Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample5.2s (74.5%)

Results

3.8s	4312×	body	2048	valid
896.0ms	2032×	body	1024	valid
319.0ms	1030×	body	512	valid
99.0ms	518×	body	256	valid
41.0ms	364×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify67.0ms (1%)

Algorithm

1×	egg-herbie

Rules

819×	`div-sub_binary64`
801×	`associate-/l*_binary64`
624×	`fma-def_binary64`
581×	`fma-neg_binary64`
548×	`unswap-sqr_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	20	13
2	35	13
3	57	13
4	112	13
5	223	13
6	481	13
7	890	13
8	1570	13
9	4778	13
10	5815	13

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

30.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 x) 2)
✓	3.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

series5.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

3.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
2.0ms	(-.f64 (exp.f64 x) 2)

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`prod-diff_binary64`
18×	`add-cube-cbrt_binary64`
13×	`associate-+l+_binary64`

Counts

2 → 69

Calls

2 calls:

7.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
5.0ms	(-.f64 (exp.f64 x) 2)

simplify78.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

650×	`fma-neg_binary64`
326×	`fma-def_binary64`
296×	`distribute-rgt-in_binary64`
282×	`distribute-lft-in_binary64`
268×	`distribute-rgt-out_binary64`

Counts

85 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	145	1174
1	295	959
2	717	942
3	2801	932
4	4435	932
5	4838	932

prune68.0ms (1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	3	115

Error

0.0b

Counts

115 → 3

Alt Table

Status	Error	Program
	30.1b	(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
▶	0.7b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
	30.1b	(cbrt.f64 (pow.f64 (-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) 3))

Compiler

Compiled 2096 to 1199 computations (42.8% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))
✓	0.0b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
✓	0.0b	(*.f64 1/20160 (pow.f64 x 8))

series12.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

5.0ms

(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))

4.0ms

(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))

3.0ms

(*.f64 1/20160 (pow.f64 x 8))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`add-exp-log_binary64`
7×	`associate-r_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

3 → 47

Calls

3 calls:

4.0ms

(*.f64 1/20160 (pow.f64 x 8))

0.0ms

(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))

0.0ms

(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))

simplify54.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

798×	`fma-def_binary64`
562×	`associate-+l+_binary64`
546×	`associate-+r+_binary64`
247×	`associate-l_binary64`
214×	`associate-r_binary64`

Counts

71 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	91	1228
1	162	1128
2	390	1110
3	1598	1110
4	5154	1110

prune70.0ms (1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	71	3	74

Error

0.0b

Counts

74 → 3

Alt Table

Status	Error	Program
	30.1b	(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
▶	0.7b	(fma.f64 1/12 (pow.f64 x 4) (.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))
	30.1b	(cbrt.f64 (pow.f64 (-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) 3))

Compiler

Compiled 1701 to 1282 computations (24.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/12 (pow.f64 x 4) (.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))
✓	0.0b	(.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))))
	0.0b	(*.f64 1/20160 (pow.f64 x 8))
✓	28.2b	(sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))

series16.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

6.0ms

(sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))

5.0ms

(*.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))))

4.0ms

(fma.f64 1/12 (pow.f64 x 4) (*.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
19×	`pow1_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 78

Calls

3 calls:

6.0ms

(*.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))))

1.0ms

(sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))

0.0ms

(fma.f64 1/12 (pow.f64 x 4) (*.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))

simplify98.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

758×	`associate-+l+_binary64`
330×	`associate-l_binary64`
285×	`associate-r_binary64`
283×	`distribute-lft-in_binary64`
283×	`distribute-rgt-in_binary64`

Counts

114 → 135

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	2875
1	254	2537
2	708	2429
3	2728	2371
4	5619	2371

prune354.0ms (5.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	235	1	236
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	235	4	239

Error

0.0b

Counts

239 → 4

Alt Table

Status	Error	Program
✓	0.7b	(fma.f64 1/12 (pow.f64 x 4) (.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))
▶	3.6b	(fma.f64 1/12 (pow.f64 x 4) (exp.f64 (log.f64 (.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))))
	30.1b	(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
	30.1b	(cbrt.f64 (pow.f64 (-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) 3))

Compiler

Compiled 9283 to 6999 computations (24.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 1/20160 (pow.f64 x 8))
✓	3.0b	(exp.f64 (log.f64 (.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))))))
	28.2b	(sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
✓	29.1b	(log.f64 (.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))

series13.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

8.0ms

(log.f64 (*.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))

5.0ms

(exp.f64 (log.f64 (*.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))))))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`pow1_binary64`
28×	`log-pow_binary64`
17×	`exp-prod_binary64`
16×	`sqrt-pow1_binary64`
16×	`pow1/2_binary64`

Counts

2 → 54

Calls

2 calls:

5.0ms

(exp.f64 (log.f64 (*.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))))))

3.0ms

(log.f64 (*.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))

simplify86.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

809×	`distribute-rgt-in_binary64`
790×	`distribute-lft-in_binary64`
354×	`fma-neg_binary64`
207×	`cancel-sign-sub-inv_binary64`
174×	`fma-def_binary64`

Counts

78 → 99

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	1469
1	206	1345
2	503	1331
3	1590	1331
4	4749	1331
5	4929	1331

prune345.0ms (4.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	237	0	237
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	237	4	241

Error

0.0b

Counts

241 → 4

Alt Table

Status	Error	Program
✓	0.7b	(fma.f64 1/12 (pow.f64 x 4) (.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))
✓	3.6b	(fma.f64 1/12 (pow.f64 x 4) (exp.f64 (log.f64 (.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))))
	30.1b	(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
	30.1b	(cbrt.f64 (pow.f64 (-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2) 3))

Compiler

Compiled 9159 to 7035 computations (23.2% saved)

regimes293.0ms (4.2%)

Accuracy

Total 0.6b remaining (97.1%)

Threshold costs 0.6b (97.1%)

Counts

107 → 1

Compiler

Compiled 4816 to 3742 computations (22.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	30
1	19	30
2	19	30

end121.0ms (1.7%)

Compiler: Compiled 137 to 105 computations (23.4% saved)

Details

analyze5.0ms (0.1%)

sample5.2s (74.5%)

simplify67.0ms (1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series5.0ms (0.1%)

rewrite16.0ms (0.2%)

simplify78.0ms (1.1%)

prune68.0ms (1%)

localize12.0ms (0.2%)

series12.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify54.0ms (0.8%)

prune70.0ms (1%)

localize13.0ms (0.2%)

series16.0ms (0.2%)

rewrite14.0ms (0.2%)

simplify98.0ms (1.4%)

prune354.0ms (5.1%)

localize16.0ms (0.2%)

series13.0ms (0.2%)

rewrite13.0ms (0.2%)

simplify86.0ms (1.2%)

prune345.0ms (4.9%)

regimes293.0ms (4.2%)

simplify2.0ms (0%)

end121.0ms (1.7%)

Profiling