Details

analyze1.6s (1.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.6%	0.4%	0
0%	99.6%	0.4%	1
0%	99.6%	0.4%	2
0%	99.6%	0.4%	3
0%	99.6%	0.4%	4
0%	99.6%	0.4%	5
0%	99.6%	0.4%	6
0%	99.6%	0.4%	7
0%	74.7%	25.3%	8
0%	74.7%	25.3%	9
0%	65.4%	34.6%	10
0%	51.4%	48.6%	11
0%	51.4%	48.6%	12
0%	51.4%	48.6%	13
0%	51.4%	48.6%	14

Compiler

Compiled 30 to 21 computations (30% saved)

sample3.9s (2.6%)

Symmetry

(sort z t a)

Results

2.0s	11028×	body	128	invalid
1.7s	8253×	body	128	valid
1.0ms	2×	body	1024	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 89 to 62 computations (30.3% saved)

simplify79.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2664×	`associate-+l+_binary64`
1041×	`associate-+r+_binary64`
923×	`+-commutative_binary64`
750×	`fma-def_binary64`
5×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	30
1	41	26
2	109	26
3	376	26
4	1118	26
5	1592	26
6	1698	26
7	1698	26
8	1698	26
9	1698	26
10	2706	26
11	2958	26
12	2958	26
13	2910	26
14	2910	26
15	2540	26
16	2524	26

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))

Compiler

Compiled 99 to 61 computations (38.4% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))
✓	0.0b	(+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)
✓	0.1b	(fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))
✓	0.1b	(fma.f64 x (log.f64 y) z)

series1.7s (1.1%)

Counts

4 → 276

Calls

4 calls:

738.0ms	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))
665.0ms	(fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))
163.0ms	(+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)
89.0ms	(fma.f64 x (log.f64 y) z)

rewrite12.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
9×	`add-log-exp_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`distribute-lft-out_binary64`

Counts

4 → 51

Calls

4 calls:

9.0ms	(+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)
0.0ms	(fma.f64 x (log.f64 y) z)
0.0ms	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))
0.0ms	(fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))

simplify150.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

856×	`associate--l+_binary64`
642×	`fma-def_binary64`
591×	`distribute-rgt-in_binary64`
564×	`distribute-lft-in_binary64`
238×	`associate-+r+_binary64`

Counts

327 → 149

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	6904
1	527	6738
2	1686	6112
3	5359	6112

prune123.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	147	3	150

Error

0.0b

Counts

150 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))
	32.0b	(fma.f64 y i (*.f64 (sqrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))) (sqrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))))
▶	1.0b	(fma.f64 y i (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))) (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))) (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))))

Compiler

Compiled 3753 to 1296 computations (65.5% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 x (log.f64 y) z)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))) (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))) (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))))
✓	0.4b	(*.f64 (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))) (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))))
✓	0.5b	(cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))

series8.3s (5.5%)

Counts

3 → 252

Calls

3 calls:

4.4s

(*.f64 (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))) (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))))

3.2s

(cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))

664.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))) (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))) (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))))

rewrite24.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

8.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))) (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))) (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))) (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))))

1.0ms

(cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))

simplify607.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

345 → 220

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6834	104870

prune2.2s (1.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	443	5	448
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	443	8	451

Error

0.0b

Counts

451 → 8

Alt Table

Status	Error	Program
✓	1.0b	(fma.f64 y i (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))) (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))) (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))))
▶	1.0b	(fma.f64 y i (pow.f64 (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))) 3))
✓	0.1b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))
	32.0b	(fma.f64 y i (*.f64 (sqrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))) (sqrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))))
	32.4b	(fma.f64 y i (.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))) (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))) (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))))) (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))))
	32.3b	(fma.f64 y i (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))) (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))) (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))))))
	1.1b	(fma.f64 y i (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))) (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))) (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))))))
	1.3b	(fma.f64 y i (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))) (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))))))

Compiler

Compiled 126274 to 74064 computations (41.3% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))
	0.1b	(fma.f64 x (log.f64 y) z)
	0.5b	(cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))) 3)

Details

analyze1.6s (1.1%)

sample3.9s (2.6%)

simplify79.0ms (0.1%)

prune4.0ms (0%)

localize16.0ms (0%)

series1.7s (1.1%)

rewrite12.0ms (0%)

simplify150.0ms (0.1%)

prune123.0ms (0.1%)

localize18.0ms (0%)

series8.3s (5.5%)

rewrite24.0ms (0%)

simplify607.0ms (0.4%)

prune2.2s (1.4%)

localize18.0ms (0%)

series2.2min (87.6%)

Profiling