Details

sample45.0ms

Algorithm

intervals

Results

10.0ms	206×	body	80	valid
7.0ms	26×	body	2560	valid
6.0ms	25×	body	1280	valid
4.0ms	75×	body	80	nan
2.0ms	12×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	5×	body	160	valid
0.0ms	1×	body	5120	valid

simplify11.0ms

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 (0.0%)

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: 32.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.4b	(- (* b b) (* (* 3.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite28.0ms

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:

12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
3.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
48.0ms	(- (* b b) (* (* 3.0 a) c))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	400	780
1	1529	686
2	5002	675

prune216.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 6.0b

Counts

83 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* 3.0 a))
1.4b	(- (* b b) (* (* 3.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite22.0ms

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:

5.0ms	(/ 1 (* 3.0 a))
4.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series212.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ 1 (* 3.0 a))
48.0ms	(- (* b b) (* (* 3.0 a) c))
75.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	338	493
1	1380	446
2	5001	430

prune177.0ms

Filtered

82 candidates to 55 candidates (67.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	82	8	90

Merged error: 6.0b

Counts

90 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
1.4b	(- (* b b) (* (* 3.0 a) c))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

5.0ms	(* (* 3.0 a) c)
4.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (* 3.0 a) c)
43.0ms	(- (* b b) (* (* 3.0 a) c))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	307	469
1	1303	428
2	5001	417

prune158.0ms

Filtered

72 candidates to 52 candidates (72.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	73	7	80

Merged error: 6.0b

Counts

80 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (* a c))
1.4b	(- (* b b) (* 3.0 (* a c)))
1.4b	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
23.0b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

9.0ms	(* 3.0 (* a c))
4.0ms	(- (* b b) (* 3.0 (* a c)))
8.0ms	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series216.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* 3.0 (* a c))
48.0ms	(- (* b b) (* 3.0 (* a c)))
82.0ms	(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
67.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify132.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (126.0ms)

Iter	Nodes	Cost
0	296	468
1	1081	427
2	4610	415
3	5001	414

prune142.0ms

Filtered

72 candidates to 51 candidates (70.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	72	7	79

Merged error: 6.0b

Counts

79 → 7

regimes271.0ms

Accuracy

89.1% (3.1b remaining)

Error of 8.7b against oracle of 5.6b and baseline of 34.0b

bsearch176.0ms

Steps

Iters	Range	Point
7	6.011887282010727e+43	5.675568733030414e+45	2.9359885461337045e+45
7	2.8088005691183282e-136	8.718282365388647e-135	6.102721236610262e-136
9	-3.270551254255918e+118	-2.1334538400483563e+110	-2.4928243975796524e+116

Iters

Range

Point

6.011887282010727e+43

5.675568733030414e+45

2.9359885461337045e+45

2.8088005691183282e-136

8.718282365388647e-135

6.102721236610262e-136

-3.270551254255918e+118

-2.1334538400483563e+110

-2.4928243975796524e+116

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.4s

Algorithm

intervals

Results

310.0ms	1058×	body	2560	valid
289.0ms	5895×	body	80	valid
202.0ms	872×	body	1280	valid
139.0ms	2907×	body	80	nan
84.0ms	449×	body	640	valid
39.0ms	107×	body	5120	valid
31.0ms	228×	body	320	valid
10.0ms	110×	body	160	valid

Details

sample45.0ms

simplify11.0ms

prune3.0ms

localize11.0ms

rewrite28.0ms

series307.0ms

simplify48.0ms

prune216.0ms

localize17.0ms

rewrite22.0ms

series212.0ms

simplify44.0ms

prune177.0ms

localize12.0ms

rewrite22.0ms

series220.0ms

simplify43.0ms

prune158.0ms

localize12.0ms

rewrite25.0ms

series216.0ms

simplify132.0ms

prune142.0ms

regimes271.0ms

bsearch176.0ms

simplify2.0ms

end0.0ms

sample1.4s

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