Details

analyze649.0ms (4.9%)

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)

sample3.2s (24.2%)

Results

1.4s	3053×	body	256	valid
1.4s	5202×	body	128	valid
232.0ms	948×	body	128	invalid
0.0ms	1×	body	512	valid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify544.0ms (4.1%)

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

prune8.0ms (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

43.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	43.7b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
▶	43.7b	(.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)

localize20.0ms (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 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
✓	0.4b	(/.f64 1/3 a)
✓	38.1b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

series314.0ms (2.4%)

Counts

4 → 76

Calls

4 calls:

174.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
101.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
23.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))
17.0ms	(/.f64 1/3 a)

rewrite51.0ms (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:

19.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
10.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
5.0ms	(/.f64 1/3 a)
1.0ms	(fma.f64 a (.f64 c -3) (.f64 b b))

simplify168.0ms (1.3%)

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 → 221

Iterations

Useful iterations: 2 (0.0ms)

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

prune315.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	214	7	221
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	216	7	223

Error

0.1b

Counts

223 → 7

Alt Table

Status	Error	Program
	43.7b	(/.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)) 1/3) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) a))
	3.7b	(.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))
	43.7b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (/.f64 (/.f64 1/3 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a)))
	2.5b	(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))
	2.9b	(.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))
	43.7b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (/.f64 1 (sqrt.f64 a))) (/.f64 1/3 (sqrt.f64 a)))

Compiler

Compiled 6125 to 3563 computations (41.8% saved)

localize18.0ms (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	(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)

series29.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

19.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
10.0ms	(fma.f64 a (*.f64 c -3) 0)

rewrite16.0ms (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:

11.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
1.0ms	(fma.f64 a (*.f64 c -3) 0)

simplify139.0ms (1.1%)

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

prune218.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	131	5	136
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	136	7	143

Error

0.0b

Counts

143 → 7

Alt Table

Status	Error	Program
	0.7b	(/.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))
	2.5b	(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)))))))
	3.7b	(.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))
	0.7b	(/.f64 (.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (sqrt.f64 (/.f64 1/3 a))) (sqrt.f64 (/.f64 1/3 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
	1.5b	(/.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))
▶	0.2b	(/.f64 (/.f64 (.f64 (neg.f64 c) a) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
	1.4b	(/.f64 (.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 (sqrt.f64 1/3) (.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (sqrt.f64 1/3) (cbrt.f64 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))

Compiler

Compiled 4177 to 2599 computations (37.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series595.0ms (4.5%)

Counts

3 → 64

Calls

3 calls:

492.0ms	(/.f64 (/.f64 (.f64 (neg.f64 c) a) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
97.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
6.0ms	(/.f64 (*.f64 (neg.f64 c) a) a)

rewrite45.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
17×	`add-cbrt-cube_binary64`

Counts

3 → 105

Calls

3 calls:

16.0ms	(/.f64 (/.f64 (.f64 (neg.f64 c) a) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
7.0ms	(/.f64 (*.f64 (neg.f64 c) a) a)
6.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

simplify192.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

477×	`distribute-frac-neg_binary64`
427×	`fma-def_binary64`
398×	`div-sub_binary64`
212×	`associate-/l*_binary64`
196×	`times-frac_binary64`

Counts

169 → 209

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	252	4073
1	684	3807
2	2673	3673
3	4971	3673

prune353.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	229	4	233
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	233	7	240

Error

Counts

240 → 7

Alt Table

Status	Error	Program
	0.7b	(/.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))
	2.5b	(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 (neg.f64 c) (sqrt.f64 a)) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))) (/.f64 (/.f64 a (sqrt.f64 a)) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))))
	3.2b	(/.f64 (/.f64 (.f64 (neg.f64 c) a) a) (fma.f64 b 2 (fma.f64 (.f64 (/.f64 c b) a) -3/2 (/.f64 -9/8 (/.f64 (pow.f64 b 3) (.f64 (.f64 c c) (*.f64 a a)))))))
✓	0.2b	(/.f64 (/.f64 (.f64 (neg.f64 c) a) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
	0.3b	(.f64 (/.f64 (/.f64 (neg.f64 c) 1) 1) (/.f64 (/.f64 a a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))
▶	0.3b	(/.f64 (/.f64 (.f64 (neg.f64 c) a) a) (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 6751 to 3193 computations (52.7% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series619.0ms (4.7%)

Counts

2 → 72

Calls

2 calls:

454.0ms

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

164.0ms

(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)

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`times-frac_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
11×	`add-cbrt-cube_binary64`

Counts

2 → 61

Calls

2 calls:

12.0ms

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

1.0ms

(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)

simplify264.0ms (2%)

Algorithm

1×	egg-herbie

Rules

782×	`times-frac_binary64`
562×	`associate-/l*_binary64`
206×	`fma-def_binary64`
158×	`*-commutative_binary64`
132×	`associate-/r/_binary64`

Counts

133 → 218

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	533	7793
1	1736	7403
2	5457	7403

prune749.0ms (5.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	304	2	306
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	306	7	313

Error

Counts

313 → 7

Alt Table

Status	Error	Program
	0.7b	(.f64 (.f64 (/.f64 (neg.f64 c) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))) a) (/.f64 (/.f64 1 a) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))))
	0.8b	(.f64 (/.f64 (/.f64 (neg.f64 c) (sqrt.f64 a)) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))) (/.f64 (/.f64 a (sqrt.f64 a)) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))))
	3.2b	(/.f64 (/.f64 (.f64 (neg.f64 c) a) a) (fma.f64 b 2 (fma.f64 (.f64 (/.f64 c b) a) -3/2 (/.f64 -9/8 (/.f64 (pow.f64 b 3) (.f64 (.f64 c c) (*.f64 a a)))))))
	2.5b	(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)))))))
✓	0.2b	(/.f64 (/.f64 (.f64 (neg.f64 c) a) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
✓	0.3b	(/.f64 (/.f64 (.f64 (neg.f64 c) a) a) (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))
	0.3b	(.f64 (neg.f64 c) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))

Compiler

Compiled 14766 to 8664 computations (41.3% saved)

regimes4.1s (31.1%)

Accuracy

Total 0.1b remaining (87.6%)

Threshold costs 0.1b (87.6%)

Counts

310 → 1

Compiler

Compiled 44611 to 29241 computations (34.5% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`
3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`*-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	21
1	24	21
2	32	21
3	34	21
4	35	21
5	33	21

end512.0ms (3.9%)

Compiler: Compiled 261 to 167 computations (36% saved)

Details

analyze649.0ms (4.9%)

sample3.2s (24.2%)

simplify544.0ms (4.1%)

prune8.0ms (0.1%)

localize20.0ms (0.2%)

series314.0ms (2.4%)

rewrite51.0ms (0.4%)

simplify168.0ms (1.3%)

prune315.0ms (2.4%)

localize18.0ms (0.1%)

series29.0ms (0.2%)

rewrite16.0ms (0.1%)

simplify139.0ms (1.1%)

prune218.0ms (1.6%)

localize12.0ms (0.1%)

series595.0ms (4.5%)

rewrite45.0ms (0.3%)

simplify192.0ms (1.5%)

prune353.0ms (2.7%)

localize28.0ms (0.2%)

series619.0ms (4.7%)

rewrite31.0ms (0.2%)

simplify264.0ms (2%)

prune749.0ms (5.7%)

regimes4.1s (31.1%)

simplify5.0ms (0%)

end512.0ms (3.9%)

Profiling