Details

analyze359.0ms (5.5%)

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 43 to 31 computations (27.9% saved)

sample2.3s (35.4%)

Results

1.1s	3925×	body	256	valid
575.0ms	1451×	body	512	valid
429.0ms	2880×	body	128	valid
124.0ms	851×	body	128	invalid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify350.0ms (5.4%)

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

51.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	51.6b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
▶	51.6b	(.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)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 a (.f64 c -3) (.f64 b b))
✓	0.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
✓	0.3b	(/.f64 1/3 a)
✓	29.1b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

series147.0ms (2.3%)

Counts

4 → 76

Calls

4 calls:

86.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
50.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
9.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))
1.0ms	(/.f64 1/3 a)

rewrite21.0ms (0.3%)

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))

simplify102.0ms (1.6%)

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 → 221

Iterations

Useful iterations: 2 (0.0ms)

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

prune157.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	215	6	221
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	217	6	223

Error

0.1b

Counts

223 → 6

Alt Table

Status	Error	Program
▶	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))
	2.9b	(.f64 (fma.f64 -3/2 (/.f64 (.f64 c a) b) (fma.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8 (.f64 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -27/16))) (/.f64 1/3 a))
	1.8b	(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)))))))
	51.6b	(.f64 (/.f64 (-.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (.f64 b b)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)) (/.f64 1/3 a))
	51.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (.f64 (sqrt.f64 1/3) (/.f64 (sqrt.f64 1/3) a)))
	2.2b	(.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 6071 to 3533 computations (41.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series321.0ms (5%)

Counts

3 → 68

Calls

3 calls:

305.0ms	(/.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))
11.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
5.0ms	(fma.f64 a (*.f64 c -3) 0)

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
14×	`times-frac_binary64`

Counts

3 → 74

Calls

3 calls:

9.0ms	(/.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))
6.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
0.0ms	(fma.f64 a (*.f64 c -3) 0)

simplify93.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

561×	`associate-/l/_binary64`
487×	`div-sub_binary64`
483×	`fma-def_binary64`
201×	`distribute-rgt-in_binary64`
155×	`associate-/l*_binary64`

Counts

142 → 149

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	202	3063
1	529	2602
2	1978	2548
3	4289	2542
4	5631	2542

prune175.0ms (2.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	174	8	182
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	180	8	188

Error

0.0b

Counts

188 → 8

Alt Table

Status	Error	Program
	0.5b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) 1/3) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) a))
▶	0.1b	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	0.7b	(.f64 (/.f64 (fma.f64 a (.f64 c -3) 0) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))) (/.f64 (/.f64 1/3 a) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))))
	0.4b	(/.f64 (/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) 1/3) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	0.6b	(/.f64 1 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))))
	1.3b	(.f64 (/.f64 (fma.f64 a (.f64 c -3) 0) (.f64 (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)) (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)))) (/.f64 (/.f64 1/3 a) (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))))
	0.7b	(cbrt.f64 (/.f64 (.f64 (.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (fma.f64 a (.f64 c -3) 0)) (fma.f64 a (.f64 c -3) 0)) (/.f64 (.f64 (.f64 1/3 1/3) 1/3) (.f64 (.f64 a a) a))) (.f64 (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))))
	1.3b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 1/3 (cbrt.f64 a)))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))

Compiler

Compiled 5981 to 3631 computations (39.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))
✓	0.1b	(+.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 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))

series323.0ms (5%)

Counts

3 → 60

Calls

3 calls:

227.0ms	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
48.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))
47.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
40×	`times-frac_binary64`
33×	`add-sqr-sqrt_binary64`
32×	`add-cube-cbrt_binary64`
15×	`distribute-lft-neg-in_binary64`

Counts

3 → 107

Calls

3 calls:

6.0ms	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
3.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
1.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

simplify159.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

473×	`fma-def_binary64`
278×	`div-sub_binary64`
247×	`associate-/l/_binary64`
187×	`cancel-sign-sub-inv_binary64`
166×	`distribute-rgt-neg-out_binary64`

Counts

167 → 223

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	253	4899
1	638	4739
2	2058	4559
3	4528	4553
4	4983	4553
5	4903	4553

prune186.0ms (2.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	243	4	247
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	250	5	255

Error

Counts

255 → 5

Alt Table

Status	Error	Program
	0.5b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) 1/3) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) a))
	0.6b	(/.f64 (sqrt.f64 c) (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (neg.f64 (sqrt.f64 c))))
	0.3b	(.f64 (neg.f64 c) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))
▶	0.1b	(/.f64 (neg.f64 c) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))))
	0.1b	(/.f64 (neg.f64 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) b))

Compiler

Compiled 6368 to 3431 computations (46.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series289.0ms (4.5%)

Counts

2 → 40

Calls

2 calls:

240.0ms	(/.f64 (neg.f64 c) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))))
48.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64`
40×	`times-frac_binary64`
29×	`add-sqr-sqrt_binary64`
29×	`add-cube-cbrt_binary64`
15×	`distribute-lft-neg-in_binary64`

Counts

2 → 89

Calls

2 calls:

6.0ms	(/.f64 (neg.f64 c) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))))
3.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))))

simplify119.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

376×	`fma-def_binary64`
331×	`associate-/r/_binary64`
318×	`div-sub_binary64`
247×	`associate-/l/_binary64`
216×	`fma-neg_binary64`

Counts

129 → 177

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	223	4119
1	574	3965
2	1916	3826
3	4714	3820
4	5233	3820

prune177.0ms (2.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	245	0	245
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	245	5	250

Error

Counts

250 → 5

Alt Table

Status	Error	Program
	0.5b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) 1/3) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) a))
	0.6b	(/.f64 (sqrt.f64 c) (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (neg.f64 (sqrt.f64 c))))
	0.3b	(.f64 (neg.f64 c) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))
✓	0.1b	(/.f64 (neg.f64 c) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))))
	0.1b	(/.f64 (neg.f64 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))) b))

Compiler

Compiled 6196 to 3325 computations (46.3% saved)

regimes1.0s (15.7%)

Accuracy

Total 0.1b remaining (79.4%)

Threshold costs 0.1b (79.4%)

Counts

179 → 1

Compiler

Compiled 25341 to 16840 computations (33.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	20	21
2	24	21
3	27	21
4	28	21
5	28	21

end86.0ms (1.3%)

Compiler: Compiled 144 to 93 computations (35.4% saved)

Details

analyze359.0ms (5.5%)

sample2.3s (35.4%)

simplify350.0ms (5.4%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

series147.0ms (2.3%)

rewrite21.0ms (0.3%)

simplify102.0ms (1.6%)

prune157.0ms (2.4%)

localize12.0ms (0.2%)

series321.0ms (5%)

rewrite20.0ms (0.3%)

simplify93.0ms (1.4%)

prune175.0ms (2.7%)

localize9.0ms (0.1%)

series323.0ms (5%)

rewrite19.0ms (0.3%)

simplify159.0ms (2.5%)

prune186.0ms (2.9%)

localize9.0ms (0.1%)

series289.0ms (4.5%)

rewrite18.0ms (0.3%)

simplify119.0ms (1.8%)

prune177.0ms (2.7%)

regimes1.0s (15.7%)

simplify3.0ms (0%)

end86.0ms (1.3%)

Profiling