Details

sample245.0ms

Algorithm

intervals

Results

188.0ms	4×	body	5120	valid
10.0ms	178×	body	80	valid
9.0ms	33×	body	2560	valid
6.0ms	26×	body	1280	valid
4.0ms	101×	body	80	nan
4.0ms	20×	body	640	valid
2.0ms	14×	body	320	valid
0.0ms	4×	body	160	valid

simplify431.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	42	13
1	42	13

prune5.0ms

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

Merged error: 35.7b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.1b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

10.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series61.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify59.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5271	1600

prune148.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	92	11	103
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	92	12	104

Merged error: 5.1b

Counts

104 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
3.4b	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.4b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
53×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
28×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/l*`
12×	`difference-of-squares`
10×	`associate-/r/`
9×	`associate-/r*` `sqrt-prod`
7×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
6×	`div-inv` `distribute-lft-out--` `add-log-exp`
5×	`pow1`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 124

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series117.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
42.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
53.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify63.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4991	2493
1	4991	2493

prune146.0ms

Filtered

102 candidates to 136 candidates (-33.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	5	5	10
Picked	1	0	1
Done	0	1	1
Total	138	10	148

Merged error: 5.0b

Counts

148 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 83

Calls

4 calls:

8.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
6.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(- (* b_2 b_2) (* a c))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series80.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4954	1383
1	4954	1383

prune107.0ms

Filtered

69 candidates to 95 candidates (-37.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	95	10	105

Merged error: 4.9b

Counts

105 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

6.2b	(cbrt (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `associate-*r/`

Counts

4 → 55

Calls

4 calls:

10.0ms	(cbrt (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(cbrt (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4976	768
1	4976	768

prune83.0ms

Filtered

57 candidates to 67 candidates (-17.5%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	64	3	67
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	65	12	77

Merged error: 4.9b

Counts

77 → 12

regimes418.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.9b against oracle of 5.7b and baseline of 29.7b

bsearch96.0ms

Steps

Iters	Range	Point
7	4.3615889733450486e+108	1.0500909612496576e+110	8.774307758349226e+108
8	5.308770701153656e-296	1.2750363377371844e-292	1.70466835256157e-294
9	-1.6796181841493287e+154	-2.4052036288306873e+149	-2.641623564130735e+150

Iters

Range

Point

4.3615889733450486e+108

1.0500909612496576e+110

8.774307758349226e+108

5.308770701153656e-296

1.2750363377371844e-292

1.70466835256157e-294

-1.6796181841493287e+154

-2.4052036288306873e+149

-2.641623564130735e+150

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	47
1	34	47

end0.0ms

sample1.4s

Algorithm

intervals

Results

285.0ms	1056×	body	2560	valid
271.0ms	5845×	body	80	valid
193.0ms	872×	body	1280	valid
124.0ms	2872×	body	80	nan
81.0ms	460×	body	640	valid
35.0ms	109×	body	5120	valid
34.0ms	229×	body	320	valid
10.0ms	110×	body	160	valid

Details

sample245.0ms

simplify431.0ms

prune5.0ms

localize12.0ms

rewrite42.0ms

series61.0ms

simplify59.0ms

prune148.0ms

localize10.0ms

rewrite33.0ms

series117.0ms

simplify63.0ms

prune146.0ms

localize10.0ms

rewrite24.0ms

series80.0ms

simplify55.0ms

prune107.0ms

localize18.0ms

rewrite22.0ms

series260.0ms

simplify44.0ms

prune83.0ms

regimes418.0ms

bsearch96.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling