Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 44 to 32 computations (27.3% saved)

sample1.2s (18.4%)

Symmetry

(sort a b c d)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 101 to 73 computations (27.7% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

114×	`fma-def_binary64`
49×	`distribute-rgt-in_binary64`
46×	`distribute-lft-in_binary64`
40×	`associate-+l+_binary64`
32×	`associate-+r+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	18	13
2	52	13
3	124	13
4	193	13
5	245	13
6	247	13
7	236	13

prune2.0ms (0%)

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

3.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	3.7b	(*.f64 (+.f64 a (+.f64 b (+.f64 c d))) 2)

Compiler

Compiled 39 to 27 computations (30.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(+.f64 b (+.f64 c d))
✓	2.9b	(+.f64 a (+.f64 b (+.f64 c d)))

series11.0ms (0.2%)

Counts

2 → 84

Calls

2 calls:

6.0ms	(+.f64 a (+.f64 b (+.f64 c d)))
4.0ms	(+.f64 b (+.f64 c d))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
16×	`add-log-exp_binary64`
9×	`distribute-lft-out_binary64`
9×	`sum-log_binary64`
6×	`fma-def_binary64`

Counts

2 → 42

Calls

2 calls:

8.0ms	(+.f64 a (+.f64 b (+.f64 c d)))
5.0ms	(+.f64 b (+.f64 c d))

simplify56.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

791×	`associate--l+_binary64`
721×	`distribute-rgt-in_binary64`
666×	`distribute-lft-in_binary64`
390×	`associate-l_binary64`
261×	`fma-def_binary64`

Counts

126 → 74

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	67	1070
1	198	1049
2	692	1049
3	3441	1049
4	5208	1049

prune50.0ms (0.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	64	10	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	10	75

Error

0.8b

Counts

75 → 10

Alt Table

Status	Error	Program
	3.9b	(.f64 (/.f64 (-.f64 (.f64 a a) (*.f64 (+.f64 b (+.f64 c d)) (+.f64 b (+.f64 c d)))) (-.f64 a (+.f64 b (+.f64 c d)))) 2)
	3.5b	(.f64 (/.f64 (+.f64 (pow.f64 a 3) (pow.f64 (+.f64 c (+.f64 d b)) 3)) (fma.f64 (+.f64 c (+.f64 d b)) (-.f64 (+.f64 c (+.f64 d b)) a) (.f64 a a))) 2)
	3.9b	(.f64 (/.f64 (+.f64 (pow.f64 a 3) (pow.f64 (+.f64 b (+.f64 c d)) 3)) (+.f64 (.f64 a a) (-.f64 (.f64 (+.f64 b (+.f64 c d)) (+.f64 b (+.f64 c d))) (.f64 a (+.f64 b (+.f64 c d)))))) 2)
	3.1b	(.f64 (.f64 (*.f64 (cbrt.f64 (+.f64 c (+.f64 (+.f64 d b) a))) (cbrt.f64 (+.f64 c (+.f64 (+.f64 d b) a)))) (cbrt.f64 (+.f64 c (+.f64 (+.f64 d b) a)))) 2)
	3.6b	(.f64 (log.f64 (.f64 (exp.f64 a) (*.f64 (exp.f64 b) (exp.f64 (+.f64 c d))))) 2)
▶	1.5b	(.f64 (log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d))))) 2)
	2.8b	(*.f64 (log1p.f64 (expm1.f64 (+.f64 c (+.f64 (+.f64 d b) a)))) 2)
	3.0b	(*.f64 (expm1.f64 (log1p.f64 (+.f64 c (+.f64 (+.f64 d b) a)))) 2)
	2.9b	(*.f64 (+.f64 a (+.f64 (+.f64 b c) d)) 2)
	3.6b	(.f64 (/.f64 (-.f64 (.f64 a a) (*.f64 (+.f64 c (+.f64 d b)) (+.f64 c (+.f64 d b)))) (-.f64 a (+.f64 c (+.f64 d b)))) 2)

Compiler

Compiled 1467 to 625 computations (57.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d)))
✓	0.3b	(.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d))))
✓	0.4b	(*.f64 (exp.f64 c) (exp.f64 d))
✓	0.9b	(log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d)))))

series1.7s (26.2%)

Counts

4 → 136

Calls

4 calls:

1.7s	(log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d)))))
34.0ms	(.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d))))
17.0ms	(.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d)))
10.0ms	(*.f64 (exp.f64 c) (exp.f64 d))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
21×	`*-un-lft-identity_binary64`
20×	`add-cbrt-cube_binary64`
16×	`prod-exp_binary64`
16×	`pow-prod-down_binary64`

Counts

4 → 85

Calls

4 calls:

11.0ms	(*.f64 (exp.f64 c) (exp.f64 d))
10.0ms	(.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d))))
9.0ms	(log.f64 (.f64 (exp.f64 a) (.f64 (exp.f64 b) (*.f64 (exp.f64 c) (exp.f64 d)))))
7.0ms	(.f64 (exp.f64 b) (.f64 (exp.f64 c) (exp.f64 d)))

simplify116.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

678×	`prod-exp_binary64`
481×	`associate-r_binary64`
385×	`distribute-rgt-out_binary64`
366×	`associate-l_binary64`
267×	`associate-+l+_binary64`

Counts

221 → 201

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	245	3683
1	693	2727
2	2359	2617
3	4148	2617
4	5037	2617

prune84.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	198	3	201
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	208	3	211

Error

Counts

211 → 3

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (+.f64 c (log.f64 (.f64 (exp.f64 b) (*.f64 (exp.f64 d) (exp.f64 a))))) 2)
	1.5b	(.f64 (log.f64 (.f64 (exp.f64 b) (.f64 (exp.f64 d) (.f64 (exp.f64 c) (exp.f64 a))))) 2)
	0.1b	(.f64 (+.f64 (log.f64 (.f64 (exp.f64 c) (*.f64 (exp.f64 d) (exp.f64 a)))) b) 2)

Compiler

Compiled 4083 to 1485 computations (63.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a))))
✓	0.0b	(+.f64 c (log.f64 (.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a)))))
✓	0.3b	(.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a)))
✓	0.3b	(*.f64 (exp.f64 d) (exp.f64 a))

series2.2s (32.6%)

Counts

4 → 53

Calls

4 calls:

1.1s	(+.f64 c (log.f64 (.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a)))))
1.0s	(log.f64 (.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a))))
19.0ms	(.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a)))
7.0ms	(*.f64 (exp.f64 d) (exp.f64 a))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`pow1_binary64`
21×	`*-un-lft-identity_binary64`
11×	`add-cbrt-cube_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`pow-prod-down_binary64`

Counts

4 → 80

Calls

4 calls:

10.0ms	(.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a)))
8.0ms	(+.f64 c (log.f64 (.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a)))))
6.0ms	(log.f64 (.f64 (exp.f64 b) (.f64 (exp.f64 d) (exp.f64 a))))
5.0ms	(*.f64 (exp.f64 d) (exp.f64 a))

simplify77.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

890×	`fma-def_binary64`
557×	`prod-exp_binary64`
416×	`distribute-rgt-in_binary64`
409×	`*-commutative_binary64`
405×	`distribute-lft-in_binary64`

Counts

133 → 172

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	1915
1	470	1432
2	1416	1362
3	4394	1362
4	5126	1362

prune99.0ms (1.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	172	3	175

Error

Counts

175 → 3

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (+.f64 c (log.f64 (.f64 (exp.f64 b) (*.f64 (exp.f64 d) (exp.f64 a))))) 2)
	1.5b	(.f64 (log.f64 (.f64 (exp.f64 b) (.f64 (exp.f64 d) (.f64 (exp.f64 c) (exp.f64 a))))) 2)
▶	0.1b	(.f64 (+.f64 (log.f64 (.f64 (exp.f64 c) (*.f64 (exp.f64 d) (exp.f64 a)))) b) 2)

Compiler

Compiled 3089 to 1175 computations (62% saved)

localize13.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series19.0ms (0.3%)

Counts

1 → 20

Calls

1 calls:

19.0ms

(*.f64 (exp.f64 c) (*.f64 (exp.f64 d) (exp.f64 a)))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`
3×	`associate-l_binary64`
3×	`cbrt-unprod_binary64`

Counts

1 → 21

Calls

1 calls:

7.0ms

(*.f64 (exp.f64 c) (*.f64 (exp.f64 d) (exp.f64 a)))

simplify79.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

849×	`prod-exp_binary64`
648×	`distribute-rgt-out_binary64`
513×	`fma-def_binary64`
484×	`*-commutative_binary64`
313×	`unswap-sqr_binary64`

Counts

41 → 54

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	87	683
1	285	538
2	900	494
3	2094	482
4	2867	475
5	4884	475
6	5088	475

prune55.0ms (0.8%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	1	0	1
Picked	1	0	1
Done	1	0	1
Total	100	1	101

Error

Counts

101 → 1

Alt Table

Status	Error	Program
	0b	(*.f64 (+.f64 (log.f64 (exp.f64 (+.f64 c (+.f64 d a)))) b) 2)

Compiler

Compiled 1857 to 794 computations (57.2% saved)

regimes640.0ms (9.7%)

Accuracy

Total 0b remaining (0%)

Threshold costs 0b (0%)

Counts

70 → 1

Compiler

Compiled 10289 to 7125 computations (30.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	16	17
2	16	17

end52.0ms (0.8%)

Remove: (sort a b c d)
Compiler: Compiled 75 to 55 computations (26.7% saved)

Details

analyze4.0ms (0.1%)

sample1.2s (18.4%)

simplify11.0ms (0.2%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series11.0ms (0.2%)

rewrite14.0ms (0.2%)

simplify56.0ms (0.8%)

prune50.0ms (0.8%)

localize16.0ms (0.2%)

series1.7s (26.2%)

rewrite43.0ms (0.7%)

simplify116.0ms (1.8%)

prune84.0ms (1.3%)

localize13.0ms (0.2%)

series2.2s (32.6%)

rewrite32.0ms (0.5%)

simplify77.0ms (1.2%)

prune99.0ms (1.5%)

localize13.0ms (0.2%)

series19.0ms (0.3%)

rewrite9.0ms (0.1%)

simplify79.0ms (1.2%)

prune55.0ms (0.8%)

regimes640.0ms (9.7%)

simplify2.0ms (0%)

end52.0ms (0.8%)

Profiling