Details

analyze185.0ms (5.8%)

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
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
49.9%	49.9%	0.2%	8
74.9%	25%	0.2%	9
74.9%	25%	0.2%	10
74.9%	25%	0.2%	11
74.9%	25%	0.2%	12
87.3%	12.5%	0.2%	13
87.3%	12.5%	0.2%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample874.0ms (27.3%)

Infinites

24.9% of outputs are infinite.

Results

681.0ms

8256×

body

128

valid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify65.0ms (2%)

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

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

Compiler

Compiled 45 to 23 computations (48.9% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series16.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

16.0ms

(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 (2%)

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

prune26.0ms (0.8%)

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
	7.6b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	34.0b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	27.7b	(cbrt.f64 (.f64 (.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x) (fma.f64 (-.f64 y x) (/.f64 z t) x)) (fma.f64 (-.f64 y x) (/.f64 z t) x)))
▶	4.3b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)

Compiler

Compiled 534 to 160 computations (70% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
✓	4.3b	(*.f64 z (/.f64 (-.f64 y x) t))

series40.0ms (1.2%)

Counts

2 → 96

Calls

2 calls:

21.0ms	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)
19.0ms	(*.f64 z (/.f64 (-.f64 y x) t))

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
19×	`associate-r_binary64`
18×	`*-un-lft-identity_binary64`
16×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`

Counts

2 → 54

Calls

2 calls:

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

simplify92.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

397×	`associate-l_binary64`
389×	`distribute-rgt-in_binary64`
374×	`distribute-lft-in_binary64`
335×	`associate-r_binary64`
294×	`associate-*r/_binary64`

Counts

150 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	2020
1	336	1709
2	1087	1700
3	4029	1700
4	4644	1700
5	4978	1700

prune72.0ms (2.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	3	0	3
Picked	0	1	1
Done	0	1	1
Total	88	6	94

Error

Counts

94 → 6

Alt Table

Status	Error	Program
	4.1b	(+.f64 (.f64 (.f64 z (-.f64 y x)) (/.f64 1 t)) x)
	34.8b	(+.f64 (.f64 (.f64 z (sqrt.f64 (-.f64 y x))) (/.f64 (sqrt.f64 (-.f64 y x)) t)) x)
▶	3.0b	(+.f64 (.f64 (.f64 z (*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))) (/.f64 (cbrt.f64 (-.f64 y x)) t)) x)
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	4.1b	(+.f64 (/.f64 (*.f64 z (-.f64 y x)) t) x)
✓	4.3b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)

Compiler

Compiled 1562 to 425 computations (72.8% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 z (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))))
✓	0.5b	(cbrt.f64 (-.f64 y x))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))
✓	3.1b	(.f64 (.f64 z (*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))) (/.f64 (cbrt.f64 (-.f64 y x)) t))

series507.0ms (15.9%)

Counts

4 → 132

Calls

4 calls:

408.0ms	(.f64 z (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))))
36.0ms	(*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))
33.0ms	(cbrt.f64 (-.f64 y x))
30.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))) (/.f64 (cbrt.f64 (-.f64 y x)) t))

rewrite59.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
51×	`*-un-lft-identity_binary64`
50×	`cbrt-div_binary64`
48×	`cbrt-prod_binary64`
37×	`associate-r_binary64`

Counts

4 → 175

Calls

4 calls:

19.0ms	(.f64 (.f64 z (*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))) (/.f64 (cbrt.f64 (-.f64 y x)) t))
10.0ms	(.f64 z (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))))
10.0ms	(*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))
2.0ms	(cbrt.f64 (-.f64 y x))

simplify152.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

656×	`associate-r_binary64`
617×	`associate-l_binary64`
594×	`times-frac_binary64`
339×	`*-commutative_binary64`
304×	`fma-neg_binary64`

Counts

307 → 327

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	435	7256
1	1211	6870
2	4445	6525
3	5708	6525

prune346.0ms (10.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	431	0	431
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	431	6	437

Error

Counts

437 → 6

Alt Table

Status	Error	Program
	4.1b	(+.f64 (.f64 (.f64 z (-.f64 y x)) (/.f64 1 t)) x)
	34.8b	(+.f64 (.f64 (.f64 z (sqrt.f64 (-.f64 y x))) (/.f64 (sqrt.f64 (-.f64 y x)) t)) x)
✓	3.0b	(+.f64 (.f64 (.f64 z (*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))) (/.f64 (cbrt.f64 (-.f64 y x)) t)) x)
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
▶	4.1b	(+.f64 (/.f64 (*.f64 z (-.f64 y x)) t) x)
✓	4.3b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)

Compiler

Compiled 14229 to 5307 computations (62.7% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (*.f64 z (-.f64 y x)) t) x)
✓	0.0b	(*.f64 z (-.f64 y x))
✓	4.4b	(/.f64 (*.f64 z (-.f64 y x)) t)

series48.0ms (1.5%)

Counts

3 → 104

Calls

3 calls:

21.0ms	(+.f64 (/.f64 (*.f64 z (-.f64 y x)) t) x)
19.0ms	(/.f64 (*.f64 z (-.f64 y x)) t)
7.0ms	(*.f64 z (-.f64 y x))

rewrite24.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 96

Calls

3 calls:

8.0ms	(+.f64 (/.f64 (*.f64 z (-.f64 y x)) t) x)
6.0ms	(/.f64 (*.f64 z (-.f64 y x)) t)
6.0ms	(*.f64 z (-.f64 y x))

simplify92.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

598×	`fma-def_binary64`
571×	`times-frac_binary64`
423×	`distribute-rgt-in_binary64`
410×	`distribute-lft-in_binary64`
252×	`fma-neg_binary64`

Counts

200 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	200	2693
1	428	2174
2	1544	2011
3	4773	2011
4	5079	2011

prune99.0ms (3.1%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	1	1	2
Picked	0	1	1
Done	0	3	3
Total	148	6	154

Error

Counts

154 → 6

Alt Table

Status	Error	Program
	34.8b	(+.f64 (.f64 (.f64 z (sqrt.f64 (-.f64 y x))) (/.f64 (sqrt.f64 (-.f64 y x)) t)) x)
✓	3.0b	(+.f64 (.f64 (.f64 z (*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))) (/.f64 (cbrt.f64 (-.f64 y x)) t)) x)
✓	1.4b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	4.1b	(fma.f64 (*.f64 z (-.f64 y x)) (/.f64 1 t) x)
✓	4.1b	(+.f64 (/.f64 (*.f64 z (-.f64 y x)) t) x)
✓	4.3b	(+.f64 (*.f64 z (/.f64 (-.f64 y x) t)) x)

Compiler

Compiled 2545 to 693 computations (72.8% saved)

regimes306.0ms (9.6%)

Accuracy

Total 1.1b remaining (99.1%)

Threshold costs 0b (0%)

Counts

53 → 1

Compiler

Compiled 5997 to 3456 computations (42.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-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	15	43
1	20	43
2	25	43
3	27	43
4	28	43
5	28	43

end78.0ms (2.4%)

Compiler: Compiled 157 to 81 computations (48.4% saved)

Details

analyze185.0ms (5.8%)

sample874.0ms (27.3%)

simplify65.0ms (2%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series16.0ms (0.5%)

rewrite1.0ms (0%)

simplify64.0ms (2%)

prune26.0ms (0.8%)

localize7.0ms (0.2%)

series40.0ms (1.2%)

rewrite18.0ms (0.5%)

simplify92.0ms (2.9%)

prune72.0ms (2.2%)

localize13.0ms (0.4%)

series507.0ms (15.9%)

rewrite59.0ms (1.8%)

simplify152.0ms (4.7%)

prune346.0ms (10.8%)

localize6.0ms (0.2%)

series48.0ms (1.5%)

rewrite24.0ms (0.8%)

simplify92.0ms (2.9%)

prune99.0ms (3.1%)

regimes306.0ms (9.6%)

simplify3.0ms (0.1%)

end78.0ms (2.4%)

Profiling