Details

analyze778.0ms (8.1%)

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
16.4%	83.4%	0.2%	9
21.4%	78.4%	0.2%	10
25.1%	74.7%	0.2%	11
28%	70.2%	1.9%	12
39.6%	55.8%	4.6%	13
43.9%	50.4%	5.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample133.0ms (1.4%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
3.0ms	74×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify76.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

973×	`fma-def_binary64`
752×	`fma-neg_binary64`
239×	`cancel-sign-sub-inv_binary64`
193×	`distribute-rgt-in_binary64`
133×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	33	11
3	64	11
4	125	11
5	238	11
6	414	11
7	791	11
8	1182	11
9	1373	11
10	1483	11
11	1532	11
12	1538	11
13	1543	11
14	1543	11
15	1458	11

prune4.0ms (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
▶	2.6b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	5.8b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.5b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series17.0ms (0.2%)

Counts

1 → 48

Calls

1 calls:

17.0ms

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

0.0ms

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

simplify69.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

539×	`distribute-rgt-neg-out_binary64`
515×	`distribute-lft-neg-out_binary64`
375×	`distribute-rgt-in_binary64`
373×	`distribute-lft-in_binary64`
270×	`times-frac_binary64`

Counts

58 → 31

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	946
1	88	635
2	194	623
3	469	623
4	2305	623
5	4632	623
6	5238	623

prune18.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	28	3	31
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	29	4	33

Error

0.0b

Counts

33 → 4

Alt Table

Status	Error	Program
	6.9b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
✓	2.6b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	5.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
▶	3.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))

Compiler

Compiled 492 to 142 computations (71.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
✓	0.6b	(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))
	2.5b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series534.0ms (5.6%)

Counts

3 → 144

Calls

3 calls:

375.0ms

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

140.0ms

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

18.0ms

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

rewrite20.0ms (0.2%)

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:

8.0ms

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

4.0ms

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

1.0ms

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

simplify267.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

938×	`fma-def_binary64`
540×	`*-commutative_binary64`
218×	`+-commutative_binary64`
210×	`associate-r_binary64`
141×	`associate-+r+_binary64`

Counts

237 → 277

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1216	19471
1	4389	19186
2	5141	19186

prune689.0ms (7.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	551	3	554
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	552	6	558

Error

0.0b

Counts

558 → 6

Alt Table

Status	Error	Program
	6.9b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
	4.6b	(.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	31.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))))
✓	2.6b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	5.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
▶	4.1b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))

Compiler

Compiled 45173 to 18419 computations (59.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))
✓	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	0.6b	(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))
	2.5b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series534.0ms (5.6%)

Counts

2 → 96

Calls

2 calls:

397.0ms	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))
136.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`cbrt-prod_binary64`
34×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
9×	`associate-r_binary64`

Counts

2 → 72

Calls

2 calls:

7.0ms	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))
1.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))

simplify395.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

916×	`fma-def_binary64`
521×	`*-commutative_binary64`
206×	`+-commutative_binary64`
199×	`associate-r_binary64`
140×	`associate-+r+_binary64`

Counts

168 → 234

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1209	19310
1	4255	19016
2	4988	19016

prune1.6s (16.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	1037	0	1037
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	1037	6	1043

Error

0.0b

Counts

1043 → 6

Alt Table

Status	Error	Program
	6.9b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
▶	4.6b	(.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	31.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))))
✓	2.6b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	5.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
✓	4.1b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))

Compiler

Compiled 110069 to 36239 computations (67.1% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))
	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	0.6b	(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))
	2.5b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

prune2.7s (27.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	1845	0	1845
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	1845	6	1851

Error

0.0b

Counts

1851 → 6

Alt Table

Status	Error	Program
	6.9b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
✓	4.6b	(.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	31.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))))
✓	2.6b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	5.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
✓	4.1b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))

Compiler

Compiled 247161 to 71983 computations (70.9% saved)

regimes890.0ms (9.3%)

Accuracy

Total 0.7b remaining (97.1%)

Threshold costs 0.7b (97.1%)

Counts

114 → 3

Compiler

Compiled 22911 to 7438 computations (67.5% saved)

bsearch7.0ms (0.1%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
8×	`*-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	79
1	38	79
2	48	79
3	59	79
4	65	79
5	68	79
6	69	79
7	69	79

end1.0ms (0%)

Compiler: Compiled 58 to 25 computations (56.9% saved)

sample830.0ms (8.7%)

Algorithm

1×

intervals

Results

328.0ms	8000×	body	128	valid
84.0ms	2078×	body	128	invalid

Compiler

Compiled 298 to 102 computations (65.8% saved)

Details

analyze778.0ms (8.1%)

sample133.0ms (1.4%)

simplify76.0ms (0.8%)

prune4.0ms (0%)

localize6.0ms (0.1%)

series17.0ms (0.2%)

rewrite1.0ms (0%)

simplify69.0ms (0.7%)

prune18.0ms (0.2%)

localize10.0ms (0.1%)

series534.0ms (5.6%)

rewrite20.0ms (0.2%)

simplify267.0ms (2.8%)

prune689.0ms (7.2%)

localize13.0ms (0.1%)

series534.0ms (5.6%)

rewrite16.0ms (0.2%)

simplify395.0ms (4.1%)

prune1.6s (16.3%)

localize21.0ms (0.2%)

prune2.7s (27.8%)

regimes890.0ms (9.3%)

bsearch7.0ms (0.1%)

simplify5.0ms (0%)

end1.0ms (0%)

sample830.0ms (8.7%)

Profiling