Details

analyze406.0ms (7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 33 to 24 computations (27.3% saved)

sample54.0ms (0.9%)

Algorithm

1×

intervals

Results

14.0ms	117×	body	256	valid
10.0ms	278×	pre	128	true
9.0ms	52×	body	512	valid
6.0ms	87×	body	128	valid
1.0ms	22×	body	128	nan

Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify365.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

1968×	`fma-neg_binary64`
1363×	`fma-def_binary64`
898×	`div-sub_binary64`
743×	`associate-/l*_binary64`
567×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	30	22
2	64	22
3	135	22
4	201	22
5	335	22
6	554	22
7	929	22
8	1477	22
9	2115	22
10	2599	22
11	2554	22
12	2602	22
13	2671	22
14	3117	22
15	2327	22
16	2375	22
17	2383	22
18	2389	22
19	2395	22
20	2397	22
21	2397	22
22	2585	22
23	2685	22
24	2619	22
25	2631	22
26	2661	22
27	2677	22
28	2707	22
29	2707	22
30	2751	22
31	2851	22
32	2827	22
33	2827	22
34	2638	22

prune4.0ms (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

53.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	53.3b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
▶	53.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 a (.f64 c -3) (.f64 b b))
✓	0.1b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
✓	0.4b	(/.f64 1/3 a)
✓	23.5b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
35×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`
18×	`prod-diff_binary64`

Counts

4 → 123

Calls

4 calls:

8.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
4.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
2.0ms	(/.f64 1/3 a)
0.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))

series160.0ms (2.8%)

Counts

4 → 76

Calls

4 calls:

73.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
46.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
34.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))
7.0ms	(/.f64 1/3 a)

simplify135.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

797×	`fma-def_binary64`
340×	`distribute-rgt-in_binary64`
235×	`cancel-sign-sub-inv_binary64`
185×	`fma-neg_binary64`
160×	`associate-r_binary64`

Counts

199 → 357

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	5008
1	661	4039
2	2464	3848
3	4911	3848

prune150.0ms (2.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	351	6	357
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	353	6	359

Error

0.0b

Counts

359 → 6

Alt Table

Status	Error	Program
	53.3b	(/.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3) a)
	53.2b	(.f64 (+.f64 (fma.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (neg.f64 (.f64 (sqrt.f64 b) (sqrt.f64 b)))) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) (.f64 (sqrt.f64 b) (sqrt.f64 b)))) (/.f64 1/3 a))
▶	0.5b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	1.2b	(neg.f64 (fma.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 135/128 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 1/2 (/.f64 c b) (.f64 3/8 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))
	53.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (exp.f64 (-.f64 (log.f64 1/3) (log.f64 a))))
	1.8b	(.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) (.f64 405/128 (/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7)))))) (/.f64 1/3 a))

Compiler

Compiled 6043 to 3509 computations (41.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 a (.f64 c -3) (.f64 b b))
✓	0.2b	(fma.f64 a (*.f64 c -3) 0)
✓	0.3b	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
	0.4b	(/.f64 1/3 a)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 44

Calls

2 calls:

5.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
0.0ms	(fma.f64 a (*.f64 c -3) 0)

series80.0ms (1.4%)

Counts

2 → 48

Calls

2 calls:

52.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
28.0ms	(fma.f64 a (*.f64 c -3) 0)

simplify106.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

517×	`distribute-rgt-in_binary64`
506×	`associate-/l/_binary64`
492×	`associate-l_binary64`
430×	`associate-/r/_binary64`
383×	`associate-r_binary64`

Counts

92 → 155

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	1049
1	175	901
2	597	847
3	2395	797
4	4205	797
5	4724	797
6	5000	797
7	4845	797

prune139.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	277	5	282
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	282	6	288

Error

Counts

288 → 6

Alt Table

Status	Error	Program
	0.6b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (cbrt.f64 (pow.f64 (/.f64 1/3 a) 3))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	0.6b	(/.f64 (cbrt.f64 (.f64 1/27 (.f64 (pow.f64 c 3) -27))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	0.7b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b))) (cbrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))) (cbrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b))))) b))
▶	0.5b	(/.f64 (.f64 (.f64 -3 (.f64 c a)) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
	1.2b	(neg.f64 (fma.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 135/128 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 1/2 (/.f64 c b) (.f64 3/8 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))
	0.5b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (.f64 a -3) (.f64 b b)) 3))) b))

Compiler

Compiled 4088 to 2542 computations (37.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 a (.f64 c -3) (.f64 b b))
✓	0.3b	(.f64 -3 (.f64 c a))
✓	0.3b	(.f64 (.f64 -3 (*.f64 c a)) (/.f64 1/3 a))
	0.4b	(/.f64 1/3 a)

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-cbrt-cube_binary64`
28×	`add-exp-log_binary64`
16×	`pow1_binary64`
15×	`cbrt-unprod_binary64`
15×	`prod-exp_binary64`

Counts

2 → 60

Calls

2 calls:

7.0ms	(.f64 (.f64 -3 (*.f64 c a)) (/.f64 1/3 a))
4.0ms	(.f64 -3 (.f64 c a))

series34.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

21.0ms	(.f64 -3 (.f64 c a))
12.0ms	(.f64 (.f64 -3 (*.f64 c a)) (/.f64 1/3 a))

simplify93.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

488×	`*-commutative_binary64`
450×	`associate-/l*_binary64`
378×	`associate-*r/_binary64`
300×	`associate-*l/_binary64`
256×	`associate-l_binary64`

Counts

84 → 147

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	108	1056
1	273	771
2	1190	744
3	3279	723
4	3759	681
5	4923	681
6	4939	681

prune128.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	400	1	401
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	401	6	407

Error

Counts

407 → 6

Alt Table

Status	Error	Program
	0.6b	(/.f64 (cbrt.f64 (.f64 1/27 (.f64 (pow.f64 c 3) -27))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
▶	0.3b	(/.f64 (.f64 -3 (.f64 c 1/3)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	0.7b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b))) (cbrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))) (cbrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b))))) b))
✓	0.5b	(/.f64 (.f64 (.f64 -3 (.f64 c a)) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
	1.2b	(neg.f64 (fma.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 135/128 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 1/2 (/.f64 c b) (.f64 3/8 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))
	0.5b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (.f64 a -3) (.f64 b b)) 3))) b))

Compiler

Compiled 3819 to 2200 computations (42.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 -3 (.f64 c 1/3)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	0.1b	(fma.f64 a (.f64 c -3) (.f64 b b))
✓	0.1b	(.f64 -3 (.f64 c 1/3))
✓	0.3b	(*.f64 c 1/3)

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
12×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`pow1_binary64`

Counts

3 → 69

Calls

3 calls:

7.0ms	(/.f64 (.f64 -3 (.f64 c 1/3)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
4.0ms	(.f64 -3 (.f64 c 1/3))
3.0ms	(*.f64 c 1/3)

series209.0ms (3.6%)

Counts

3 → 44

Calls

3 calls:

196.0ms	(/.f64 (.f64 -3 (.f64 c 1/3)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
7.0ms	(.f64 -3 (.f64 c 1/3))
5.0ms	(*.f64 c 1/3)

simplify94.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

840×	`fma-def_binary64`
411×	`associate-*l/_binary64`
349×	`associate-*r/_binary64`
310×	`associate-/r/_binary64`
232×	`associate-/l/_binary64`

Counts

113 → 199

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	182	2144
1	475	1735
2	1719	1683
3	4825	1677
4	5351	1677

prune141.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	555	4	559
Fresh	4	0	4
Picked	1	0	1
Done	0	1	1
Total	560	5	565

Error

Counts

565 → 5

Alt Table

Status	Error	Program
	0.6b	(/.f64 (.f64 -3 (.f64 c 1/3)) (+.f64 (sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))))) b))
	0.4b	(/.f64 (.f64 -3 (.f64 c 1/3)) (+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (.f64 a -3) (.f64 b b)) 3))) b))
	0.6b	(/.f64 (cbrt.f64 (pow.f64 (neg.f64 c) 3)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	1.2b	(fma.f64 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7)) -135/128 (fma.f64 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5)) -9/16 (fma.f64 (/.f64 (.f64 (.f64 c c) a) (pow.f64 b 3)) -3/8 (.f64 -1/2 (/.f64 c b)))))
✓	0.5b	(/.f64 (.f64 (.f64 -3 (.f64 c a)) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))

Compiler

Compiled 3773 to 2317 computations (38.6% saved)

regimes1.6s (28.3%)

Accuracy

Total 0.1b remaining (71.2%)

Threshold costs 0.1b (71.2%)

Compiler

Compiled 33311 to 22979 computations (31% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
1×	`distribute-frac-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	17	21
2	21	21
3	24	21
4	27	21
5	28	21
6	28	21

end1.0ms (0%)

Compiler: Compiled 17 to 11 computations (35.3% saved)

sample1.7s (30%)

Algorithm

1×

intervals

Results

465.0ms	3757×	body	256	valid
276.0ms	8799×	pre	128	true
270.0ms	1489×	body	512	valid
183.0ms	2754×	body	128	valid
50.0ms	799×	body	128	nan

Compiler

Compiled 206 to 142 computations (31.1% saved)

Details

analyze406.0ms (7%)

sample54.0ms (0.9%)

simplify365.0ms (6.3%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite20.0ms (0.4%)

series160.0ms (2.8%)

simplify135.0ms (2.3%)

prune150.0ms (2.6%)

localize13.0ms (0.2%)

rewrite7.0ms (0.1%)

series80.0ms (1.4%)

simplify106.0ms (1.8%)

prune139.0ms (2.4%)

localize13.0ms (0.2%)

rewrite13.0ms (0.2%)

series34.0ms (0.6%)

simplify93.0ms (1.6%)

prune128.0ms (2.2%)

localize11.0ms (0.2%)

rewrite16.0ms (0.3%)

series209.0ms (3.6%)

simplify94.0ms (1.6%)

prune141.0ms (2.4%)

regimes1.6s (28.3%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.7s (30%)

Profiling