Details

sample68.0ms

Algorithm

intervals

Results

12.0ms	212×	body	80	valid
10.0ms	23×	body	1280	valid
6.0ms	20×	body	2560	valid
4.0ms	87×	body	80	nan
3.0ms	14×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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

Merged error: 31.1b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
22.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

11.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(- (* b b) (* (* 3.0 a) c))
17.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	391	774
1	1518	684
2	5001	674

prune160.0ms

Filtered

82 candidates to 63 candidates (23.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	9	83

Merged error: 7.2b

Counts

83 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* 3.0 a))
0.8b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
22.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-exp-log`
11×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube`
8×	`pow1` `add-sqr-sqrt`
7×	`add-cube-cbrt`
4×	`div-exp`
3×	`times-frac` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `flip3--` `pow-flip` `sqrt-div` `1-exp` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `pow-prod-down` `neg-log` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `div-inv` `inv-pow`

Counts

4 → 70

Calls

4 calls:

4.0ms	(/ 1 (* 3.0 a))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
3.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ 1 (* 3.0 a))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
8.0ms	(- (* b b) (* (* 3.0 a) c))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	333	493
1	1372	443
2	5002	427

prune125.0ms

Filtered

82 candidates to 54 candidates (34.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	80	11	91

Merged error: 7.2b

Counts

91 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* 3.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.8b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
22.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/r*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 69

Calls

4 calls:

10.0ms	(/ (* 3.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (* 3.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
8.0ms	(- (* b b) (* (* 3.0 a) c))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	374	757
1	1611	658
2	5001	645

prune145.0ms

Filtered

81 candidates to 61 candidates (24.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	79	13	92

Merged error: 7.1b

Counts

92 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (/ a (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
0.8b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
22.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
21×	`add-sqr-sqrt` `associate-r`
16×	`times-frac`
15×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out`
7×	`pow1`
4×	`distribute-rgt-neg-in`
3×	`associate-l` `sqrt-prod`
2×	`flip3--` `flip3-+` `sqrt-div` `prod-exp` `sum-log` `associate-/r/` `flip--` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `neg-log` `-commutative` `div-inv`

Counts

4 → 82

Calls

4 calls:

14.0ms	(* 3.0 (/ a (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* 3.0 (/ a (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(- (* b b) (* (* 3.0 a) c))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	428	848
1	1858	751
2	5001	739

prune127.0ms

Filtered

94 candidates to 68 candidates (27.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	2	9	11
Picked	0	1	1
Done	0	1	1
Total	94	13	107

Merged error: 7.1b

Counts

107 → 13

regimes626.0ms

Accuracy

88.4% (3.1b remaining)

Error of 9.1b against oracle of 6.0b and baseline of 32.7b

bsearch113.0ms

Steps

Iters	Range	Point
10	5.5981910563155256e+85	9.646889156889423e+104	5.695144519498344e+85
10	-1.2297628842452552e-269	-6.511992195658075e-280	-6.585474327581511e-280
6	-2.980315415731742e+97	-1.9078754765461935e+96	-2.6104707893455453e+97

Iters

Range

Point

5.5981910563155256e+85

9.646889156889423e+104

5.695144519498344e+85

-1.2297628842452552e-269

-6.511992195658075e-280

-6.585474327581511e-280

-2.980315415731742e+97

-1.9078754765461935e+96

-2.6104707893455453e+97

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	30
1	52	30
2	52	30

end0.0ms

sample1.4s

Algorithm

intervals

Results

330.0ms	6322×	body	80	valid
251.0ms	838×	body	2560	valid
189.0ms	755×	body	1280	valid
126.0ms	2490×	body	80	nan
70.0ms	369×	body	640	valid
27.0ms	76×	body	5120	valid
24.0ms	166×	body	320	valid
9.0ms	97×	body	160	valid

Details

sample68.0ms

simplify12.0ms

prune3.0ms

localize11.0ms

rewrite27.0ms

series66.0ms

simplify46.0ms

prune160.0ms

localize14.0ms

rewrite20.0ms

series40.0ms

simplify43.0ms

prune125.0ms

localize12.0ms

rewrite27.0ms

series91.0ms

simplify46.0ms

prune145.0ms

localize14.0ms

rewrite32.0ms

series91.0ms

simplify55.0ms

prune127.0ms

regimes626.0ms

bsearch113.0ms

simplify5.0ms

end0.0ms

sample1.4s

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