Details

analyze1.9s (18.5%)

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
3.1%	96.7%	0.2%	8
17.2%	82.7%	0.2%	9
21.8%	78%	0.2%	10
30%	68.8%	1.2%	11
31.8%	65.3%	2.9%	12
40.1%	55.3%	4.6%	13
44.5%	50.1%	5.4%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample67.0ms (0.7%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
6.0ms	70×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify85.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

938×	`fma-def_binary64`
721×	`fma-neg_binary64`
220×	`cancel-sign-sub-inv_binary64`
144×	`distribute-rgt-in_binary64`
108×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	16	11
2	37	11
3	72	11
4	140	11
5	242	11
6	395	11
7	682	11
8	1049	11
9	1368	11
10	1492	11
11	1530	11
12	1536	11
13	1541	11
14	1541	11
15	1456	11

prune9.0ms (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

1.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	1.4b	(fma.f64 (/.f64 x y) (-.f64 z t) t)
▶	1.4b	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

Compiler

Compiled 71 to 39 computations (45.1% saved)

localize14.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)
✓	7.2b	(*.f64 (/.f64 x y) (-.f64 z t))

rewrite85.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-cube-cbrt_binary64`
15×	`pow1_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`
10×	`prod-diff_binary64`

Counts

2 → 96

Calls

2 calls:

39.0ms	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)
33.0ms	(*.f64 (/.f64 x y) (-.f64 z t))

series276.0ms (2.7%)

Counts

2 → 96

Calls

2 calls:

147.0ms	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)
129.0ms	(*.f64 (/.f64 x y) (-.f64 z t))

simplify262.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

807×	`fma-def_binary64`
520×	`times-frac_binary64`
518×	`fma-neg_binary64`
318×	`cancel-sign-sub-inv_binary64`
141×	`associate-l_binary64`

Counts

192 → 323

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	2570
1	469	2333
2	1856	2285
3	4414	2284
4	4964	2284
5	4838	2284

prune225.0ms (2.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	316	7	323
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	317	8	325

Error

Counts

325 → 8

Alt Table

Status	Error	Program
	1.8b	(+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 z) (neg.f64 (.f64 (cbrt.f64 t) (.f64 (cbrt.f64 t) (cbrt.f64 t))))) (/.f64 x y)) (fma.f64 (/.f64 x y) 0 t))
	38.4b	(*.f64 (-.f64 (/.f64 z y) (/.f64 t y)) x)
	19.0b	(+.f64 (.f64 (cbrt.f64 (.f64 (.f64 (/.f64 x y) (-.f64 z t)) (.f64 (/.f64 x y) (-.f64 z t)))) (cbrt.f64 (*.f64 (/.f64 x y) (-.f64 z t)))) t)
	7.3b	(+.f64 (/.f64 (*.f64 (-.f64 z t) x) y) t)
	42.6b	(/.f64 (+.f64 (pow.f64 (.f64 (/.f64 x y) (-.f64 z t)) 3) (pow.f64 t 3)) (+.f64 (.f64 (.f64 (/.f64 x y) (-.f64 z t)) (.f64 (/.f64 x y) (-.f64 z t))) (-.f64 (.f64 t t) (.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t))))
	1.8b	(+.f64 (.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t))) t)
	1.8b	(+.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 x y) (-.f64 z t))) 3) t)
▶	1.4b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

Compiler

Compiled 3346 to 827 computations (75.3% saved)

localize13.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.3b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-cube-cbrt_binary64`
5×	`fma-udef_binary64`
4×	`pow1_binary64`
4×	`add-sqr-sqrt_binary64`
3×	`add-cbrt-cube_binary64`

Counts

1 → 33

Calls

1 calls:

24.0ms

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

series101.0ms (1%)

Counts

1 → 48

Calls

1 calls:

100.0ms

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

simplify118.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

767×	`fma-def_binary64`
587×	`fma-neg_binary64`
543×	`associate-*l/_binary64`
522×	`times-frac_binary64`
458×	`associate-*r/_binary64`

Counts

81 → 128

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	987
1	154	892
2	420	871
3	1334	869
4	4128	869
5	5411	869

prune60.0ms (0.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	128	8	136

Error

Counts

136 → 8

Alt Table

Status	Error	Program
	1.8b	(+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 z) (neg.f64 (.f64 (cbrt.f64 t) (.f64 (cbrt.f64 t) (cbrt.f64 t))))) (/.f64 x y)) (fma.f64 (/.f64 x y) 0 t))
	38.4b	(*.f64 (-.f64 (/.f64 z y) (/.f64 t y)) x)
	19.0b	(+.f64 (.f64 (cbrt.f64 (.f64 (.f64 (/.f64 x y) (-.f64 z t)) (.f64 (/.f64 x y) (-.f64 z t)))) (cbrt.f64 (*.f64 (/.f64 x y) (-.f64 z t)))) t)
	7.3b	(+.f64 (/.f64 (*.f64 (-.f64 z t) x) y) t)
▶	1.8b	(+.f64 (.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t))) t)
	42.6b	(/.f64 (+.f64 (pow.f64 (.f64 (/.f64 x y) (-.f64 z t)) 3) (pow.f64 t 3)) (fma.f64 t t (.f64 (*.f64 (/.f64 x y) (-.f64 t z)) (fma.f64 (/.f64 x y) (-.f64 t z) t))))
	1.8b	(+.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 x y) (-.f64 z t))) 3) t)
✓	1.4b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

Compiler

Compiled 928 to 290 computations (68.8% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t)))
	12.7b	(cbrt.f64 (/.f64 x y))
	12.7b	(cbrt.f64 (/.f64 x y))
✓	12.7b	(cbrt.f64 (/.f64 x y))

rewrite79.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`cbrt-div_binary64`
26×	`add-cube-cbrt_binary64`
23×	`frac-times_binary64`
14×	`distribute-rgt-in_binary64`
12×	`add-exp-log_binary64`

Counts

2 → 87

Calls

2 calls:

35.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t)))
25.0ms	(cbrt.f64 (/.f64 x y))

series2.6s (25.7%)

Counts

2 → 72

Calls

2 calls:

2.4s	(cbrt.f64 (/.f64 x y))
222.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t)))

simplify192.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

543×	`fma-def_binary64`
441×	`times-frac_binary64`
423×	`fma-neg_binary64`
320×	`cancel-sign-sub-inv_binary64`
264×	`unswap-sqr_binary64`

Counts

159 → 274

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	2222
1	501	1849
2	1847	1751
3	4516	1740
4	4965	1740

prune359.0ms (3.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	542	2	544
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	545	7	552

Error

Counts

552 → 7

Alt Table

Status	Error	Program
	1.8b	(+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 z) (neg.f64 (.f64 (cbrt.f64 t) (.f64 (cbrt.f64 t) (cbrt.f64 t))))) (/.f64 x y)) (fma.f64 (/.f64 x y) 0 t))
	38.4b	(*.f64 (-.f64 (/.f64 z y) (/.f64 t y)) x)
	1.8b	(+.f64 (.f64 (cbrt.f64 (/.f64 x y)) (.f64 (cbrt.f64 (/.f64 x y)) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t)))) t)
▶	1.8b	(+.f64 (.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) (-.f64 z t))) t)
	7.3b	(+.f64 (/.f64 (*.f64 (-.f64 z t) x) y) t)
	1.8b	(+.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 x y) (-.f64 z t))) 3) t)
✓	1.4b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

Compiler

Compiled 5615 to 1279 computations (77.2% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 x)
✓	1.0b	(.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) (-.f64 z t)))
	12.7b	(cbrt.f64 (/.f64 x y))
	12.7b	(cbrt.f64 (/.f64 x y))

rewrite74.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-cube-cbrt_binary64`
23×	`frac-times_binary64`
16×	`cbrt-div_binary64`
14×	`add-exp-log_binary64`
14×	`distribute-rgt-in_binary64`

Counts

2 → 82

Calls

2 calls:

41.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) (-.f64 z t)))
19.0ms	(cbrt.f64 x)

series712.0ms (6.9%)

Counts

2 → 60

Calls

2 calls:

525.0ms	(cbrt.f64 x)
186.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) (-.f64 z t)))

simplify183.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

863×	`times-frac_binary64`
569×	`fma-def_binary64`
274×	`unswap-sqr_binary64`
249×	`associate-r_binary64`
244×	`associate-l_binary64`

Counts

142 → 231

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	2703
1	469	2095
2	2149	1917
3	5001	1917

prune336.0ms (3.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	1311	0	1311
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	1311	7	1318

Error

Counts

1318 → 7

Alt Table

Status	Error	Program
	1.8b	(+.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (cbrt.f64 z) (neg.f64 (.f64 (cbrt.f64 t) (.f64 (cbrt.f64 t) (cbrt.f64 t))))) (/.f64 x y)) (fma.f64 (/.f64 x y) 0 t))
	38.4b	(*.f64 (-.f64 (/.f64 z y) (/.f64 t y)) x)
	1.8b	(+.f64 (.f64 (cbrt.f64 (/.f64 x y)) (.f64 (cbrt.f64 (/.f64 x y)) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t)))) t)
✓	1.8b	(+.f64 (.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) (-.f64 z t))) t)
	7.3b	(+.f64 (/.f64 (*.f64 (-.f64 z t) x) y) t)
	1.8b	(+.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 x y) (-.f64 z t))) 3) t)
✓	1.4b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

Compiler

Compiled 5584 to 1242 computations (77.8% saved)

regimes654.0ms (6.4%)

Accuracy

Total 2.0b remaining (99.1%)

Threshold costs 0b (0%)

Compiler

Compiled 7233 to 3683 computations (49.1% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
2	15	11
3	17	11
4	18	11
5	18	11

end2.0ms (0%)

Compiler: Compiled 12 to 7 computations (41.7% saved)

sample1.7s (17%)

Algorithm

1×

intervals

Results

652.0ms	8000×	body	128	valid
175.0ms	2201×	body	128	invalid

Compiler

Compiled 165 to 95 computations (42.4% saved)

Details

analyze1.9s (18.5%)

sample67.0ms (0.7%)

simplify85.0ms (0.8%)

prune9.0ms (0.1%)

localize14.0ms (0.1%)

rewrite85.0ms (0.8%)

series276.0ms (2.7%)

simplify262.0ms (2.6%)

prune225.0ms (2.2%)

localize13.0ms (0.1%)

rewrite27.0ms (0.3%)

series101.0ms (1%)

simplify118.0ms (1.1%)

prune60.0ms (0.6%)

localize21.0ms (0.2%)

rewrite79.0ms (0.8%)

series2.6s (25.7%)

simplify192.0ms (1.9%)

prune359.0ms (3.5%)

localize31.0ms (0.3%)

rewrite74.0ms (0.7%)

series712.0ms (6.9%)

simplify183.0ms (1.8%)

prune336.0ms (3.3%)

regimes654.0ms (6.4%)

simplify8.0ms (0.1%)

end2.0ms (0%)

sample1.7s (17%)

Profiling