Details

analyze1.8s (26.3%)

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)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
7.0ms	130×	body	128	invalid

Compiler

Compiled 49 to 33 computations (32.7% saved)

simplify12.0ms (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
▶	3.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	3.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 105 to 60 computations (42.9% saved)

localize8.0ms (0.1%)

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))
✓	2.9b	(fma.f64 a (fma.f64 z b t) x)

series46.0ms (0.7%)

Counts

2 → 132

Calls

2 calls:

31.0ms	(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))

simplify56.0ms (0.8%)

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

prune59.0ms (0.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	63	3	66
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	64	4	68

Error

0.0b

Counts

68 → 4

Alt Table

Status	Error	Program
	3.1b	(fma.f64 y z (+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 a t) x)))
▶	2.8b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
	3.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
	4.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 a t (fma.f64 z (fma.f64 a b y) x))) (cbrt.f64 (fma.f64 a t (fma.f64 z (fma.f64 a b y) x)))) (cbrt.f64 (fma.f64 a t (fma.f64 z (fma.f64 a b y) x))))

Compiler

Compiled 1049 to 250 computations (76.2% saved)

localize8.0ms (0.1%)

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))
✓	2.7b	(fma.f64 z (fma.f64 a b y) x)

series40.0ms (0.6%)

Counts

2 → 132

Calls

2 calls:

23.0ms	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
17.0ms	(fma.f64 z (fma.f64 a b y) x)

rewrite7.0ms (0.1%)

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:

6.0ms	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
0.0ms	(fma.f64 z (fma.f64 a b y) x)

simplify167.0ms (2.5%)

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

prune101.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	52	4	56

Error

0.0b

Counts

56 → 4

Alt Table

Status	Error	Program
▶	3.1b	(fma.f64 y z (+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 a t) x)))
✓	2.8b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
	3.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
	3.7b	(fma.f64 a t (.f64 (.f64 (cbrt.f64 (fma.f64 z (fma.f64 a b y) x)) (cbrt.f64 (fma.f64 z (fma.f64 a b y) x))) (cbrt.f64 (fma.f64 z (fma.f64 a b y) x))))

Compiler

Compiled 796 to 199 computations (75% saved)

localize23.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 a t) x)
✓	0.0b	(fma.f64 y z (+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 a t) x)))
✓	5.9b	(.f64 a (.f64 b z))

series86.0ms (1.3%)

Counts

3 → 97

Calls

3 calls:

59.0ms	(fma.f64 y z (+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 a t) x)))
17.0ms	(.f64 a (.f64 b z))
10.0ms	(+.f64 (*.f64 a t) x)

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
5×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64`

Counts

3 → 44

Calls

3 calls:

8.0ms	(+.f64 (*.f64 a t) x)
7.0ms	(.f64 a (.f64 b z))
1.0ms	(fma.f64 y z (+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 a t) x)))

simplify125.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

923×	`fma-def_binary64`
552×	`associate-l_binary64`
387×	`associate-+l+_binary64`
385×	`associate-+r+_binary64`
379×	`associate-r_binary64`

Counts

141 → 94

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	95	1709
1	243	1418
2	683	1413
3	2090	1413
4	4540	1413
5	5135	1413

prune106.0ms (1.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	94	4	98

Error

0.0b

Counts

98 → 4

Alt Table

Status	Error	Program
✓	3.1b	(fma.f64 y z (+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 a t) x)))
✓	2.8b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
▶	3.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
	3.7b	(fma.f64 a t (.f64 (.f64 (cbrt.f64 (fma.f64 z (fma.f64 a b y) x)) (cbrt.f64 (fma.f64 z (fma.f64 a b y) x))) (cbrt.f64 (fma.f64 z (fma.f64 a b y) x))))

Compiler

Compiled 1694 to 394 computations (76.7% saved)

localize20.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	0.0b	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
✓	5.9b	(.f64 (.f64 a z) b)

series130.0ms (1.9%)

Counts

3 → 168

Calls

3 calls:

61.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
38.0ms	(.f64 (.f64 a z) b)
30.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))

rewrite42.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-log-exp_binary64`
9×	`sum-log_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`

Counts

3 → 57

Calls

3 calls:

22.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
8.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
6.0ms	(.f64 (.f64 a z) b)

simplify156.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

704×	`distribute-rgt-in_binary64`
704×	`fma-def_binary64`
676×	`distribute-lft-in_binary64`
542×	`fma-neg_binary64`
164×	`cancel-sign-sub-inv_binary64`

Counts

225 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	2565
1	340	2260
2	1287	2248
3	4764	2248
4	5136	2248

prune129.0ms (1.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	108	6	114

Error

Counts

114 → 6

Alt Table

Status	Error	Program
	45.0b	(/.f64 (+.f64 (pow.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) 3) (pow.f64 (.f64 (.f64 a z) b) 3)) (+.f64 (.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (+.f64 (+.f64 x (.f64 y z)) (.f64 t a))) (-.f64 (.f64 (.f64 (.f64 a z) b) (.f64 (.f64 a z) b)) (.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (*.f64 a z) b)))))
✓	3.3b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	3.1b	(fma.f64 y z (+.f64 (.f64 a (.f64 b z)) (+.f64 (*.f64 a t) x)))
✓	2.8b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
	33.7b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))
	3.7b	(fma.f64 a t (.f64 (.f64 (cbrt.f64 (fma.f64 z (fma.f64 a b y) x)) (cbrt.f64 (fma.f64 z (fma.f64 a b y) x))) (cbrt.f64 (fma.f64 z (fma.f64 a b y) x))))

Compiler

Compiled 2361 to 427 computations (81.9% saved)

regimes2.2s (32.5%)

Accuracy

Total 0.2b remaining (94.9%)

Threshold costs 0.2b (94.9%)

Counts

92 → 3

Compiler

Compiled 11039 to 6559 computations (40.6% saved)

bsearch31.0ms (0.5%)

Steps

Iters	Range		Point
7	4.463007922207221e+69	8.438722600358235e+71	6.248196026292757e+70
1	-3.038812191278894e+28	-9.519361406777389e+24	-5.4202676746054004e+26

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	60
1	39	60
2	38	60

end1.0ms (0%)

Compiler: Compiled 49 to 25 computations (49% saved)

sample1.3s (20%)

Algorithm

1×

intervals

Results

449.0ms	8000×	body	128	valid
220.0ms	3882×	body	128	invalid

Compiler

Compiled 267 to 129 computations (51.7% saved)

Details

analyze1.8s (26.3%)

sample39.0ms (0.6%)

simplify12.0ms (0.2%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series46.0ms (0.7%)

rewrite1.0ms (0%)

simplify56.0ms (0.8%)

prune59.0ms (0.9%)

localize8.0ms (0.1%)

series40.0ms (0.6%)

rewrite7.0ms (0.1%)

simplify167.0ms (2.5%)

prune101.0ms (1.5%)

localize23.0ms (0.3%)

series86.0ms (1.3%)

rewrite19.0ms (0.3%)

simplify125.0ms (1.9%)

prune106.0ms (1.6%)

localize20.0ms (0.3%)

series130.0ms (1.9%)

rewrite42.0ms (0.6%)

simplify156.0ms (2.3%)

prune129.0ms (1.9%)

regimes2.2s (32.5%)

bsearch31.0ms (0.5%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.3s (20%)

Profiling