Details

analyze317.0ms (10.8%)

Algorithm

1×

Search

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

Compiler

Compiled 42 to 30 computations (28.6% saved)

sample51.0ms (1.7%)

Algorithm

1×

intervals

Results

11.0ms	256×	pre	128	true
8.0ms	256×	body	128	valid
0.0ms	2×	pre	128	false

Compiler

Compiled 57 to 41 computations (28.1% saved)

simplify11.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

28×	`fma-def_binary64`
10×	`distribute-lft-in_binary64`
10×	`distribute-rgt-in_binary64`
7×	`*-commutative_binary64`
6×	`associate-+r+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	19	10
2	39	10
3	60	10
4	70	10
5	67	10

prune2.0ms (0.1%)

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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 a (+.f64 (+.f64 b c) d))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 a (+.f64 (+.f64 b c) d))

series10.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

10.0ms

(*.f64 a (+.f64 (+.f64 b c) d))

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
5×	`associate-r_binary64`
5×	`add-sqr-sqrt_binary64`
3×	`distribute-lft-out_binary64`
3×	`associate-l_binary64`

Counts

1 → 26

Calls

1 calls:

7.0ms

(*.f64 a (+.f64 (+.f64 b c) d))

simplify87.0ms (3%)

Algorithm

1×	egg-herbie

Rules

755×	`fma-neg_binary64`
558×	`distribute-rgt-in_binary64`
556×	`distribute-lft-in_binary64`
324×	`associate-l_binary64`
318×	`unswap-sqr_binary64`

Counts

74 → 49

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	62	792
1	170	750
2	596	750
3	2225	750
4	2696	750
5	3308	750
6	4843	750
7	5406	750

prune37.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	45	4	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	4	50

Error

Counts

50 → 4

Alt Table

Status	Error	Program
	0.1b	(expm1.f64 (log1p.f64 (*.f64 a (+.f64 (+.f64 b c) d))))
	0.6b	(.f64 (sqrt.f64 a) (.f64 (sqrt.f64 a) (+.f64 (+.f64 b c) d)))
▶	0.0b	(+.f64 (.f64 (+.f64 b c) a) (.f64 d a))
	0.7b	(.f64 (.f64 (sqrt.f64 a) (sqrt.f64 (+.f64 (+.f64 b c) d))) (*.f64 (sqrt.f64 a) (sqrt.f64 (+.f64 (+.f64 b c) d))))

Compiler

Compiled 747 to 209 computations (72% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (+.f64 b c) a) (.f64 d a))
✓	0.1b	(*.f64 (+.f64 b c) a)

series19.0ms (0.7%)

Counts

2 → 84

Calls

2 calls:

13.0ms	(+.f64 (.f64 (+.f64 b c) a) (.f64 d a))
6.0ms	(*.f64 (+.f64 b c) a)

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
4×	`associate-l_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 38

Calls

2 calls:

5.0ms	(+.f64 (.f64 (+.f64 b c) a) (.f64 d a))
5.0ms	(*.f64 (+.f64 b c) a)

simplify97.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

477×	`associate-l_binary64`
445×	`distribute-rgt-in_binary64`
425×	`distribute-lft-in_binary64`
384×	`associate-r_binary64`
375×	`fma-def_binary64`

Counts

122 → 73

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	1223
1	232	1120
2	786	1117
3	2904	1116
4	3987	1116
5	4981	1116
6	4963	1116

prune48.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	73	4	77

Error

Counts

77 → 4

Alt Table

Status	Error	Program
▶	0.1b	(expm1.f64 (log1p.f64 (*.f64 a (+.f64 (+.f64 b c) d))))
	0.6b	(.f64 (sqrt.f64 a) (.f64 (sqrt.f64 a) (+.f64 (+.f64 b c) d)))
✓	0.0b	(+.f64 (.f64 (+.f64 b c) a) (.f64 d a))
	0.7b	(.f64 (.f64 (sqrt.f64 a) (sqrt.f64 (+.f64 (+.f64 b c) d))) (*.f64 (sqrt.f64 a) (sqrt.f64 (+.f64 (+.f64 b c) d))))

Compiler

Compiled 1168 to 316 computations (72.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 a (+.f64 (+.f64 b c) d))
✓	0.0b	(log1p.f64 (*.f64 a (+.f64 (+.f64 b c) d)))
✓	0.1b	(expm1.f64 (log1p.f64 (*.f64 a (+.f64 (+.f64 b c) d))))

series324.0ms (11%)

Counts

2 → 96

Calls

2 calls:

313.0ms	(log1p.f64 (*.f64 a (+.f64 (+.f64 b c) d)))
11.0ms	(expm1.f64 (log1p.f64 (*.f64 a (+.f64 (+.f64 b c) d))))

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(expm1.f64 (log1p.f64 (*.f64 a (+.f64 (+.f64 b c) d))))
0.0ms	(log1p.f64 (*.f64 a (+.f64 (+.f64 b c) d)))

simplify94.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

524×	`fma-def_binary64`
334×	`associate-r_binary64`
282×	`associate-/r*_binary64`
267×	`times-frac_binary64`
247×	`+-commutative_binary64`

Counts

118 → 136

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	559	4929
1	1853	4771
2	5104	4771

prune172.0ms (5.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	185	4	189

Error

Counts

189 → 4

Alt Table

Status	Error	Program
✓	0.1b	(expm1.f64 (log1p.f64 (*.f64 a (+.f64 (+.f64 b c) d))))
▶	0.6b	(.f64 (sqrt.f64 a) (.f64 (sqrt.f64 a) (+.f64 (+.f64 b c) d)))
✓	0.0b	(+.f64 (.f64 (+.f64 b c) a) (.f64 d a))
	0.7b	(.f64 (.f64 (sqrt.f64 a) (sqrt.f64 (+.f64 (+.f64 b c) d))) (*.f64 (sqrt.f64 a) (sqrt.f64 (+.f64 (+.f64 b c) d))))

Compiler

Compiled 7156 to 3394 computations (52.6% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (sqrt.f64 a) (+.f64 (+.f64 b c) d))
✓	0.3b	(.f64 (sqrt.f64 a) (.f64 (sqrt.f64 a) (+.f64 (+.f64 b c) d)))

series50.0ms (1.7%)

Counts

2 → 80

Calls

2 calls:

30.0ms	(*.f64 (sqrt.f64 a) (+.f64 (+.f64 b c) d))
20.0ms	(.f64 (sqrt.f64 a) (.f64 (sqrt.f64 a) (+.f64 (+.f64 b c) d)))

rewrite21.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-l_binary64`
12×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`

Counts

2 → 59

Calls

2 calls:

10.0ms	(.f64 (sqrt.f64 a) (.f64 (sqrt.f64 a) (+.f64 (+.f64 b c) d)))
8.0ms	(*.f64 (sqrt.f64 a) (+.f64 (+.f64 b c) d))

simplify125.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

668×	`fma-def_binary64`
359×	`+-commutative_binary64`
342×	`*-commutative_binary64`
274×	`sqr-pow_binary64`
221×	`associate-+l+_binary64`

Counts

139 → 108

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	101	1695
1	258	1596
2	1020	1596
3	1572	1596
4	2612	1596
5	3578	1596
6	4783	1596
7	4953	1596

prune48.0ms (1.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	108	4	112

Error

Counts

112 → 4

Alt Table

Status	Error	Program
✓	0.1b	(expm1.f64 (log1p.f64 (*.f64 a (+.f64 (+.f64 b c) d))))
✓	0.6b	(.f64 (sqrt.f64 a) (.f64 (sqrt.f64 a) (+.f64 (+.f64 b c) d)))
✓	0.0b	(+.f64 (.f64 (+.f64 b c) a) (.f64 d a))
	0.7b	(.f64 (.f64 (sqrt.f64 a) (sqrt.f64 (+.f64 (+.f64 b c) d))) (*.f64 (sqrt.f64 a) (sqrt.f64 (+.f64 (+.f64 b c) d))))

Compiler

Compiled 1776 to 357 computations (79.9% saved)

regimes345.0ms (11.7%)

Accuracy

Total 0.0b remaining (56.8%)

Threshold costs 0.0b (56.8%)

Counts

53 → 1

Compiler

Compiled 5930 to 3573 computations (39.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
2	10	11

end17.0ms (0.6%)

Remove: (sort b c d)
Compiler: Compiled 36 to 21 computations (41.7% saved)

sample1.0s (34.6%)

Algorithm

1×

intervals

Results

344.0ms	8000×	pre	128	true
261.0ms	8000×	body	128	valid

Compiler

Compiled 122 to 77 computations (36.9% saved)

Details

analyze317.0ms (10.8%)

sample51.0ms (1.7%)

simplify11.0ms (0.4%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series10.0ms (0.3%)

rewrite8.0ms (0.3%)

simplify87.0ms (3%)

prune37.0ms (1.3%)

localize6.0ms (0.2%)

series19.0ms (0.7%)

rewrite11.0ms (0.4%)

simplify97.0ms (3.3%)

prune48.0ms (1.6%)

localize7.0ms (0.2%)

series324.0ms (11%)

rewrite2.0ms (0.1%)

simplify94.0ms (3.2%)

prune172.0ms (5.8%)

localize7.0ms (0.2%)

series50.0ms (1.7%)

rewrite21.0ms (0.7%)

simplify125.0ms (4.2%)

prune48.0ms (1.6%)

regimes345.0ms (11.7%)

simplify2.0ms (0.1%)

end17.0ms (0.6%)

sample1.0s (34.6%)

Profiling