Details

analyze1.0s (14%)

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
13.3%	86.5%	0.2%	9
19.9%	79.9%	0.2%	10
22.8%	77%	0.2%	11
25.4%	72.7%	1.9%	12
35.8%	59.6%	4.6%	13
42%	52.3%	5.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.4s (19.6%)

Results

964.0ms	8256×	body	128	valid
270.0ms	2145×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify66.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-def_binary64`
730×	`fma-neg_binary64`
228×	`cancel-sign-sub-inv_binary64`
138×	`distribute-rgt-in_binary64`
97×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	11
2	31	11
3	72	11
4	146	11
5	255	11
6	409	11
7	668	11
8	1099	11
9	1352	11
10	1478	11
11	1525	11
12	1531	11
13	1536	11
14	1536	11
15	1451	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

2.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

Compiler

Compiled 45 to 23 computations (48.9% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.2b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series18.0ms (0.2%)

Counts

1 → 48

Calls

1 calls:

18.0ms

(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 (1%)

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

prune19.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	28	3	31
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	4	32

Error

0.0b

Counts

32 → 4

Alt Table

Status	Error	Program
	7.7b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
✓	2.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
▶	3.6b	(.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)))
	36.8b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)

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))
	2.2b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series607.0ms (8.4%)

Counts

3 → 144

Calls

3 calls:

461.0ms

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

125.0ms

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

20.0ms

(*.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 (0.3%)

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 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))

simplify313.0ms (4.3%)

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

prune619.0ms (8.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	553	1	554
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	553	5	558

Error

0.0b

Counts

558 → 5

Alt Table

Status	Error	Program
	7.7b	(-.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))) (.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)))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))))
✓	2.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	3.6b	(.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)))
	36.8b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)

Compiler

Compiled 44958 to 18377 computations (59.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.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))))
✓	0.5b	(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))
	2.2b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series531.0ms (7.4%)

Counts

2 → 96

Calls

2 calls:

402.0ms	(*.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))))
129.0ms	(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:

6.0ms	(*.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)))

simplify273.0ms (3.8%)

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

prune1.2s (17.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	1037	0	1037
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	1037	5	1042

Error

0.0b

Counts

1042 → 5

Alt Table

Status	Error	Program
▶	7.7b	(-.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))) (.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)))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))))
✓	2.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	3.6b	(.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)))
	36.8b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)

Compiler

Compiled 109854 to 36169 computations (67.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (*.f64 y z) t) x)
✓	0.0b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
✓	6.5b	(/.f64 (*.f64 z x) t)
✓	6.8b	(/.f64 (*.f64 y z) t)

series61.0ms (0.8%)

Counts

4 → 24

Calls

4 calls:

23.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
13.0ms	(/.f64 (*.f64 z x) t)
12.0ms	(+.f64 (/.f64 (*.f64 y z) t) x)
12.0ms	(/.f64 (*.f64 y z) t)

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
28×	`prod-diff_binary64`
28×	`add-cube-cbrt_binary64`
24×	`times-frac_binary64`

Counts

4 → 126

Calls

4 calls:

9.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
5.0ms	(+.f64 (/.f64 (*.f64 y z) t) x)
5.0ms	(/.f64 (*.f64 z x) t)
3.0ms	(/.f64 (*.f64 y z) t)

simplify101.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

634×	`fma-def_binary64`
419×	`associate-/l/_binary64`
316×	`distribute-rgt-in_binary64`
298×	`distribute-lft-in_binary64`
193×	`cancel-sign-sub-inv_binary64`

Counts

150 → 185

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	3546
1	541	2217
2	1901	1872
3	4868	1872
4	4866	1872

prune104.0ms (1.4%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	184	1	185
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	184	6	190

Error

0.0b

Counts

190 → 6

Alt Table

Status	Error	Program
✓	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))) (.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)))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))))
	8.0b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 y z) t)) (cbrt.f64 (/.f64 (.f64 y z) t))) (cbrt.f64 (/.f64 (.f64 y z) t))) x) (/.f64 (.f64 z x) t))
✓	7.7b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
✓	2.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	3.6b	(.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)))
	36.8b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)

Compiler

Compiled 4403 to 803 computations (81.8% saved)

regimes555.0ms (7.7%)

Accuracy

Total 1.5b remaining (98.3%)

Threshold costs 0b (0%)

Counts

50 → 3

Compiler

Compiled 9290 to 3845 computations (58.6% saved)

bsearch19.0ms (0.3%)

Steps

Iters	Range		Point
1	9.853281756793958e-59	5.376912642358568e-58	2.3295563362690378e-58
4	-3.8844560163823866e-157	-2.0700850518381815e-157	-2.5268772841685277e-157

Compiler

Compiled 5 to 4 computations (20% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`+-rgt-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	38
1	28	38
2	32	38
3	34	38
4	35	38
5	35	38

end82.0ms (1.1%)

Compiler: Compiled 223 to 95 computations (57.4% saved)

Details

analyze1.0s (14%)

sample1.4s (19.6%)

simplify66.0ms (0.9%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series18.0ms (0.2%)

rewrite1.0ms (0%)

simplify69.0ms (1%)

prune19.0ms (0.3%)

localize10.0ms (0.1%)

series607.0ms (8.4%)

rewrite20.0ms (0.3%)

simplify313.0ms (4.3%)

prune619.0ms (8.6%)

localize13.0ms (0.2%)

series531.0ms (7.4%)

rewrite16.0ms (0.2%)

simplify273.0ms (3.8%)

prune1.2s (17.1%)

localize15.0ms (0.2%)

series61.0ms (0.8%)

rewrite29.0ms (0.4%)

simplify101.0ms (1.4%)

prune104.0ms (1.4%)

regimes555.0ms (7.7%)

bsearch19.0ms (0.3%)

simplify6.0ms (0.1%)

end82.0ms (1.1%)

Profiling