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)

sample164.0ms (3.7%)

Algorithm

1×

intervals

Results

69.0ms	129×	body	2048	valid
15.0ms	63×	body	1024	valid
3.0ms	26×	body	512	valid
2.0ms	22×	body	256	valid
1.0ms	16×	body	128	valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify57.0ms (1.3%)

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

29.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.0b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 x) 2)
✓	6.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

series4.0ms (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)

rewrite15.0ms (0.3%)

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)))
4.0ms	(-.f64 (exp.f64 x) 2)

simplify84.0ms (1.9%)

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

prune95.0ms (2.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	109	5	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	5	115

Error

0.0b

Counts

115 → 5

Alt Table

Status	Error	Program
	29.0b	(+.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 8) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4)) (exp.f64 (neg.f64 x)))
	29.1b	(fma.f64 (*.f64 (cbrt.f64 (-.f64 (exp.f64 x) 2)) (cbrt.f64 (-.f64 (exp.f64 x) 2))) (cbrt.f64 (-.f64 (exp.f64 x) 2)) (exp.f64 (neg.f64 x)))
▶	1.0b	(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)))))
	1.1b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
	1.2b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

Compiler

Compiled 2182 to 1255 computations (42.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))
✓	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)))))
✓	0.1b	(*.f64 1/20160 (pow.f64 x 8))

series70.0ms (1.6%)

Counts

4 → 36

Calls

4 calls:

57.0ms	(*.f64 1/20160 (pow.f64 x 8))
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 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)))))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
9×	`add-exp-log_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`

Counts

4 → 57

Calls

4 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 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))))

simplify59.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

946×	`fma-def_binary64`
610×	`associate-+r+_binary64`
610×	`associate-+l+_binary64`
262×	`associate-l_binary64`
230×	`associate-r_binary64`

Counts

93 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	1505
1	172	1382
2	418	1364
3	1707	1364
4	5576	1364

prune103.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	83	6	89

Error

Counts

89 → 6

Alt Table

Status	Error	Program
	29.0b	(+.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 8) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4)) (exp.f64 (neg.f64 x)))
	29.1b	(fma.f64 (*.f64 (cbrt.f64 (-.f64 (exp.f64 x) 2)) (cbrt.f64 (-.f64 (exp.f64 x) 2))) (cbrt.f64 (-.f64 (exp.f64 x) 2)) (exp.f64 (neg.f64 x)))
	19.1b	(cbrt.f64 (pow.f64 (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))
✓	1.0b	(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)))))
▶	1.1b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
	1.2b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

Compiler

Compiled 2082 to 1556 computations (25.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (*.f64 1/360 (pow.f64 x 6)))
✓	0.0b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
✓	0.1b	(*.f64 1/360 (pow.f64 x 6))

series14.0ms (0.3%)

Counts

3 → 24

Calls

3 calls:

6.0ms	(fma.f64 x x (*.f64 1/360 (pow.f64 x 6)))
5.0ms	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
3.0ms	(*.f64 1/360 (pow.f64 x 6))

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 1/360 (pow.f64 x 6))
0.0ms	(fma.f64 x x (*.f64 1/360 (pow.f64 x 6)))
0.0ms	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))

simplify68.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

624×	`distribute-rgt-in_binary64`
613×	`distribute-lft-in_binary64`
563×	`fma-def_binary64`
396×	`unswap-sqr_binary64`
364×	`log-prod_binary64`

Counts

71 → 67

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	85	979
1	145	907
2	358	875
3	1518	875
4	4945	875
5	5315	875

prune80.0ms (1.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	67	6	73

Error

Counts

73 → 6

Alt Table

Status	Error	Program
	29.0b	(+.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 8) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4)) (exp.f64 (neg.f64 x)))
	29.1b	(fma.f64 (*.f64 (cbrt.f64 (-.f64 (exp.f64 x) 2)) (cbrt.f64 (-.f64 (exp.f64 x) 2))) (cbrt.f64 (-.f64 (exp.f64 x) 2)) (exp.f64 (neg.f64 x)))
	19.1b	(cbrt.f64 (pow.f64 (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))
✓	1.0b	(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)))))
✓	1.1b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
▶	1.2b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

Compiler

Compiled 1373 to 1007 computations (26.7% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
✓	0.1b	(*.f64 1/12 (pow.f64 x 4))

series8.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

4.0ms	(*.f64 1/12 (pow.f64 x 4))
4.0ms	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`
7×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 37

Calls

2 calls:

4.0ms	(*.f64 1/12 (pow.f64 x 4))
0.0ms	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

simplify78.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

703×	`fma-def_binary64`
562×	`unswap-sqr_binary64`
352×	`*-commutative_binary64`
333×	`distribute-rgt-out_binary64`
291×	`distribute-lft-out_binary64`

Counts

49 → 49

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	66	570
1	110	535
2	240	517
3	668	517
4	1295	511
5	3475	506
6	4962	506
7	4950	506

prune54.0ms (1.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	49	6	55

Error

Counts

55 → 6

Alt Table

Status	Error	Program
	29.0b	(+.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 8) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4)) (exp.f64 (neg.f64 x)))
	29.1b	(fma.f64 (*.f64 (cbrt.f64 (-.f64 (exp.f64 x) 2)) (cbrt.f64 (-.f64 (exp.f64 x) 2))) (cbrt.f64 (-.f64 (exp.f64 x) 2)) (exp.f64 (neg.f64 x)))
	19.1b	(cbrt.f64 (pow.f64 (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))
✓	1.0b	(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)))))
✓	1.1b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
✓	1.2b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

Compiler

Compiled 751 to 525 computations (30.1% saved)

regimes115.0ms (2.6%)

Accuracy

Total 0.0b remaining (76.2%)

Threshold costs 0.0b (76.2%)

Counts

66 → 2

Compiler

Compiled 1930 to 1451 computations (24.8% saved)

bsearch2.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	73
1	46	73
2	50	73
3	51	73
4	49	73

end1.0ms (0%)

Compiler: Compiled 49 to 33 computations (32.7% saved)

sample3.3s (74.7%)

Algorithm

1×

intervals

Results

2.3s	4211×	body	2048	valid
503.0ms	2016×	body	1024	valid
125.0ms	943×	body	512	valid
44.0ms	494×	body	256	valid
20.0ms	336×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 165 to 118 computations (28.5% saved)

Details

analyze5.0ms (0.1%)

sample164.0ms (3.7%)

simplify57.0ms (1.3%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite15.0ms (0.3%)

simplify84.0ms (1.9%)

prune95.0ms (2.1%)

localize10.0ms (0.2%)

series70.0ms (1.6%)

rewrite7.0ms (0.2%)

simplify59.0ms (1.3%)

prune103.0ms (2.3%)

localize8.0ms (0.2%)

series14.0ms (0.3%)

rewrite6.0ms (0.1%)

simplify68.0ms (1.5%)

prune80.0ms (1.8%)

localize5.0ms (0.1%)

series8.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify78.0ms (1.8%)

prune54.0ms (1.2%)

regimes115.0ms (2.6%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample3.3s (74.7%)

Profiling