Details

sample397.0ms

Algorithm

intervals

Results

18.0ms	192×	body	80	valid
15.0ms	31×	body	2560	valid
14.0ms	36×	body	1280	valid
7.0ms	89×	body	80	nan
3.0ms	10×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
1.0ms	5×	body	160	valid

simplify768.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	713	13
1	713	13

prune9.0ms

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: 38.4b

Counts

2 → 1

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.2b	(- (* b_2 b_2) (* a c))
1.8b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite64.0ms

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:

21.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series97.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
32.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify101.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4936	1600
1	4936	1600

prune283.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	93	11	104

Merged error: 6.1b

Counts

104 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.1b	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.3b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
57×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
28×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
14×	`difference-of-squares`
13×	`associate-/l*`
10×	`sqrt-prod` `associate-/r/`
9×	`associate-/r*`
7×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `distribute-lft-out--`
6×	`div-inv` `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 → 127

Calls

4 calls:

16.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
19.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
75.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
93.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify95.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5022	2594

prune275.0ms

Filtered

105 candidates to 139 candidates (-32.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	134	5	139
Fresh	6	3	9
Picked	0	1	1
Done	0	1	1
Total	140	10	150

Merged error: 6.0b

Counts

150 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
1.2b	(- (* b_2 b_2) (* a c))
1.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite57.0ms

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:

19.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
8.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series156.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
17.0ms	(- (* b_2 b_2) (* a c))
26.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify104.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4871	1380
1	4871	1380

prune208.0ms

Filtered

69 candidates to 95 candidates (-37.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	2	5	7
Picked	0	1	1
Done	0	2	2
Total	95	10	105

Merged error: 5.9b

Counts

105 → 10

localize29.0ms

Local error

Found 4 expressions with local error:

1.6b	(* (/ a (* (cbrt a) (cbrt a))) (/ c (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (cbrt a))))
1.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0b	(/ c (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (cbrt a)))
24.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
35×	`add-cbrt-cube`
20×	`add-sqr-sqrt`
16×	`prod-exp` `cbrt-unprod`
14×	`cbrt-undiv` `div-exp`
13×	`*-un-lft-identity`
11×	`add-cube-cbrt`
10×	`times-frac`
9×	`associate-r`
7×	`pow1` `associate-l`
6×	`add-log-exp`
5×	`associate-*l/`
4×	`flip3--` `sqrt-prod` `associate-/r/` `flip--`
3×	`div-inv` `associate-/l*`
2×	`sqrt-div` `difference-of-squares` `unswap-sqr`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `*-commutative` `distribute-lft-out--`

Counts

4 → 101

Calls

4 calls:

36.0ms	(* (/ a (* (cbrt a) (cbrt a))) (/ c (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (cbrt a))))
12.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
20.0ms	(/ c (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (cbrt a)))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (/ a (* (cbrt a) (cbrt a))) (/ c (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (cbrt a))))
24.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
154.0ms	(/ c (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (cbrt a)))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4938	1748
1	4938	1748

prune179.0ms

Filtered

80 candidates to 113 candidates (-41.3%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	112	11	123

Merged error: 5.9b

Counts

123 → 11

regimes944.0ms

Accuracy

95.2% (1.2b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 30.0b

bsearch124.0ms

Steps

Iters	Range	Point
5	1.1994113433831075e+59	2.551497614016684e+59	1.9930311221408239e+59
9	8.181651543211295e-234	3.895310942336471e-227	3.872731709600237e-232
4	-2.2327321462329562e+137	-1.3518192462889248e+137	-2.0155757731311035e+137

Iters

Range

Point

1.1994113433831075e+59

2.551497614016684e+59

1.9930311221408239e+59

8.181651543211295e-234

3.895310942336471e-227

3.872731709600237e-232

-2.2327321462329562e+137

-1.3518192462889248e+137

-2.0155757731311035e+137

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	105	61
1	105	61

end0.0ms

sample2.7s

Algorithm

intervals

Results

513.0ms	1018×	body	2560	valid
497.0ms	5871×	body	80	valid
378.0ms	923×	body	1280	valid
239.0ms	2932×	body	80	nan
147.0ms	465×	body	640	valid
61.0ms	98×	body	5120	valid
54.0ms	225×	body	320	valid
17.0ms	109×	body	160	valid

Details

sample397.0ms

simplify768.0ms

prune9.0ms

localize39.0ms

rewrite64.0ms

series97.0ms

simplify101.0ms

prune283.0ms

localize17.0ms

rewrite76.0ms

series211.0ms

simplify95.0ms

prune275.0ms

localize19.0ms

rewrite57.0ms

series156.0ms

simplify104.0ms

prune208.0ms

localize29.0ms

rewrite86.0ms

series285.0ms

simplify67.0ms

prune179.0ms

regimes944.0ms

bsearch124.0ms

simplify4.0ms

end0.0ms

sample2.7s

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