Details

analyze926.0ms (19.1%)

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
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)

sample1.3s (27.5%)

Results

921.0ms	8256×	body	128	valid
235.0ms	2157×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify65.0ms (1.3%)

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 (0.1%)

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

2.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
▶	2.1b	(+.f64 x (*.f64 (-.f64 y x) (/.f64 z t)))

Compiler

Compiled 71 to 39 computations (45.1% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (-.f64 y x) (/.f64 z t)))
✓	5.3b	(*.f64 (-.f64 y x) (/.f64 z t))

series45.0ms (0.9%)

Counts

2 → 96

Calls

2 calls:

24.0ms	(+.f64 x (*.f64 (-.f64 y x) (/.f64 z t)))
21.0ms	(*.f64 (-.f64 y x) (/.f64 z t))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 56

Calls

2 calls:

8.0ms	(*.f64 (-.f64 y x) (/.f64 z t))
2.0ms	(+.f64 x (*.f64 (-.f64 y x) (/.f64 z t)))

simplify99.0ms (2%)

Algorithm

1×	egg-herbie

Rules

459×	`associate-l_binary64`
418×	`distribute-rgt-in_binary64`
404×	`distribute-lft-in_binary64`
371×	`fma-neg_binary64`
332×	`associate-*r/_binary64`

Counts

152 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	2220
1	372	1737
2	1225	1733
3	4189	1733
4	4687	1733
5	4979	1733

prune73.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	95	7	102
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	96	8	104

Error

0.0b

Counts

104 → 8

Alt Table

Status	Error	Program
	36.6b	(+.f64 x (*.f64 (/.f64 (-.f64 y x) (sqrt.f64 t)) (/.f64 z (sqrt.f64 t))))
	6.4b	(fma.f64 z (/.f64 (-.f64 y x) t) x)
	2.6b	(+.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t))))
	31.2b	(+.f64 x (.f64 (sqrt.f64 (.f64 z (/.f64 (-.f64 y x) t))) (sqrt.f64 (*.f64 z (/.f64 (-.f64 y x) t)))))
	27.9b	(+.f64 x (.f64 (sqrt.f64 (.f64 (-.f64 y x) (/.f64 z t))) (sqrt.f64 (*.f64 (-.f64 y x) (/.f64 z t)))))
▶	2.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	7.1b	(+.f64 x (.f64 (.f64 (-.f64 y x) z) (/.f64 1 t)))
	6.2b	(+.f64 x (.f64 (.f64 (-.f64 y x) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 z) t)))

Compiler

Compiled 1858 to 551 computations (70.3% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.0b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series17.0ms (0.3%)

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)

simplify64.0ms (1.3%)

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

prune22.0ms (0.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	31	8	39

Error

0.0b

Counts

39 → 8

Alt Table

Status	Error	Program
	36.6b	(+.f64 x (*.f64 (/.f64 (-.f64 y x) (sqrt.f64 t)) (/.f64 z (sqrt.f64 t))))
	6.4b	(fma.f64 z (/.f64 (-.f64 y x) t) x)
▶	2.6b	(+.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t))))
	31.2b	(+.f64 x (.f64 (sqrt.f64 (.f64 z (/.f64 (-.f64 y x) t))) (sqrt.f64 (*.f64 z (/.f64 (-.f64 y x) t)))))
	27.9b	(+.f64 x (.f64 (sqrt.f64 (.f64 (-.f64 y x) (/.f64 z t))) (sqrt.f64 (*.f64 (-.f64 y x) (/.f64 z t)))))
✓	2.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	7.1b	(+.f64 x (.f64 (.f64 (-.f64 y x) z) (/.f64 1 t)))
	6.2b	(+.f64 x (.f64 (.f64 (-.f64 y x) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 z) t)))

Compiler

Compiled 634 to 224 computations (64.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))
✓	0.6b	(cbrt.f64 (-.f64 y x))
✓	2.2b	(*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t))
✓	3.3b	(.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)))

series634.0ms (13.1%)

Counts

4 → 144

Calls

4 calls:

536.0ms	(*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t))
34.0ms	(*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))
32.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)))
30.0ms	(cbrt.f64 (-.f64 y x))

rewrite58.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

126×	`cbrt-div_binary64`
88×	`frac-times_binary64`
63×	`flip--_binary64`
63×	`flip3--_binary64`
52×	`add-sqr-sqrt_binary64`

Counts

4 → 201

Calls

4 calls:

14.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)))
8.0ms	(*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t))
8.0ms	(*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))
2.0ms	(cbrt.f64 (-.f64 y x))

simplify186.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

714×	`associate-r_binary64`
681×	`associate-l_binary64`
584×	`fma-def_binary64`
245×	`fma-neg_binary64`
229×	`*-commutative_binary64`

Counts

345 → 368

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	499	9455
1	1417	8611
2	4662	8609
3	5187	8609

prune351.0ms (7.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	472	0	472
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	472	8	480

Error

0.0b

Counts

480 → 8

Alt Table

Status	Error	Program
	36.6b	(+.f64 x (*.f64 (/.f64 (-.f64 y x) (sqrt.f64 t)) (/.f64 z (sqrt.f64 t))))
	6.4b	(fma.f64 z (/.f64 (-.f64 y x) t) x)
✓	2.6b	(+.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t))))
	31.2b	(+.f64 x (.f64 (sqrt.f64 (.f64 z (/.f64 (-.f64 y x) t))) (sqrt.f64 (*.f64 z (/.f64 (-.f64 y x) t)))))
	27.9b	(+.f64 x (.f64 (sqrt.f64 (.f64 (-.f64 y x) (/.f64 z t))) (sqrt.f64 (*.f64 (-.f64 y x) (/.f64 z t)))))
✓	2.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	7.1b	(+.f64 x (.f64 (.f64 (-.f64 y x) z) (/.f64 1 t)))
▶	6.2b	(+.f64 x (.f64 (.f64 (-.f64 y x) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 z) t)))

Compiler

Compiled 16735 to 5699 computations (65.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 y x) (.f64 (cbrt.f64 z) (cbrt.f64 z)))
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)
✓	6.8b	(.f64 (.f64 (-.f64 y x) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 z) t))

series274.0ms (5.7%)

Counts

4 → 108

Calls

4 calls:

175.0ms	(.f64 (-.f64 y x) (.f64 (cbrt.f64 z) (cbrt.f64 z)))
37.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
34.0ms	(.f64 (.f64 (-.f64 y x) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 z) t))
28.0ms	(cbrt.f64 z)

rewrite33.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

12.0ms	(.f64 (.f64 (-.f64 y x) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 z) t))
7.0ms	(.f64 (-.f64 y x) (.f64 (cbrt.f64 z) (cbrt.f64 z)))
4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)

simplify110.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

950×	`fma-def_binary64`
440×	`times-frac_binary64`
432×	`distribute-rgt-in_binary64`
426×	`distribute-lft-in_binary64`
357×	`associate-l_binary64`

Counts

241 → 212

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	3539
1	494	2686
2	2025	2547
3	4745	2547
4	5543	2547

prune157.0ms (3.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	247	1	248
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	248	8	256

Error

0.0b

Counts

256 → 8

Alt Table

Status	Error	Program
	36.6b	(+.f64 x (*.f64 (/.f64 (-.f64 y x) (sqrt.f64 t)) (/.f64 z (sqrt.f64 t))))
	6.4b	(fma.f64 z (/.f64 (-.f64 y x) t) x)
✓	2.6b	(+.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t))))
	31.2b	(+.f64 x (.f64 (sqrt.f64 (.f64 z (/.f64 (-.f64 y x) t))) (sqrt.f64 (*.f64 z (/.f64 (-.f64 y x) t)))))
✓	2.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	6.2b	(+.f64 x (.f64 (.f64 (*.f64 (-.f64 y x) (cbrt.f64 z)) (cbrt.f64 z)) (/.f64 (cbrt.f64 z) t)))
	7.1b	(+.f64 x (.f64 (.f64 (-.f64 y x) z) (/.f64 1 t)))
✓	6.2b	(+.f64 x (.f64 (.f64 (-.f64 y x) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 z) t)))

Compiler

Compiled 5398 to 1481 computations (72.6% saved)

regimes265.0ms (5.5%)

Accuracy

Total 1.8b remaining (99.1%)

Threshold costs 0b (0%)

Counts

50 → 1

Compiler

Compiled 4964 to 2932 computations (40.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	13	13
2	18	13
3	20	13
4	21	13
5	21	13

end87.0ms (1.8%)

Compiler: Compiled 169 to 93 computations (45% saved)

Details

analyze926.0ms (19.1%)

sample1.3s (27.5%)

simplify65.0ms (1.3%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series45.0ms (0.9%)

rewrite13.0ms (0.3%)

simplify99.0ms (2%)

prune73.0ms (1.5%)

localize5.0ms (0.1%)

series17.0ms (0.3%)

rewrite1.0ms (0%)

simplify64.0ms (1.3%)

prune22.0ms (0.5%)

localize10.0ms (0.2%)

series634.0ms (13.1%)

rewrite58.0ms (1.2%)

simplify186.0ms (3.8%)

prune351.0ms (7.2%)

localize11.0ms (0.2%)

series274.0ms (5.7%)

rewrite33.0ms (0.7%)

simplify110.0ms (2.3%)

prune157.0ms (3.2%)

regimes265.0ms (5.5%)

simplify2.0ms (0%)

end87.0ms (1.8%)

Profiling