Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample1.1s (44.2%)

Results

863.0ms	8256×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 47 to 38 computations (19.1% saved)

simplify228.0ms (9.1%)

Algorithm

1×	egg-herbie

Rules

2682×	`fma-neg_binary64`
690×	`times-frac_binary64`
636×	`fma-def_binary64`
533×	`sub-neg_binary64`
432×	`distribute-rgt-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	25	19
2	45	17
3	65	17
4	78	17
5	89	17
6	129	17
7	180	17
8	288	17
9	497	17
10	671	17
11	811	17
12	976	17
13	1611	17
14	3407	17
15	3743	17
16	3727	17
17	3787	17
18	3819	17
19	3887	17
20	3898	17
21	4186	17
22	4220	17
23	4236	17
24	4236	17
25	4236	17
26	6212	17

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))
▶	0.4b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

Compiler

Compiled 83 to 64 computations (22.9% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
✓	0.1b	(fma.f64 6 x -6)
✓	0.3b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

series20.0ms (0.8%)

Counts

3 → 18

Calls

3 calls:

14.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
4.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
1.0ms	(fma.f64 6 x -6)

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

2.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
0.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
0.0ms	(fma.f64 6 x -6)

simplify84.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

492×	`div-sub_binary64`
426×	`fma-neg_binary64`
384×	`*-commutative_binary64`
348×	`distribute-rgt-in_binary64`
336×	`distribute-lft-in_binary64`

Counts

67 → 64

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	1136
1	110	1034
2	285	1034
3	751	1025
4	2413	1025
5	3154	1025
6	4752	1025
7	4942	1025

prune61.0ms (2.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	56	8	64
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	58	8	66

Error

0.0b

Counts

66 → 8

Alt Table

Status	Error	Program
	3.0b	(/.f64 (fma.f64 6 x -6) (expm1.f64 (log1p.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	31.3b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	0.6b	(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (fma.f64 6 x -6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
▶	0.3b	(log.f64 (exp.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	21.3b	(/.f64 (cbrt.f64 (pow.f64 (fma.f64 6 x -6) 3)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
	33.6b	6
	31.8b	(/.f64 (sqrt.f64 (fma.f64 6 x -6)) (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (sqrt.f64 (fma.f64 6 x -6))))
	0.5b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))

Compiler

Compiled 1443 to 1052 computations (27.1% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
	0.1b	(fma.f64 6 x -6)
✓	0.2b	(exp.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
	0.3b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

series21.0ms (0.8%)

Counts

1 → 3

Calls

1 calls:

21.0ms

(exp.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`exp-prod_binary64`
9×	`times-frac_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`

Counts

1 → 23

Calls

1 calls:

2.0ms

(exp.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

simplify96.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

706×	`unswap-sqr_binary64`
492×	`associate-/l*_binary64`
426×	`times-frac_binary64`
402×	`associate-l_binary64`
365×	`fma-def_binary64`

Counts

26 → 30

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	53	542
1	80	505
2	136	505
3	188	505
4	272	505
5	425	504
6	787	502
7	1759	502
8	4675	500
9	4884	500
10	5000	500
11	4959	500

prune88.0ms (3.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	95	7	102

Error

Counts

102 → 7

Alt Table

Status	Error	Program
	0.6b	(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (fma.f64 6 x -6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	31.3b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	21.3b	(/.f64 (cbrt.f64 (pow.f64 (fma.f64 6 x -6) 3)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
▶	0.3b	(log.f64 (exp.f64 (/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))))
	33.6b	6
	0.4b	(log.f64 (cbrt.f64 (exp.f64 (/.f64 (fma.f64 x 18 -18) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))))
	0.5b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))

Compiler

Compiled 2264 to 1694 computations (25.2% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (sqrt.f64 x) x)
✓	0.1b	(fma.f64 -6 x 6)
✓	0.2b	(exp.f64 (/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x))))
✓	0.3b	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))

series48.0ms (1.9%)

Counts

4 → 20

Calls

4 calls:

24.0ms	(exp.f64 (/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x))))
17.0ms	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
5.0ms	(fma.f64 4 (sqrt.f64 x) x)
2.0ms	(fma.f64 -6 x 6)

rewrite18.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
37×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
21×	`exp-prod_binary64`

Counts

4 → 90

Calls

4 calls:

8.0ms	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
4.0ms	(exp.f64 (/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x))))
0.0ms	(fma.f64 -6 x 6)
0.0ms	(fma.f64 4 (sqrt.f64 x) x)

simplify92.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

507×	`times-frac_binary64`
447×	`distribute-rgt-in_binary64`
430×	`distribute-lft-in_binary64`
338×	`associate-/l*_binary64`
244×	`fma-def_binary64`

Counts

110 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	2095
1	199	1953
2	433	1953
3	1155	1951
4	4711	1951
5	4928	1951

prune94.0ms (3.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	105	7	112

Error

Counts

112 → 7

Alt Table

Status	Error	Program
	0.6b	(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (fma.f64 6 x -6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	31.3b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	21.3b	(/.f64 (cbrt.f64 (pow.f64 (fma.f64 6 x -6) 3)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
✓	0.3b	(log.f64 (exp.f64 (/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))))
	33.6b	6
▶	0.4b	(log.f64 (cbrt.f64 (exp.f64 (/.f64 (fma.f64 x 18 -18) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))))
	0.5b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))

Compiler

Compiled 2682 to 1985 computations (26% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 18 -18)
✓	0.3b	(/.f64 (fma.f64 x 18 -18) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
✓	0.4b	(exp.f64 (/.f64 (fma.f64 x 18 -18) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
✓	0.5b	(cbrt.f64 (exp.f64 (/.f64 (fma.f64 x 18 -18) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

series63.0ms (2.5%)

Counts

4 → 21

Calls

4 calls:

29.0ms	(cbrt.f64 (exp.f64 (/.f64 (fma.f64 x 18 -18) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
19.0ms	(exp.f64 (/.f64 (fma.f64 x 18 -18) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
13.0ms	(/.f64 (fma.f64 x 18 -18) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
3.0ms	(fma.f64 x 18 -18)

rewrite10.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
13×	`exp-prod_binary64`

Counts

4 → 75

Calls

4 calls:

2.0ms	(cbrt.f64 (exp.f64 (/.f64 (fma.f64 x 18 -18) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
2.0ms	(exp.f64 (/.f64 (fma.f64 x 18 -18) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
2.0ms	(/.f64 (fma.f64 x 18 -18) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
0.0ms	(fma.f64 x 18 -18)

simplify96.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

576×	`fma-neg_binary64`
482×	`distribute-rgt-in_binary64`
468×	`distribute-lft-in_binary64`
364×	`associate-/r/_binary64`
213×	`associate-l_binary64`

Counts

96 → 141

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	101	1899
1	151	1781
2	360	1781
3	957	1743
4	3327	1735
5	4889	1735
6	5114	1735

prune139.0ms (5.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	142	6	148

Error

Counts

148 → 6

Alt Table

Status	Error	Program
	0.3b	(log.f64 (pow.f64 (exp.f64 (/.f64 (fma.f64 x 18 -18) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) 1/3))
	21.3b	(/.f64 (cbrt.f64 (pow.f64 (fma.f64 6 x -6) 3)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
	31.3b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
✓	0.3b	(log.f64 (exp.f64 (/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))))
	33.6b	6
	0.5b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))

Compiler

Compiled 3536 to 2671 computations (24.5% saved)

regimes83.0ms (3.3%)

Accuracy

Total 0.2b remaining (94%)

Threshold costs 0.2b (94%)

Counts

43 → 1

Compiler

Compiled 1452 to 1161 computations (20% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	18	24
2	17	24

end102.0ms (4.1%)

Compiler: Compiled 114 to 93 computations (18.4% saved)

Details

analyze3.0ms (0.1%)

sample1.1s (44.2%)

simplify228.0ms (9.1%)

prune4.0ms (0.1%)

localize8.0ms (0.3%)

series20.0ms (0.8%)

rewrite4.0ms (0.2%)

simplify84.0ms (3.3%)

prune61.0ms (2.4%)

localize10.0ms (0.4%)

series21.0ms (0.8%)

rewrite4.0ms (0.1%)

simplify96.0ms (3.8%)

prune88.0ms (3.5%)

localize10.0ms (0.4%)

series48.0ms (1.9%)

rewrite18.0ms (0.7%)

simplify92.0ms (3.7%)

prune94.0ms (3.7%)

localize11.0ms (0.4%)

series63.0ms (2.5%)

rewrite10.0ms (0.4%)

simplify96.0ms (3.8%)

prune139.0ms (5.5%)

regimes83.0ms (3.3%)

simplify4.0ms (0.1%)

end102.0ms (4.1%)

Profiling