Details

analyze1.6s (10.8%)

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)

sample4.6s (30.3%)

Symmetry

(sort z t a)

Results

2.4s	11377×	body	128	invalid
2.1s	8255×	body	128	valid
2.0ms	1×	body	1024	valid

Compiler

Compiled 89 to 62 computations (30.3% saved)

simplify79.0ms (0.5%)

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)

localize22.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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)

series1.0s (6.9%)

Counts

3 → 180

Calls

3 calls:

782.0ms	(fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))
156.0ms	(+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)
103.0ms	(fma.f64 x (log.f64 y) z)

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
4×	`distribute-lft-out_binary64`
4×	`fma-def_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

3 → 41

Calls

3 calls:

5.0ms	(+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)
0.0ms	(fma.f64 x (log.f64 y) z)
0.0ms	(fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a))

simplify82.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

561×	`distribute-rgt-in_binary64`
559×	`associate-+r+_binary64`
534×	`distribute-lft-in_binary64`
432×	`fma-def_binary64`
406×	`associate--l+_binary64`

Counts

221 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	3890
1	359	3777
2	1086	3403
3	5043	3403

prune110.0ms (0.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	3	107

Error

0.1b

Counts

107 → 3

Alt Table

Status	Error	Program
	0.1b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (+.f64 (fma.f64 x (log.f64 y) z) (+.f64 t a))))
	32.2b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (*.f64 (sqrt.f64 (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)) (sqrt.f64 (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))))
▶	0.1b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (log.f64 c) b) z)))) (*.f64 1/2 (log.f64 c))))

Compiler

Compiled 2654 to 938 computations (64.7% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (log.f64 c) b) z))
✓	0.0b	(+.f64 (*.f64 (log.f64 c) b) z)
✓	0.2b	(*.f64 (log.f64 c) b)
✓	0.2b	(*.f64 (log.f64 y) x)

series1.1s (7.3%)

Counts

4 → 94

Calls

4 calls:

595.0ms	(+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (log.f64 c) b) z))
222.0ms	(*.f64 (log.f64 c) b)
194.0ms	(*.f64 (log.f64 y) x)
98.0ms	(+.f64 (*.f64 (log.f64 c) b) z)

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
11×	`add-log-exp_binary64`
10×	`pow1_binary64`
8×	`associate-l_binary64`
8×	`*-un-lft-identity_binary64`

Counts

4 → 72

Calls

4 calls:

5.0ms	(+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (log.f64 c) b) z))
5.0ms	(*.f64 (log.f64 c) b)
3.0ms	(+.f64 (*.f64 (log.f64 c) b) z)
3.0ms	(*.f64 (log.f64 y) x)

simplify104.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

614×	`fma-neg_binary64`
581×	`fma-def_binary64`
578×	`unsub-neg_binary64`
319×	`distribute-rgt-in_binary64`
297×	`*-commutative_binary64`

Counts

166 → 128

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	1822
1	383	1679
2	1034	1674
3	3259	1674
4	4992	1674
5	4972	1674

prune162.0ms (1.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	122	6	128
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	124	7	131

Error

0.0b

Counts

131 → 7

Alt Table

Status	Error	Program
	34.6b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (.f64 (log.f64 c) (sqrt.f64 b)) (sqrt.f64 b)) z)))) (.f64 1/2 (log.f64 c))))
	32.2b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (*.f64 (sqrt.f64 (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)) (sqrt.f64 (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))))
	0.3b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (.f64 (log.f64 c) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)) z)))) (*.f64 1/2 (log.f64 c))))
	34.1b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (sqrt.f64 (log.f64 c)) (.f64 (sqrt.f64 (log.f64 c)) b)) z)))) (.f64 1/2 (log.f64 c))))
	0.2b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (.f64 (cbrt.f64 (log.f64 c)) (cbrt.f64 (log.f64 c))) (.f64 (cbrt.f64 (log.f64 c)) b)) z)))) (*.f64 1/2 (log.f64 c))))
▶	0.2b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (.f64 (log.f64 y) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)) (+.f64 (.f64 (log.f64 c) b) z)))) (*.f64 1/2 (log.f64 c))))
	37.5b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (sqrt.f64 (log.f64 y)) (.f64 (sqrt.f64 (log.f64 y)) x)) (+.f64 (.f64 (log.f64 c) b) z)))) (.f64 1/2 (log.f64 c))))

Compiler

Compiled 4142 to 1560 computations (62.3% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (log.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))
✓	0.3b	(.f64 (log.f64 y) (.f64 (cbrt.f64 x) (cbrt.f64 x)))
✓	0.4b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)

series788.0ms (5.2%)

Counts

4 → 72

Calls

4 calls:

506.0ms	(.f64 (log.f64 y) (.f64 (cbrt.f64 x) (cbrt.f64 x)))
211.0ms	(.f64 (.f64 (log.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))
37.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
34.0ms	(cbrt.f64 x)

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`pow1_binary64`
25×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 103

Calls

4 calls:

8.0ms	(.f64 (.f64 (log.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))
7.0ms	(.f64 (log.f64 y) (.f64 (cbrt.f64 x) (cbrt.f64 x)))
4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify111.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

629×	`unswap-sqr_binary64`
471×	`distribute-rgt-in_binary64`
444×	`distribute-lft-in_binary64`
416×	`*-commutative_binary64`
408×	`log-prod_binary64`

Counts

175 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	1805
1	244	1524
2	880	1413
3	1415	1385
4	4684	1385
5	4974	1385

prune491.0ms (3.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	188	2	190
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	190	7	197

Error

0.0b

Counts

197 → 7

Alt Table

Status	Error	Program
	34.6b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (.f64 (log.f64 c) (sqrt.f64 b)) (sqrt.f64 b)) z)))) (.f64 1/2 (log.f64 c))))
	32.2b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (*.f64 (sqrt.f64 (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)) (sqrt.f64 (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))))
	0.3b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (.f64 (log.f64 c) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)) z)))) (*.f64 1/2 (log.f64 c))))
	34.1b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (sqrt.f64 (log.f64 c)) (.f64 (sqrt.f64 (log.f64 c)) b)) z)))) (.f64 1/2 (log.f64 c))))
	0.2b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (.f64 (cbrt.f64 (log.f64 c)) (cbrt.f64 (log.f64 c))) (.f64 (cbrt.f64 (log.f64 c)) b)) z)))) (*.f64 1/2 (log.f64 c))))
▶	0.2b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (.f64 (.f64 (log.f64 y) (cbrt.f64 x)) (cbrt.f64 x)) (cbrt.f64 x)) (+.f64 (.f64 (log.f64 c) b) z)))) (*.f64 1/2 (log.f64 c))))
	0.2b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (.f64 (log.f64 y) (.f64 (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x))) (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 x)))) (cbrt.f64 x)) (+.f64 (.f64 (log.f64 c) b) z)))) (*.f64 1/2 (log.f64 c))))

Compiler

Compiled 7029 to 2484 computations (64.7% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (*.f64 (log.f64 y) (cbrt.f64 x)) (cbrt.f64 x)) (cbrt.f64 x))
✓	0.4b	(.f64 (.f64 (log.f64 y) (cbrt.f64 x)) (cbrt.f64 x))
✓	0.4b	(*.f64 (log.f64 y) (cbrt.f64 x))
	0.6b	(cbrt.f64 x)

series1.3s (8.3%)

Counts

3 → 72

Calls

3 calls:

539.0ms	(.f64 (.f64 (log.f64 y) (cbrt.f64 x)) (cbrt.f64 x))
437.0ms	(*.f64 (log.f64 y) (cbrt.f64 x))
239.0ms	(.f64 (.f64 (*.f64 (log.f64 y) (cbrt.f64 x)) (cbrt.f64 x)) (cbrt.f64 x))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`pow1_binary64`
19×	`add-exp-log_binary64`
18×	`associate-r_binary64`
14×	`add-sqr-sqrt_binary64`
10×	`cbrt-prod_binary64`

Counts

3 → 74

Calls

3 calls:

7.0ms	(.f64 (.f64 (*.f64 (log.f64 y) (cbrt.f64 x)) (cbrt.f64 x)) (cbrt.f64 x))
5.0ms	(.f64 (.f64 (log.f64 y) (cbrt.f64 x)) (cbrt.f64 x))
4.0ms	(*.f64 (log.f64 y) (cbrt.f64 x))

simplify114.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

439×	`distribute-rgt-in_binary64`
411×	`distribute-lft-in_binary64`
361×	`*-commutative_binary64`
310×	`log-prod_binary64`
229×	`associate-l_binary64`

Counts

146 → 115

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	113	1984
1	255	1565
2	853	1426
3	1279	1426
4	3904	1363
5	4916	1363
6	4993	1363

prune299.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	169	7	176

Error

0.0b

Counts

176 → 7

Alt Table

Status	Error	Program
	34.6b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (.f64 (log.f64 c) (sqrt.f64 b)) (sqrt.f64 b)) z)))) (.f64 1/2 (log.f64 c))))
	32.2b	(fma.f64 y i (fma.f64 (-.f64 b 1/2) (log.f64 c) (*.f64 (sqrt.f64 (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)) (sqrt.f64 (+.f64 (+.f64 (fma.f64 x (log.f64 y) z) t) a)))))
	0.3b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (.f64 (log.f64 c) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)) z)))) (*.f64 1/2 (log.f64 c))))
	34.1b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (sqrt.f64 (log.f64 c)) (.f64 (sqrt.f64 (log.f64 c)) b)) z)))) (.f64 1/2 (log.f64 c))))
	0.2b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (log.f64 y) x) (+.f64 (.f64 (.f64 (cbrt.f64 (log.f64 c)) (cbrt.f64 (log.f64 c))) (.f64 (cbrt.f64 (log.f64 c)) b)) z)))) (*.f64 1/2 (log.f64 c))))
✓	0.2b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (.f64 (.f64 (log.f64 y) (cbrt.f64 x)) (cbrt.f64 x)) (cbrt.f64 x)) (+.f64 (.f64 (log.f64 c) b) z)))) (*.f64 1/2 (log.f64 c))))
	0.2b	(fma.f64 y i (-.f64 (+.f64 a (+.f64 t (+.f64 (.f64 (.f64 (log.f64 y) (.f64 (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x))) (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 x)))) (cbrt.f64 x)) (+.f64 (.f64 (log.f64 c) b) z)))) (*.f64 1/2 (log.f64 c))))

Compiler

Compiled 6050 to 2039 computations (66.3% saved)

regimes2.3s (15%)

Accuracy

Total 0.0b remaining (44.6%)

Threshold costs 0.0b (44.6%)

Counts

127 → 1

Compiler

Compiled 52130 to 33007 computations (36.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	33
1	31	33
2	39	33
3	43	33
4	46	33
5	47	33
6	46	33

end745.0ms (4.9%)

Compiler: Compiled 392 to 234 computations (40.3% saved)

Details

analyze1.6s (10.8%)

sample4.6s (30.3%)

simplify79.0ms (0.5%)

prune4.0ms (0%)

localize22.0ms (0.1%)

series1.0s (6.9%)

rewrite7.0ms (0%)

simplify82.0ms (0.5%)

prune110.0ms (0.7%)

localize18.0ms (0.1%)

series1.1s (7.3%)

rewrite18.0ms (0.1%)

simplify104.0ms (0.7%)

prune162.0ms (1.1%)

localize22.0ms (0.1%)

series788.0ms (5.2%)

rewrite25.0ms (0.2%)

simplify111.0ms (0.7%)

prune491.0ms (3.2%)

localize22.0ms (0.1%)

series1.3s (8.3%)

rewrite21.0ms (0.1%)

simplify114.0ms (0.8%)

prune299.0ms (2%)

regimes2.3s (15%)

simplify3.0ms (0%)

end745.0ms (4.9%)

Profiling