Details

analyze907.0ms (13.3%)

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 (19.1%)

Results

904.0ms	8256×	body	128	valid
225.0ms	2105×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify64.0ms (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

1.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

Compiler

Compiled 45 to 23 computations (48.9% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series15.0ms (0.2%)

Counts

1 → 48

Calls

1 calls:

15.0ms

(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)

simplify63.0ms (0.9%)

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

prune21.0ms (0.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	27	4	31
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	5	32

Error

0.0b

Counts

32 → 5

Alt Table

Status	Error	Program
✓	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
▶	2.3b	(.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)))
	42.8b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 z t) (-.f64 y x) x) 3))
	6.4b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
	7.2b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))

Compiler

Compiled 522 to 162 computations (69% saved)

localize9.0ms (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)))
✓	0.5b	(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))
	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series500.0ms (7.3%)

Counts

3 → 144

Calls

3 calls:

362.0ms

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

119.0ms

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

17.0ms

(*.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)))

rewrite21.0ms (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:

6.0ms

(*.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)))

5.0ms

(*.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))

simplify249.0ms (3.6%)

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

prune569.0ms (8.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	552	2	554
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	553	6	559

Error

0.0b

Counts

559 → 6

Alt Table

Status	Error	Program
✓	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
▶	2.3b	(.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 (.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)))))
	42.8b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 z t) (-.f64 y x) x) 3))
	6.4b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
	34.4b	(.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))) (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))))
	7.2b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))

Compiler

Compiled 45041 to 18411 computations (59.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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)))
	0.5b	(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))
✓	0.5b	(cbrt.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))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))
	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series123.0ms (1.8%)

Counts

1 → 48

Calls

1 calls:

122.0ms

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

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`rem-cbrt-cube_binary64`
1×	`pow3_binary64`
1×	`cbrt-prod_binary64`

Counts

1 → 12

Calls

1 calls:

5.0ms

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

simplify86.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

593×	`times-frac_binary64`
370×	`associate-/r*_binary64`
344×	`associate-/l*_binary64`
296×	`fma-def_binary64`
195×	`associate-*r/_binary64`

Counts

60 → 96

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	446	5390
1	1530	5195
2	5105	5195

prune1.2s (18%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	961	0	961
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	961	6	967

Error

0.0b

Counts

967 → 6

Alt Table

Status	Error	Program
✓	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	2.3b	(.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 (.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)))))
	42.8b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 z t) (-.f64 y x) x) 3))
▶	6.4b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
	34.4b	(.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))) (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))))
	7.2b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))

Compiler

Compiled 104166 to 37074 computations (64.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 y x) t)
✓	0.0b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
✓	7.0b	(*.f64 z (/.f64 (-.f64 y x) t))

series47.0ms (0.7%)

Counts

3 → 124

Calls

3 calls:

21.0ms	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
17.0ms	(*.f64 z (/.f64 (-.f64 y x) t))
9.0ms	(/.f64 (-.f64 y x) t)

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
19×	`associate-r_binary64`

Counts

3 → 94

Calls

3 calls:

7.0ms	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
7.0ms	(*.f64 z (/.f64 (-.f64 y x) t))
4.0ms	(/.f64 (-.f64 y x) t)

simplify92.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

409×	`distribute-rgt-in_binary64`
396×	`distribute-lft-in_binary64`
346×	`associate-*l/_binary64`
330×	`associate-*r/_binary64`
276×	`fma-def_binary64`

Counts

218 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	166	2779
1	425	2436
2	1259	2427
3	4230	2427
4	4978	2427

prune76.0ms (1.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	3	0	3
Picked	0	1	1
Done	0	2	2
Total	136	5	141

Error

0.0b

Counts

141 → 5

Alt Table

Status	Error	Program
✓	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	2.3b	(.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 (.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)))))
	7.2b	(+.f64 (/.f64 (*.f64 z (-.f64 y x)) t) x)
✓	6.4b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
	33.1b	(+.f64 (.f64 (.f64 z (/.f64 1 (sqrt.f64 t))) (/.f64 (-.f64 y x) (sqrt.f64 t))) x)

Compiler

Compiled 2228 to 569 computations (74.5% saved)

regimes1.3s (19.4%)

Accuracy

Total 2.2b remaining (99.1%)

Threshold costs 0b (0%)

Counts

105 → 1

Compiler

Compiled 20126 to 7684 computations (61.8% saved)

simplify3.0ms (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

end65.0ms (0.9%)

Compiler: Compiled 135 to 61 computations (54.8% saved)

Details

analyze907.0ms (13.3%)

sample1.3s (19.1%)

simplify64.0ms (0.9%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series15.0ms (0.2%)

rewrite1.0ms (0%)

simplify63.0ms (0.9%)

prune21.0ms (0.3%)

localize9.0ms (0.1%)

series500.0ms (7.3%)

rewrite21.0ms (0.3%)

simplify249.0ms (3.6%)

prune569.0ms (8.3%)

localize10.0ms (0.2%)

series123.0ms (1.8%)

rewrite5.0ms (0.1%)

simplify86.0ms (1.3%)

prune1.2s (18%)

localize8.0ms (0.1%)

series47.0ms (0.7%)

rewrite24.0ms (0.3%)

simplify92.0ms (1.3%)

prune76.0ms (1.1%)

regimes1.3s (19.4%)

simplify3.0ms (0%)

end65.0ms (0.9%)

Profiling