Details

analyze1.7s (33.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.8%	98%	0.3%	13
2.4%	97.3%	0.3%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample95.0ms (1.9%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
6.0ms	114×	body	128	invalid

Compiler

Compiled 49 to 33 computations (32.7% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

89×	`fma-def_binary64`
24×	`associate-+l+_binary64`
22×	`associate-+r+_binary64`
19×	`+-commutative_binary64`
10×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	27	16
2	66	15
3	122	13
4	157	13
5	164	13
6	167	13
7	167	13

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	3.3b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
▶	2.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 105 to 60 computations (42.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y z))
✓	0.0b	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
✓	0.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	6.3b	(.f64 (.f64 a z) b)

series55.0ms (1.1%)

Counts

4 → 204

Calls

4 calls:

27.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
12.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
11.0ms	(.f64 (.f64 a z) b)
5.0ms	(+.f64 x (*.f64 y z))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-log-exp_binary64`
10×	`sum-log_binary64`
9×	`fma-def_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`

Counts

4 → 73

Calls

4 calls:

9.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
4.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
4.0ms	(.f64 (.f64 a z) b)
2.0ms	(+.f64 x (*.f64 y z))

simplify76.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-def_binary64`
720×	`distribute-rgt-in_binary64`
683×	`distribute-lft-in_binary64`
194×	`cancel-sign-sub-inv_binary64`
192×	`fma-neg_binary64`

Counts

277 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	135	2855
1	406	2550
2	1474	2538
3	5045	2538

prune127.0ms (2.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	131	5	136

Error

Counts

136 → 5

Alt Table

Status	Error	Program
✓	2.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
	16.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 a z) b) (.f64 (.f64 a z) b)) (.f64 (.f64 a z) b))))
	3.3b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
▶	1.8b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
	34.1b	(*.f64 (sqrt.f64 (fma.f64 a t (fma.f64 z (fma.f64 a b y) x))) (sqrt.f64 (fma.f64 a t (fma.f64 z (fma.f64 a b y) x))))

Compiler

Compiled 2829 to 549 computations (80.6% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
✓	1.7b	(fma.f64 z (fma.f64 a b y) x)

series104.0ms (2%)

Counts

2 → 132

Calls

2 calls:

87.0ms	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
17.0ms	(fma.f64 z (fma.f64 a b y) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 z (fma.f64 a b y) x)
0.0ms	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

simplify109.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

576×	`fma-def_binary64`
520×	`associate-+r+_binary64`
505×	`associate-l_binary64`
470×	`associate-+l+_binary64`
444×	`associate-r_binary64`

Counts

152 → 52

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	56	1796
1	103	1579
2	236	1579
3	906	1579
4	3548	1579
5	3771	1579
6	4661	1579
7	4888	1579
8	4888	1579

prune37.0ms (0.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	52	5	57

Error

Counts

57 → 5

Alt Table

Status	Error	Program
✓	2.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
	16.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 a z) b) (.f64 (.f64 a z) b)) (.f64 (.f64 a z) b))))
▶	3.3b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	34.3b	(fma.f64 a t (*.f64 (sqrt.f64 (fma.f64 z (fma.f64 a b y) x)) (sqrt.f64 (fma.f64 z (fma.f64 a b y) x))))
✓	1.8b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 817 to 210 computations (74.3% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	3.1b	(fma.f64 a (fma.f64 z b t) x)

series41.0ms (0.8%)

Counts

2 → 132

Calls

2 calls:

25.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
15.0ms	(fma.f64 a (fma.f64 z b t) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 a (fma.f64 z b t) x)
0.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))

simplify75.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

739×	`associate-+l+_binary64`
732×	`associate-+r+_binary64`
701×	`fma-def_binary64`
559×	`associate-l_binary64`
480×	`associate-r_binary64`

Counts

152 → 66

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	55	1737
1	97	1579
2	249	1579
3	1063	1579
4	5721	1579

prune51.0ms (1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	66	5	71

Error

Counts

71 → 5

Alt Table

Status	Error	Program
✓	2.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
▶	16.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 a z) b) (.f64 (.f64 a z) b)) (.f64 (.f64 a z) b))))
✓	3.3b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	34.3b	(fma.f64 a t (*.f64 (sqrt.f64 (fma.f64 z (fma.f64 a b y) x)) (sqrt.f64 (fma.f64 z (fma.f64 a b y) x))))
✓	1.8b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 1026 to 243 computations (76.3% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (.f64 (.f64 a z) b) (.f64 (.f64 a z) b)) (.f64 (.f64 a z) b))
✓	0.3b	(.f64 (.f64 (.f64 a z) b) (.f64 (*.f64 a z) b))
	6.3b	(.f64 (.f64 a z) b)
✓	29.6b	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 a z) b) (.f64 (.f64 a z) b)) (.f64 (.f64 a z) b)))

series145.0ms (2.8%)

Counts

3 → 108

Calls

3 calls:

63.0ms

(*.f64 (*.f64 (*.f64 (*.f64 a z) b) (*.f64 (*.f64 a z) b)) (*.f64 (*.f64 a z) b))

41.0ms

(cbrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 a z) b) (*.f64 (*.f64 a z) b)) (*.f64 (*.f64 a z) b)))

41.0ms

(*.f64 (*.f64 (*.f64 a z) b) (*.f64 (*.f64 a z) b))

rewrite112.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

732×	`pow1_binary64`
429×	`pow-prod-down_binary64`
228×	`add-cbrt-cube_binary64`
210×	`add-exp-log_binary64`
177×	`cbrt-unprod_binary64`

Counts

3 → 268

Calls

3 calls:

21.0ms

(*.f64 (*.f64 (*.f64 (*.f64 a z) b) (*.f64 (*.f64 a z) b)) (*.f64 (*.f64 a z) b))

16.0ms

(cbrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 a z) b) (*.f64 (*.f64 a z) b)) (*.f64 (*.f64 a z) b)))

8.0ms

(*.f64 (*.f64 (*.f64 a z) b) (*.f64 (*.f64 a z) b))

simplify171.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

681×	`*-commutative_binary64`
613×	`associate-l_binary64`
503×	`log-prod_binary64`
468×	`exp-prod_binary64`
429×	`cube-prod_binary64`

Counts

376 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	165	6706
1	317	3353
2	1139	3213
3	2972	3213
4	4926	3213
5	5009	3213

prune180.0ms (3.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	246	0	246
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	246	5	251

Error

Counts

251 → 5

Alt Table

Status	Error	Program
✓	2.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	16.1b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 a z) b) (.f64 (.f64 a z) b)) (.f64 (.f64 a z) b))))
✓	3.3b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	34.3b	(fma.f64 a t (*.f64 (sqrt.f64 (fma.f64 z (fma.f64 a b y) x)) (sqrt.f64 (fma.f64 z (fma.f64 a b y) x))))
✓	1.8b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 9039 to 1182 computations (86.9% saved)

regimes573.0ms (11.2%)

Accuracy

Total 0.3b remaining (97.5%)

Threshold costs 0.3b (97.5%)

Counts

63 → 3

Compiler

Compiled 8593 to 4970 computations (42.2% saved)

bsearch50.0ms (1%)

Steps

Iters	Range		Point
6	2.11039526587156e-105	1.0291474824778919e-104	1.0044562690950302e-104
8	-6.454551321879296e+70	-1.0367418657072682e+68	-1.111935272820311e+68

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`if-if-or-not_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	40
1	23	40
2	23	40

end1.0ms (0%)

Compiler: Compiled 35 to 19 computations (45.7% saved)

sample1.3s (26.1%)

Algorithm

1×

intervals

Results

438.0ms	8000×	body	128	valid
274.0ms	4018×	body	128	invalid

Compiler

Compiled 176 to 97 computations (44.9% saved)

Details

analyze1.7s (33.2%)

sample95.0ms (1.9%)

simplify9.0ms (0.2%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series55.0ms (1.1%)

rewrite23.0ms (0.5%)

simplify76.0ms (1.5%)

prune127.0ms (2.5%)

localize8.0ms (0.2%)

series104.0ms (2%)

rewrite1.0ms (0%)

simplify109.0ms (2.1%)

prune37.0ms (0.7%)

localize8.0ms (0.2%)

series41.0ms (0.8%)

rewrite1.0ms (0%)

simplify75.0ms (1.5%)

prune51.0ms (1%)

localize16.0ms (0.3%)

series145.0ms (2.8%)

rewrite112.0ms (2.2%)

simplify171.0ms (3.3%)

prune180.0ms (3.5%)

regimes573.0ms (11.2%)

bsearch50.0ms (1%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.3s (26.1%)

Profiling