results

456.0ms	8000×	body	128	valid
38.0ms	733×	body	128	invalid

Compiler

Compiled 148 to 81 computations (45.3% saved)

Details

analyze934.0ms (14.3%)

sample28.0ms (0.4%)

simplify243.0ms (3.7%)

prune6.0ms (0.1%)

localize9.0ms (0.1%)

series27.0ms (0.4%)

rewrite1.0ms (0%)

simplify134.0ms (2.1%)

prune27.0ms (0.4%)

localize10.0ms (0.2%)

series30.0ms (0.5%)

rewrite29.0ms (0.4%)

simplify161.0ms (2.5%)

prune100.0ms (1.5%)

localize12.0ms (0.2%)

series796.0ms (12.2%)

rewrite127.0ms (2%)

simplify170.0ms (2.6%)

prune301.0ms (4.6%)

localize30.0ms (0.5%)

series957.0ms (14.7%)

rewrite55.0ms (0.8%)

simplify261.0ms (4%)

prune249.0ms (3.8%)

regimes716.0ms (11%)

bsearch45.0ms (0.7%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.1s (16.2%)

Profiling