Details

analyze967.0ms (13.5%)

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
24%	75.2%	0.8%	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 (19.5%)

Results

965.0ms	8256×	body	128	valid
245.0ms	2130×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify67.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

799×	`fma-def_binary64`
661×	`fma-neg_binary64`
203×	`cancel-sign-sub-inv_binary64`
145×	`distribute-rgt-in_binary64`
99×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	30	11
3	61	11
4	129	11
5	232	11
6	397	11
7	667	11
8	1062	11
9	1355	11
10	1480	11
11	1529	11
12	1535	11
13	1540	11
14	1540	11
15	1455	11

prune7.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	7.3b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
▶	6.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
✓	0.0b	(*.f64 y (-.f64 z x))
✓	6.9b	(/.f64 (*.f64 y (-.f64 z x)) t)

series50.0ms (0.7%)

Counts

3 → 104

Calls

3 calls:

22.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
19.0ms	(/.f64 (*.f64 y (-.f64 z x)) t)
10.0ms	(*.f64 y (-.f64 z x))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 92

Calls

3 calls:

11.0ms	(*.f64 y (-.f64 z x))
6.0ms	(/.f64 (*.f64 y (-.f64 z x)) t)
4.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

simplify101.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

611×	`fma-def_binary64`
609×	`times-frac_binary64`
591×	`distribute-rgt-in_binary64`
370×	`fma-neg_binary64`
158×	`associate-l_binary64`

Counts

196 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	200	2470
1	431	2151
2	1681	2001
3	4818	2001
4	4992	2001

prune102.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	135	5	140
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	136	6	142

Error

Counts

142 → 6

Alt Table

Status	Error	Program
	7.3b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
▶	1.7b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	2.2b	(+.f64 x (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x)))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))))
	6.8b	(+.f64 x (/.f64 (*.f64 (-.f64 z x) y) t))
	7.2b	(+.f64 x (/.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x)))) (cbrt.f64 (-.f64 z x))) t))
	6.8b	(+.f64 x (.f64 (.f64 y (-.f64 z x)) (/.f64 1 t)))

Compiler

Compiled 2558 to 731 computations (71.4% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.6b	(fma.f64 (/.f64 y t) (-.f64 z x) x)

series21.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

21.0ms

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

simplify77.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

546×	`distribute-rgt-neg-out_binary64`
522×	`distribute-lft-neg-out_binary64`
389×	`distribute-rgt-in_binary64`
386×	`distribute-lft-in_binary64`
294×	`times-frac_binary64`

Counts

58 → 24

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	946
1	87	635
2	197	623
3	473	623
4	2335	623
5	4674	623
6	5331	623

prune16.0ms (0.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	24	6	30

Error

Counts

30 → 6

Alt Table

Status	Error	Program
	7.3b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
✓	1.7b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
▶	2.2b	(+.f64 x (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x)))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))))
	6.8b	(+.f64 x (/.f64 (*.f64 (-.f64 z x) y) t))
	7.2b	(+.f64 x (/.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x)))) (cbrt.f64 (-.f64 z x))) t))
	6.8b	(+.f64 x (.f64 (.f64 y (-.f64 z x)) (/.f64 1 t)))

Compiler

Compiled 465 to 164 computations (64.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x)))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x))))
✓	6.3b	(cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))
✓	8.2b	(*.f64 (/.f64 y t) (-.f64 z x))

series2.1s (29.4%)

Counts

4 → 192

Calls

4 calls:

1.3s	(.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x))))
693.0ms	(cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))
122.0ms	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x)))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x))))
21.0ms	(*.f64 (/.f64 y t) (-.f64 z x))

rewrite253.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

605×	`cbrt-div_binary64`
594×	`frac-times_binary64`
284×	`associate-*r/_binary64`
244×	`flip--_binary64`
244×	`flip3--_binary64`

Counts

4 → 400

Calls

4 calls:

100.0ms	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x)))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x))))
8.0ms	(*.f64 (/.f64 y t) (-.f64 z x))
7.0ms	(.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x))))
5.0ms	(cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))

simplify504.0ms (7%)

Algorithm

1×	egg-herbie

Rules

584×	`fma-def_binary64`
476×	`*-commutative_binary64`
359×	`associate-l_binary64`
354×	`times-frac_binary64`
263×	`associate-/r*_binary64`

Counts

592 → 650

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	980	24883
1	1977	24485
2	4889	24469
3	5277	24469

prune811.0ms (11.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	1004	0	1004
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	1004	6	1010

Error

Counts

1010 → 6

Alt Table

Status	Error	Program
	7.3b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
✓	1.7b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
✓	2.2b	(+.f64 x (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x)))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))))
▶	6.8b	(+.f64 x (/.f64 (*.f64 (-.f64 z x) y) t))
	7.2b	(+.f64 x (/.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x)))) (cbrt.f64 (-.f64 z x))) t))
	6.8b	(+.f64 x (.f64 (.f64 y (-.f64 z x)) (/.f64 1 t)))

Compiler

Compiled 47101 to 11812 computations (74.9% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 (-.f64 z x) y) t))
✓	0.0b	(*.f64 (-.f64 z x) y)
✓	6.9b	(/.f64 (*.f64 (-.f64 z x) y) t)

series53.0ms (0.7%)

Counts

3 → 132

Calls

3 calls:

24.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 z x) y) t))
22.0ms	(/.f64 (*.f64 (-.f64 z x) y) t)
7.0ms	(*.f64 (-.f64 z x) y)

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
8×	`add-cube-cbrt_binary64`

Counts

3 → 66

Calls

3 calls:

6.0ms	(/.f64 (*.f64 (-.f64 z x) y) t)
5.0ms	(*.f64 (-.f64 z x) y)
4.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 z x) y) t))

simplify92.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

550×	`times-frac_binary64`
524×	`associate-/l*_binary64`
427×	`distribute-rgt-in_binary64`
406×	`distribute-lft-in_binary64`
234×	`fma-def_binary64`

Counts

198 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	138	2349
1	366	2066
2	1246	1970
3	4957	1970
4	5036	1970

prune81.0ms (1.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	122	6	128

Error

Counts

128 → 6

Alt Table

Status	Error	Program
	7.3b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
✓	1.7b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
✓	2.2b	(+.f64 x (.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x)))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))))
✓	6.8b	(+.f64 x (/.f64 (*.f64 (-.f64 z x) y) t))
	7.2b	(+.f64 x (/.f64 (.f64 (.f64 y (*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x)))) (cbrt.f64 (-.f64 z x))) t))
	6.8b	(+.f64 x (.f64 (.f64 y (-.f64 z x)) (/.f64 1 t)))

Compiler

Compiled 1876 to 518 computations (72.4% saved)

regimes305.0ms (4.3%)

Accuracy

Total 1.9b remaining (99.1%)

Threshold costs 0b (0%)

Counts

57 → 1

Compiler

Compiled 5476 to 3178 computations (42% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-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	9	13
1	12	13
2	17	13
3	19	13
4	20	13
5	20	13

end71.0ms (1%)

Compiler: Compiled 134 to 70 computations (47.8% saved)

Details

analyze967.0ms (13.5%)

sample1.4s (19.5%)

simplify67.0ms (0.9%)

prune7.0ms (0.1%)

localize6.0ms (0.1%)

series50.0ms (0.7%)

rewrite27.0ms (0.4%)

simplify101.0ms (1.4%)

prune102.0ms (1.4%)

localize6.0ms (0.1%)

series21.0ms (0.3%)

rewrite1.0ms (0%)

simplify77.0ms (1.1%)

prune16.0ms (0.2%)

localize15.0ms (0.2%)

series2.1s (29.4%)

rewrite253.0ms (3.5%)

simplify504.0ms (7%)

prune811.0ms (11.3%)

localize6.0ms (0.1%)

series53.0ms (0.7%)

rewrite19.0ms (0.3%)

simplify92.0ms (1.3%)

prune81.0ms (1.1%)

regimes305.0ms (4.3%)

simplify3.0ms (0%)

end71.0ms (1%)

Profiling