Details

analyze890.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
13.2%	86.5%	0.2%	10
17%	82.8%	0.2%	11
18.2%	81.5%	0.2%	12
21.7%	78.1%	0.2%	13
32.9%	66.9%	0.2%	14

sample23.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
1.0ms	22×	body	80	invalid

simplify138.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (135.0ms)

Iter	Nodes	Cost
0	4900	11
1	4900	11

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 9.4b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(-.f64 x (*.f64 y z))
0.0b	(-.f64 t (*.f64 a z))
9.2b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r_binary64` `pow1_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

3 → 54

Calls

3 calls:

3.0ms	(-.f64 x (*.f64 y z))
3.0ms	(-.f64 t (*.f64 a z))
7.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

series41.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(-.f64 x (*.f64 y z))
7.0ms	(-.f64 t (*.f64 a z))
27.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

simplify46.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5502	755

prune77.0ms

Filtered

52 candidates to 63 candidates (-21.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	52	11	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	11	64

Merged error: 9.1b

Counts

64 → 11

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 t (*.f64 z a))
0.0b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 (.f64 y z) (-.f64 t (*.f64 z a))))
2.1b	(/.f64 x (-.f64 t (*.f64 z a)))
9.6b	(/.f64 (.f64 y z) (-.f64 t (.f64 z a)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
13×	`times-frac_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `associate-/r/_binary64`
6×	`associate-/r*_binary64` `flip3--_binary64` `flip--_binary64`
4×	`pow1_binary64` `associate-/l*_binary64` `div-inv_binary64`
3×	`distribute-rgt-out--_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64`
1×	`cbrt-unprod_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `sub-div_binary64` `frac-sub_binary64`

Counts

4 → 82

Calls

4 calls:

3.0ms	(-.f64 t (*.f64 z a))
17.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 (.f64 y z) (-.f64 t (*.f64 z a))))
5.0ms	(/.f64 x (-.f64 t (*.f64 z a)))
6.0ms	(/.f64 (.f64 y z) (-.f64 t (.f64 z a)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(-.f64 t (*.f64 z a))
32.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 (.f64 y z) (-.f64 t (*.f64 z a))))
13.0ms	(/.f64 x (-.f64 t (*.f64 z a)))
15.0ms	(/.f64 (.f64 y z) (-.f64 t (.f64 z a)))

simplify43.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4996	1187
1	4996	1187

prune64.0ms

Filtered

72 candidates to 94 candidates (-30.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	97	8	105

Merged error: 6.2b

Counts

105 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 y (/.f64 (-.f64 t (.f64 z a)) z)))
2.1b	(/.f64 x (-.f64 t (*.f64 z a)))
3.2b	(/.f64 y (/.f64 (-.f64 t (*.f64 z a)) z))
8.7b	(/.f64 (-.f64 t (*.f64 z a)) z)

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

104×	`times-frac_binary64`
83×	`add-sqr-sqrt_binary64`
68×	`*-un-lft-identity_binary64`
62×	`add-cube-cbrt_binary64`
19×	`associate-/r*_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-/l*_binary64`
7×	`div-inv_binary64`
6×	`add-log-exp_binary64` `difference-of-squares_binary64`
5×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`pow1_binary64`
3×	`flip3--_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `distribute-lft-out--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `div-sub_binary64` `frac-sub_binary64`

Counts

4 → 149

Calls

4 calls:

39.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 y (/.f64 (-.f64 t (.f64 z a)) z)))
5.0ms	(/.f64 x (-.f64 t (*.f64 z a)))
8.0ms	(/.f64 y (/.f64 (-.f64 t (*.f64 z a)) z))
6.0ms	(/.f64 (-.f64 t (*.f64 z a)) z)

series67.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 y (/.f64 (-.f64 t (.f64 z a)) z)))
12.0ms	(/.f64 x (-.f64 t (*.f64 z a)))
15.0ms	(/.f64 y (/.f64 (-.f64 t (*.f64 z a)) z))
8.0ms	(/.f64 (-.f64 t (*.f64 z a)) z)

simplify58.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5431	2319

prune103.0ms

Filtered

131 candidates to 161 candidates (-22.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	156	5	161
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	159	10	169

Merged error: 0.7b

Counts

169 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 t (*.f64 z a))
0.0b	(-.f64 (/.f64 x (-.f64 t (*.f64 z a))) (/.f64 y (-.f64 (/.f64 t z) a)))
2.1b	(/.f64 x (-.f64 t (*.f64 z a)))
3.2b	(/.f64 y (-.f64 (/.f64 t z) a))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
39×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`
9×	`associate-/r*_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
6×	`associate-/l*_binary64`
4×	`pow1_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`frac-sub_binary64`

Counts

4 → 100

Calls

4 calls:

3.0ms	(-.f64 t (*.f64 z a))
28.0ms	(-.f64 (/.f64 x (-.f64 t (*.f64 z a))) (/.f64 y (-.f64 (/.f64 t z) a)))
5.0ms	(/.f64 x (-.f64 t (*.f64 z a)))
9.0ms	(/.f64 y (-.f64 (/.f64 t z) a))

series62.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(-.f64 t (*.f64 z a))
28.0ms	(-.f64 (/.f64 x (-.f64 t (*.f64 z a))) (/.f64 y (-.f64 (/.f64 t z) a)))
12.0ms	(/.f64 x (-.f64 t (*.f64 z a)))
14.0ms	(/.f64 y (-.f64 (/.f64 t z) a))

simplify65.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4906	1444
1	4906	1444

prune44.0ms

Filtered

84 candidates to 112 candidates (-33.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	112	10	122

Merged error: 0.7b

Counts

122 → 10

regimes361.0ms

Accuracy

59% (0.7b remaining)

Error of 2.2b against oracle of 1.5b and baseline of 3.1b

bsearch30.0ms

Steps

Iters	Range		Point
8	5.291385555919985e-132	3.433440868707807e-128	2.4670334241868483e-128
6	-3.7426956940954827e-119	-3.9367435865132606e-120	-2.550938907169579e-119

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	84	37
1	84	37

end0.0ms

sample620.0ms

Algorithm

intervals

Results

311.0ms	8000×	body	80	valid
31.0ms	741×	body	80	invalid

Details

analyze890.0ms

sample23.0ms

simplify138.0ms

prune6.0ms

localize8.0ms

rewrite15.0ms

series41.0ms

simplify46.0ms

prune77.0ms

localize9.0ms

rewrite34.0ms

series68.0ms

simplify43.0ms

prune64.0ms

localize9.0ms

rewrite65.0ms

series67.0ms

simplify58.0ms

prune103.0ms

localize10.0ms

rewrite49.0ms

series62.0ms

simplify65.0ms

prune44.0ms

regimes361.0ms

bsearch30.0ms

simplify3.0ms

end0.0ms

sample620.0ms

Profiling