Details

analyze974.0ms (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
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)

sample35.0ms (0%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
3.0ms	68×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify68.0ms (0.1%)

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

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

1.4b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 45 to 23 computations (48.9% saved)

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

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

series28.0ms (0%)

Counts

1 → 48

Calls

1 calls:

28.0ms

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

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:

0.0ms

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

simplify68.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

550×	`distribute-rgt-neg-out_binary64`
522×	`distribute-lft-neg-out_binary64`
356×	`distribute-rgt-in_binary64`
354×	`distribute-lft-in_binary64`
297×	`times-frac_binary64`

Counts

58 → 23

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	730
1	85	635
2	196	623
3	466	623
4	2285	623
5	4620	623
6	5293	623

prune19.0ms (0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	19	4	23
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	19	5	24

Error

0.0b

Counts

24 → 5

Alt Table

Status	Error	Program
	7.0b	(+.f64 (*.f64 x (/.f64 (-.f64 z t) y)) t)
	6.9b	(-.f64 (+.f64 t (/.f64 (.f64 z x) y)) (/.f64 (.f64 t x) y))
✓	1.4b	(fma.f64 (/.f64 x y) (-.f64 z t) t)
	34.8b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (sqrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))
▶	2.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))

Compiler

Compiled 438 to 141 computations (67.8% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))
✓	0.5b	(cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))
	1.3b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

series594.0ms (0.6%)

Counts

3 → 144

Calls

3 calls:

437.0ms

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

136.0ms

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

20.0ms

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

rewrite24.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

7.0ms

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

4.0ms

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

1.0ms

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

simplify295.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

974×	`fma-def_binary64`
500×	`*-commutative_binary64`
223×	`+-commutative_binary64`
205×	`associate-r_binary64`
151×	`associate-+r+_binary64`

Counts

237 → 275

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1180	19736
1	4348	19386
2	5129	19386

prune623.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	525	3	528
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	527	6	533

Error

0.0b

Counts

533 → 6

Alt Table

Status	Error	Program
	2.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))))) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))
	7.0b	(+.f64 (*.f64 x (/.f64 (-.f64 z t) y)) t)
	6.9b	(+.f64 t (/.f64 (*.f64 x (-.f64 z t)) y))
✓	1.4b	(fma.f64 (/.f64 x y) (-.f64 z t) t)
▶	2.5b	(pow.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) 3)
	34.8b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (sqrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))

Compiler

Compiled 44822 to 18884 computations (57.9% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.5b	(cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) 3)
	1.3b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

series1.5min (93.9%)

Counts

1 → 48

Calls

1 calls:

1.5min

(pow.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) 3)

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`cube-prod_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`cbrt-prod_binary64`
6×	`unpow-prod-down_binary64`

Counts

1 → 32

Calls

1 calls:

2.0ms

(pow.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) 3)

simplify93.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

833×	`fma-def_binary64`
354×	`unswap-sqr_binary64`
173×	`associate-/r/_binary64`
134×	`fma-neg_binary64`
129×	`distribute-rgt-in_binary64`

Counts

80 → 71

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	183	2942
1	489	2760
2	1856	2203
3	4586	2197
4	5154	2197

prune136.0ms (0.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	186	6	192

Error

0.0b

Counts

192 → 6

Alt Table

Status	Error	Program
▶	2.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))))) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))
	7.0b	(+.f64 (*.f64 x (/.f64 (-.f64 z t) y)) t)
	6.9b	(+.f64 t (/.f64 (*.f64 x (-.f64 z t)) y))
✓	1.4b	(fma.f64 (/.f64 x y) (-.f64 z t) t)
✓	2.5b	(pow.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) 3)
	34.8b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (sqrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))

Compiler

Compiled 8652 to 4177 computations (51.7% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))))
✓	0.5b	(cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))
	0.5b	(cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))
	1.3b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

series524.0ms (0.5%)

Counts

2 → 96

Calls

2 calls:

400.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))))
124.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`cbrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 27

Calls

2 calls:

3.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))))
1.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))

simplify261.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

517×	`*-commutative_binary64`
227×	`+-commutative_binary64`
206×	`associate-r_binary64`
197×	`sub-neg_binary64`
196×	`sqr-pow_binary64`

Counts

123 → 183

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1233	18092
1	4525	17966
2	5091	17966

prune907.0ms (0.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	757	1	758
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	757	7	764

Error

0.0b

Counts

764 → 7

Alt Table

Status	Error	Program
✓	2.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))))) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))
	7.0b	(+.f64 (*.f64 x (/.f64 (-.f64 z t) y)) t)
	6.9b	(+.f64 t (/.f64 (*.f64 x (-.f64 z t)) y))
	2.9b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))))
✓	1.4b	(fma.f64 (/.f64 x y) (-.f64 z t) t)
✓	2.5b	(pow.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) 3)
	34.8b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (sqrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))

Compiler

Compiled 84084 to 29989 computations (64.3% saved)

regimes276.0ms (0.3%)

Accuracy

Total 2.0b remaining (99%)

Threshold costs 0b (0%)

Counts

43 → 1

Compiler

Compiled 7370 to 3028 computations (58.9% saved)

simplify2.0ms (0%)

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

end0.0ms (0%)

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

sample853.0ms (0.9%)

Algorithm

1×

intervals

Results

337.0ms	8000×	body	128	valid
79.0ms	2093×	body	128	invalid

Compiler

Compiled 238 to 90 computations (62.2% saved)

Details

analyze974.0ms (1%)

sample35.0ms (0%)

simplify68.0ms (0.1%)

prune3.0ms (0%)

localize6.0ms (0%)

series28.0ms (0%)

rewrite1.0ms (0%)

simplify68.0ms (0.1%)

prune19.0ms (0%)

localize10.0ms (0%)

series594.0ms (0.6%)

rewrite24.0ms (0%)

simplify295.0ms (0.3%)

prune623.0ms (0.6%)

localize8.0ms (0%)

series1.5min (93.9%)

rewrite4.0ms (0%)

simplify93.0ms (0.1%)

prune136.0ms (0.1%)

localize13.0ms (0%)

series524.0ms (0.5%)

rewrite5.0ms (0%)

simplify261.0ms (0.3%)

prune907.0ms (0.9%)

regimes276.0ms (0.3%)

simplify2.0ms (0%)

end0.0ms (0%)

sample853.0ms (0.9%)

Profiling