Details

analyze1.1s (15.1%)

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
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 (19.2%)

Results

928.0ms	8256×	body	128	valid
283.0ms	2245×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify66.0ms (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

prune3.0ms (0%)

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
	8.1b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
▶	6.3b	(+.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))
✓	6.7b	(/.f64 (*.f64 y (-.f64 z x)) t)

series48.0ms (0.7%)

Counts

3 → 104

Calls

3 calls:

22.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
20.0ms	(/.f64 (*.f64 y (-.f64 z x)) t)
6.0ms	(*.f64 y (-.f64 z x))

rewrite21.0ms (0.3%)

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:

7.0ms	(/.f64 (*.f64 y (-.f64 z x)) t)
5.0ms	(*.f64 y (-.f64 z x))
3.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

simplify100.0ms (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

prune84.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	136	4	140
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	136	6	142

Error

0.0b

Counts

142 → 6

Alt Table

Status	Error	Program
	6.4b	(+.f64 x (/.f64 1 (/.f64 t (*.f64 y (-.f64 z x)))))
	2.6b	(+.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)))))
	8.1b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
✓	6.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
▶	2.1b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	32.7b	(+.f64 x (/.f64 (*.f64 (/.f64 y (sqrt.f64 t)) (-.f64 z x)) (sqrt.f64 t)))

Compiler

Compiled 2531 to 721 computations (71.5% saved)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series15.0ms (0.2%)

Counts

1 → 48

Calls

1 calls:

15.0ms

(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)

simplify65.0ms (0.9%)

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

prune19.0ms (0.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	24	6	30

Error

0.0b

Counts

30 → 6

Alt Table

Status	Error	Program
	6.4b	(+.f64 x (/.f64 1 (/.f64 t (*.f64 y (-.f64 z x)))))
▶	2.6b	(+.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)))))
	8.1b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
✓	6.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
✓	2.1b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	32.7b	(+.f64 x (/.f64 (*.f64 (/.f64 y (sqrt.f64 t)) (-.f64 z x)) (sqrt.f64 t)))

Compiler

Compiled 438 to 154 computations (64.8% saved)

localize11.0ms (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))))
✓	6.4b	(cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))
✓	7.2b	(*.f64 (/.f64 y t) (-.f64 z x))

series2.2s (30.6%)

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))))
866.0ms	(cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))
58.0ms	(.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))))
18.0ms	(*.f64 (/.f64 y t) (-.f64 z x))

rewrite182.0ms (2.5%)

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:

13.0ms	(.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))
6.0ms	(cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x)))
6.0ms	(.f64 (cbrt.f64 (.f64 (/.f64 y t) (-.f64 z x))) (cbrt.f64 (*.f64 (/.f64 y t) (-.f64 z x))))

simplify482.0ms (6.7%)

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

prune723.0ms (10%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	1004	0	1004
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	1004	6	1010

Error

0.0b

Counts

1010 → 6

Alt Table

Status	Error	Program
▶	6.4b	(+.f64 x (/.f64 1 (/.f64 t (*.f64 y (-.f64 z x)))))
✓	2.6b	(+.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)))))
	8.1b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
✓	6.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
✓	2.1b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	32.7b	(+.f64 x (/.f64 (*.f64 (/.f64 y (sqrt.f64 t)) (-.f64 z x)) (sqrt.f64 t)))

Compiler

Compiled 47074 to 11802 computations (74.9% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 1 (/.f64 t (*.f64 y (-.f64 z x)))))
	0.0b	(*.f64 y (-.f64 z x))
✓	0.7b	(/.f64 1 (/.f64 t (*.f64 y (-.f64 z x))))
✓	6.6b	(/.f64 t (*.f64 y (-.f64 z x)))

series74.0ms (1%)

Counts

3 → 128

Calls

3 calls:

35.0ms	(/.f64 t (*.f64 y (-.f64 z x)))
22.0ms	(+.f64 x (/.f64 1 (/.f64 t (*.f64 y (-.f64 z x)))))
17.0ms	(/.f64 1 (/.f64 t (*.f64 y (-.f64 z x))))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`times-frac_binary64`
29×	`add-exp-log_binary64`
27×	`*-un-lft-identity_binary64`
24×	`add-sqr-sqrt_binary64`
24×	`add-cube-cbrt_binary64`

Counts

3 → 109

Calls

3 calls:

10.0ms	(/.f64 1 (/.f64 t (*.f64 y (-.f64 z x))))
8.0ms	(+.f64 x (/.f64 1 (/.f64 t (*.f64 y (-.f64 z x)))))
5.0ms	(/.f64 t (*.f64 y (-.f64 z x)))

simplify123.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

474×	`fma-def_binary64`
458×	`distribute-rgt-in_binary64`
423×	`distribute-lft-in_binary64`
269×	`associate-/l/_binary64`
178×	`fma-neg_binary64`

Counts

237 → 178

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	4017
1	500	3446
2	1832	3256
3	4772	3256
4	5027	3256

prune161.0ms (2.2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	236	7	243

Error

Counts

243 → 7

Alt Table

Status	Error	Program
✓	6.4b	(+.f64 x (/.f64 1 (/.f64 t (*.f64 y (-.f64 z x)))))
✓	2.6b	(+.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)))))
	8.1b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
✓	6.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
	8.0b	(+.f64 x (/.f64 1 (*.f64 (/.f64 1 y) (/.f64 t (-.f64 z x)))))
✓	2.1b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	32.7b	(+.f64 x (/.f64 (*.f64 (/.f64 y (sqrt.f64 t)) (-.f64 z x)) (sqrt.f64 t)))

Compiler

Compiled 4580 to 1651 computations (64% saved)

regimes219.0ms (3%)

Accuracy

Total 2.1b remaining (99.5%)

Threshold costs 0b (0%)

Counts

46 → 1

Compiler

Compiled 4306 to 2568 computations (40.4% saved)

simplify2.0ms (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	11	16
1	16	16
2	20	16
3	22	16
4	23	16
5	22	16

end85.0ms (1.2%)

Compiler: Compiled 148 to 85 computations (42.6% saved)

Details

analyze1.1s (15.1%)

sample1.4s (19.2%)

simplify66.0ms (0.9%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series48.0ms (0.7%)

rewrite21.0ms (0.3%)

simplify100.0ms (1.4%)

prune84.0ms (1.2%)

localize9.0ms (0.1%)

series15.0ms (0.2%)

rewrite1.0ms (0%)

simplify65.0ms (0.9%)

prune19.0ms (0.3%)

localize11.0ms (0.2%)

series2.2s (30.6%)

rewrite182.0ms (2.5%)

simplify482.0ms (6.7%)

prune723.0ms (10%)

localize7.0ms (0.1%)

series74.0ms (1%)

rewrite29.0ms (0.4%)

simplify123.0ms (1.7%)

prune161.0ms (2.2%)

regimes219.0ms (3%)

simplify2.0ms (0%)

end85.0ms (1.2%)

Profiling