Details

analyze366.0ms (5.2%)

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)

sample1.5s (21.7%)

Results

1.2s	7955×	body	128	valid
138.0ms	986×	body	128	invalid
84.0ms	301×	body	256	valid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify363.0ms (5.2%)

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

prune5.0ms (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

29.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	29.6b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	29.6b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 a (.f64 c -3) (.f64 b b))
✓	0.3b	(/.f64 1/3 a)
✓	0.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
✓	29.5b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

series148.0ms (2.1%)

Counts

4 → 76

Calls

4 calls:

83.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
53.0ms	(-.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)

rewrite24.0ms (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:

10.0ms	(.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 (1.5%)

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

prune155.0ms (2.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	213	8	221
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	215	8	223

Error

0.1b

Counts

223 → 8

Alt Table

Status	Error	Program
	29.6b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (sqrt.f64 (/.f64 1/3 a))) (sqrt.f64 (/.f64 1/3 a)))
	29.7b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (*.f64 (cbrt.f64 (/.f64 1/3 a)) (cbrt.f64 (/.f64 1/3 a)))) (cbrt.f64 (/.f64 1/3 a)))
	5.7b	(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)))))))
▶	0.6b	(/.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))
	29.7b	(/.f64 (.f64 (-.f64 (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 3) (pow.f64 b 3)) 1/3) (.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 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))) a))
	6.0b	(.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))
	7.8b	(.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))
	29.6b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) 1/3) (/.f64 1 a))

Compiler

Compiled 6205 to 3625 computations (41.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series61.0ms (0.9%)

Counts

3 → 68

Calls

3 calls:

47.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
9.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
5.0ms	(fma.f64 a (*.f64 c -3) 0)

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 64

Calls

3 calls:

5.0ms	(.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a))
3.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
0.0ms	(fma.f64 a (*.f64 c -3) 0)

simplify82.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

623×	`times-frac_binary64`
538×	`associate-/l*_binary64`
487×	`fma-def_binary64`
394×	`associate-/r*_binary64`
151×	`distribute-rgt-in_binary64`

Counts

132 → 130

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	165	1963
1	414	1772
2	1326	1748
3	4883	1748
4	4961	1748

prune180.0ms (2.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	155	8	163
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	160	11	171

Error

0.0b

Counts

171 → 11

Alt Table

Status	Error	Program
	0.7b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (cbrt.f64 (/.f64 (.f64 (.f64 1/3 1/3) 1/3) (.f64 (.f64 a a) a)))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	1.0b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (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)))) b))
	5.7b	(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 c (.f64 a -3)) (/.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))
	0.5b	(/.f64 (/.f64 (.f64 (.f64 c (.f64 a -3)) 1/3) a) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))
	0.5b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 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))
▶	0.2b	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	29.5b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (/.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)))
	6.0b	(.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))
	0.7b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 a)) (fma.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))) b))
	29.6b	(.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) 1/3) (/.f64 1 a))

Compiler

Compiled 5621 to 3537 computations (37.1% 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)))
✓	0.2b	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
	0.2b	(fma.f64 a (.f64 c -3) (.f64 b b))
	0.3b	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)

series274.0ms (3.9%)

Counts

2 → 40

Calls

2 calls:

233.0ms	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b))
41.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 87

Calls

2 calls:

6.0ms	(/.f64 (neg.f64 c) (+.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)))

simplify115.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

349×	`fma-def_binary64`
320×	`associate-/r/_binary64`
306×	`div-sub_binary64`
243×	`associate-/l/_binary64`
221×	`fma-neg_binary64`

Counts

127 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	228	3973
1	566	3858
2	1878	3711
3	4616	3705
4	5106	3705

prune322.0ms (4.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	242	5	247
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	252	6	258

Error

Counts

258 → 6

Alt Table

Status	Error	Program
	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))))
	5.7b	(fma.f64 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5)) -9/16 (fma.f64 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7)) -135/128 (fma.f64 (/.f64 (.f64 (.f64 c c) a) (pow.f64 b 3)) -3/8 (.f64 -1/2 (/.f64 c b)))))
	0.5b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 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))
	0.4b	(/.f64 -1 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) c))
	0.4b	(.f64 (neg.f64 c) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))
▶	0.3b	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (.f64 a -3) (.f64 b b)) 3))) b))

Compiler

Compiled 6472 to 3512 computations (45.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 c (.f64 a -3) (.f64 b b))
✓	0.3b	(+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (.f64 a -3) (.f64 b b)) 3))) b)
✓	0.6b	(cbrt.f64 (pow.f64 (fma.f64 c (.f64 a -3) (.f64 b b)) 3))
✓	0.7b	(pow.f64 (fma.f64 c (.f64 a -3) (.f64 b b)) 3)

series138.0ms (2%)

Counts

4 → 128

Calls

4 calls:

88.0ms	(+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (.f64 a -3) (.f64 b b)) 3))) b)
32.0ms	(pow.f64 (fma.f64 c (.f64 a -3) (.f64 b b)) 3)
10.0ms	(cbrt.f64 (pow.f64 (fma.f64 c (.f64 a -3) (.f64 b b)) 3))
9.0ms	(fma.f64 c (.f64 a -3) (.f64 b b))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-prod_binary64`
18×	`fma-def_binary64`
17×	`*-un-lft-identity_binary64`
15×	`sqrt-prod_binary64`
15×	`add-sqr-sqrt_binary64`

Counts

4 → 90

Calls

4 calls:

8.0ms	(+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (.f64 a -3) (.f64 b b)) 3))) b)
1.0ms	(pow.f64 (fma.f64 c (.f64 a -3) (.f64 b b)) 3)
1.0ms	(cbrt.f64 (pow.f64 (fma.f64 c (.f64 a -3) (.f64 b b)) 3))
0.0ms	(fma.f64 c (.f64 a -3) (.f64 b b))

simplify109.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

452×	`fma-def_binary64`
422×	`times-frac_binary64`
278×	`unswap-sqr_binary64`
247×	`associate-/l*_binary64`
237×	`associate-/r*_binary64`

Counts

218 → 153

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	158	4004
1	392	3668
2	1254	3533
3	4507	3533
4	4964	3533

prune157.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	153	6	159

Error

Counts

159 → 6

Alt Table

Status	Error	Program
	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))))
	5.7b	(fma.f64 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5)) -9/16 (fma.f64 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7)) -135/128 (fma.f64 (/.f64 (.f64 (.f64 c c) a) (pow.f64 b 3)) -3/8 (.f64 -1/2 (/.f64 c b)))))
	0.5b	(/.f64 (.f64 (fma.f64 a (.f64 c -3) 0) (/.f64 1/3 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))
	0.4b	(/.f64 -1 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) c))
	0.4b	(.f64 (neg.f64 c) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)))
✓	0.3b	(/.f64 (neg.f64 c) (+.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 c (.f64 a -3) (.f64 b b)) 3))) b))

Compiler

Compiled 4018 to 2292 computations (43% saved)

regimes2.7s (38.3%)

Accuracy

Total 0.2b remaining (86.7%)

Threshold costs 0.2b (86.7%)

Counts

325 → 1

Compiler

Compiled 47145 to 31348 computations (33.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-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	14	21
1	25	21
2	29	21
3	32	21
4	33	21
5	32	21

end118.0ms (1.7%)

Compiler: Compiled 193 to 129 computations (33.2% saved)

Details

analyze366.0ms (5.2%)

sample1.5s (21.7%)

simplify363.0ms (5.2%)

prune5.0ms (0.1%)

localize10.0ms (0.1%)

series148.0ms (2.1%)

rewrite24.0ms (0.3%)

simplify102.0ms (1.5%)

prune155.0ms (2.2%)

localize13.0ms (0.2%)

series61.0ms (0.9%)

rewrite11.0ms (0.2%)

simplify82.0ms (1.2%)

prune180.0ms (2.6%)

localize9.0ms (0.1%)

series274.0ms (3.9%)

rewrite15.0ms (0.2%)

simplify115.0ms (1.6%)

prune322.0ms (4.6%)

localize12.0ms (0.2%)

series138.0ms (2%)

rewrite16.0ms (0.2%)

simplify109.0ms (1.6%)

prune157.0ms (2.2%)

regimes2.7s (38.3%)

simplify2.0ms (0%)

end118.0ms (1.7%)

Profiling