Details

analyze350.0ms (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)

sample2.2s (35.1%)

Results

1.0s	3960×	body	256	valid
562.0ms	1498×	body	512	valid
419.0ms	2798×	body	128	valid
116.0ms	824×	body	128	invalid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify358.0ms (5.6%)

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

55.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	55.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
▶	55.2b	(.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))
✓	0.1b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
✓	0.4b	(/.f64 1/3 a)
✓	27.1b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

series102.0ms (1.6%)

Counts

4 → 76

Calls

4 calls:

56.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
33.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
9.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))
3.0ms	(/.f64 1/3 a)

rewrite23.0ms (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))

simplify99.0ms (1.5%)

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

prune135.0ms (2.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	218	3	221
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	220	3	223

Error

0.0b

Counts

223 → 3

Alt Table

Status	Error	Program
	0.9b	(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 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	1.9b	(.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))

Compiler

Compiled 5835 to 3381 computations (42.1% 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)
✓	0.2b	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
	0.4b	(/.f64 1/3 a)

series14.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

9.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
5.0ms	(fma.f64 a (*.f64 c -3) 0)

rewrite9.0ms (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)

simplify94.0ms (1.5%)

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 → 79

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

prune138.0ms (2.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	134	5	139

Error

0.0b

Counts

139 → 5

Alt Table

Status	Error	Program
	0.8b	(/.f64 (.f64 (cbrt.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 1/3 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	0.9b	(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)))))))
	0.8b	(/.f64 (.f64 (.f64 (.f64 -3 (.f64 c a)) (/.f64 (sqrt.f64 1/3) (sqrt.f64 a))) (/.f64 (sqrt.f64 1/3) (sqrt.f64 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
▶	0.3b	(/.f64 (.f64 (.f64 (neg.f64 c) a) (/.f64 1 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	2.0b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (+.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (fma.f64 c (.f64 a -3) (.f64 b b))))) b))

Compiler

Compiled 4055 to 2519 computations (37.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (.f64 (.f64 (neg.f64 c) a) (/.f64 1 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b 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))
✓	0.2b	(.f64 (.f64 (neg.f64 c) a) (/.f64 1 a))

series157.0ms (2.5%)

Counts

3 → 64

Calls

3 calls:

122.0ms

(/.f64 (*.f64 (*.f64 (neg.f64 c) a) (/.f64 1 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))

32.0ms

(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)

3.0ms

(*.f64 (*.f64 (neg.f64 c) a) (/.f64 1 a))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-exp-log_binary64`
33×	`add-cbrt-cube_binary64`
24×	`prod-exp_binary64`
20×	`*-un-lft-identity_binary64`
17×	`div-exp_binary64`

Counts

3 → 101

Calls

3 calls:

9.0ms

(/.f64 (*.f64 (*.f64 (neg.f64 c) a) (/.f64 1 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b))

7.0ms

(*.f64 (*.f64 (neg.f64 c) a) (/.f64 1 a))

3.0ms

(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -3) (*.f64 b b))) b)

simplify124.0ms (2%)

Algorithm

1×	egg-herbie

Rules

564×	`fma-def_binary64`
352×	`distribute-frac-neg_binary64`
237×	`div-sub_binary64`
233×	`associate-/l*_binary64`
186×	`associate-l_binary64`

Counts

165 → 189

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	238	3498
1	674	2907
2	2568	2812
3	4763	2812
4	4977	2812
5	4918	2812

prune172.0ms (2.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	209	4	213
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	213	5	218

Error

Counts

218 → 5

Alt Table

Status	Error	Program
	0.9b	(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)))))))
▶	0.4b	(/.f64 (.f64 (neg.f64 c) a) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) a))
	0.5b	(.f64 (.f64 (.f64 (neg.f64 c) a) (/.f64 1 a)) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))
	0.5b	(/.f64 1 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (.f64 (.f64 (neg.f64 c) a) (/.f64 1 a))))
	0.7b	(cbrt.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 (neg.f64 c) a) (/.f64 1 a)) (.f64 (.f64 (neg.f64 c) a) (/.f64 1 a))) (.f64 (.f64 (neg.f64 c) a) (/.f64 1 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))))

Compiler

Compiled 6265 to 3261 computations (47.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) a)
	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))
✓	0.4b	(/.f64 (.f64 (neg.f64 c) a) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) a))

series164.0ms (2.6%)

Counts

2 → 40

Calls

2 calls:

122.0ms	(/.f64 (.f64 (neg.f64 c) a) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) a))
41.0ms	(.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) a)

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`cbrt-unprod_binary64`

Counts

2 → 49

Calls

2 calls:

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

simplify90.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

618×	`fma-def_binary64`
351×	`distribute-frac-neg_binary64`
301×	`times-frac_binary64`
213×	`distribute-rgt-neg-out_binary64`
189×	`associate-/l*_binary64`

Counts

89 → 125

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	193	2920
1	588	2489
2	2565	2400
3	4805	2394
4	4952	2394

prune160.0ms (2.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	197	2	199
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	199	5	204

Error

Counts

204 → 5

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 (.f64 (neg.f64 c) a) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) a))
	0.5b	(.f64 (.f64 (.f64 (neg.f64 c) a) (/.f64 1 a)) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))
	0.5b	(/.f64 1 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (.f64 (.f64 (neg.f64 c) a) (/.f64 1 a))))
	0.9b	(fma.f64 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5)) -9/16 (fma.f64 -1/2 (/.f64 c b) (fma.f64 (/.f64 (.f64 (.f64 c c) a) (pow.f64 b 3)) -3/8 (/.f64 -135/128 (/.f64 (pow.f64 b 7) (*.f64 (pow.f64 c 4) (pow.f64 a 3)))))))
	0.7b	(cbrt.f64 (/.f64 (.f64 (.f64 (.f64 (neg.f64 c) (neg.f64 c)) (neg.f64 c)) (.f64 (.f64 a a) a)) (.f64 (.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)) (.f64 (.f64 a a) a))))

Compiler

Compiled 5663 to 2885 computations (49.1% saved)

regimes1.7s (27.2%)

Accuracy

Total 0.1b remaining (76.7%)

Threshold costs 0.1b (76.7%)

Counts

272 → 1

Compiler

Compiled 42316 to 27676 computations (34.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`
5×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	23	27
2	31	27
3	38	27
4	45	27
5	50	27
6	53	27
7	54	27
8	54	27

end115.0ms (1.8%)

Compiler: Compiled 218 to 135 computations (38.1% saved)

Details

analyze350.0ms (5.5%)

sample2.2s (35.1%)

simplify358.0ms (5.6%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

series102.0ms (1.6%)

rewrite23.0ms (0.4%)

simplify99.0ms (1.5%)

prune135.0ms (2.1%)

localize13.0ms (0.2%)

series14.0ms (0.2%)

rewrite9.0ms (0.1%)

simplify94.0ms (1.5%)

prune138.0ms (2.2%)

localize13.0ms (0.2%)

series157.0ms (2.5%)

rewrite29.0ms (0.4%)

simplify124.0ms (2%)

prune172.0ms (2.7%)

localize11.0ms (0.2%)

series164.0ms (2.6%)

rewrite18.0ms (0.3%)

simplify90.0ms (1.4%)

prune160.0ms (2.5%)

regimes1.7s (27.2%)

simplify3.0ms (0%)

end115.0ms (1.8%)

Profiling