Details

analyze1.3s (11.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0%	100%	0%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample9.4s (81.7%)

Results

4.5s	8196×	body	8192	exit
3.4s	4278×	body	2048	valid
931.0ms	2109×	body	1024	valid
289.0ms	998×	body	512	valid
123.0ms	514×	body	256	valid
44.0ms	357×	body	128	valid

Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify57.0ms (0.5%)

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

28.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 x) 2)
✓	4.3b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

series5.0ms (0%)

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)

rewrite19.0ms (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:

11.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
4.0ms	(-.f64 (exp.f64 x) 2)

simplify82.0ms (0.7%)

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 (0.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	113	2	115

Error

0.0b

Counts

115 → 2

Alt Table

Status	Error	Program
▶	0.6b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
✓	28.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 2053 to 1164 computations (43.3% saved)

localize8.0ms (0.1%)

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))))
✓	0.0b	(*.f64 1/360 (pow.f64 x 6))

series14.0ms (0.1%)

Counts

3 → 24

Calls

3 calls:

6.0ms	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
4.0ms	(fma.f64 x x (*.f64 1/360 (pow.f64 x 6)))
4.0ms	(*.f64 1/360 (pow.f64 x 6))

rewrite7.0ms (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))))

simplify73.0ms (0.6%)

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

prune54.0ms (0.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	66	3	69

Error

Counts

69 → 3

Alt Table

Status	Error	Program
✓	0.6b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
✓	28.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
▶	21.6b	(cbrt.f64 (pow.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6)))) 3))

Compiler

Compiled 1253 to 922 computations (26.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
	0.0b	(*.f64 1/360 (pow.f64 x 6))
✓	0.1b	(pow.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6)))) 3)
✓	21.0b	(cbrt.f64 (pow.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6)))) 3))

series13.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

9.0ms	(cbrt.f64 (pow.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6)))) 3))
5.0ms	(pow.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6)))) 3)

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

2 → 48

Calls

2 calls:

2.0ms	(cbrt.f64 (pow.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6)))) 3))
2.0ms	(pow.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6)))) 3)

simplify117.0ms (1%)

Algorithm

1×	egg-herbie

Rules

434×	`associate-l_binary64`
368×	`exp-prod_binary64`
360×	`log-prod_binary64`
351×	`associate-r_binary64`
231×	`associate-+l+_binary64`

Counts

72 → 77

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	97	1811
1	189	1602
2	518	1582
3	2549	1582
4	4739	1582
5	4958	1579
6	4926	1579

prune119.0ms (1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	131	3	134

Error

Counts

134 → 3

Alt Table

Status	Error	Program
✓	0.6b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
✓	28.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
✓	21.6b	(cbrt.f64 (pow.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6)))) 3))

Compiler

Compiled 2926 to 2251 computations (23.1% saved)

regimes37.0ms (0.3%)

Accuracy

Total 0.7b remaining (95.8%)

Threshold costs 0.7b (95.8%)

Counts

21 → 1

Compiler

Compiled 474 to 362 computations (23.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	12	18
2	12	18

end70.0ms (0.6%)

Compiler: Compiled 68 to 50 computations (26.5% saved)

Details

analyze1.3s (11.6%)

sample9.4s (81.7%)

simplify57.0ms (0.5%)

prune2.0ms (0%)

localize6.0ms (0%)

series5.0ms (0%)

rewrite19.0ms (0.2%)

simplify82.0ms (0.7%)

prune68.0ms (0.6%)

localize8.0ms (0.1%)

series14.0ms (0.1%)

rewrite7.0ms (0.1%)

simplify73.0ms (0.6%)

prune54.0ms (0.5%)

localize11.0ms (0.1%)

series13.0ms (0.1%)

rewrite6.0ms (0.1%)

simplify117.0ms (1%)

prune119.0ms (1%)

regimes37.0ms (0.3%)

simplify2.0ms (0%)

end70.0ms (0.6%)

Profiling