Details

sample58.0ms

Algorithm

intervals

Results

14.0ms	191×	body	80	valid
8.0ms	24×	body	2560	valid
7.0ms	27×	body	1280	valid
6.0ms	106×	body	80	nan
3.0ms	15×	body	640	valid
2.0ms	11×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	2×	body	160	valid

simplify9.0ms

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

prune4.0ms

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: 30.9b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.0b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.6b	(- (* b b) (* (* 3.0 a) c))
20.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite26.0ms

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))
3.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
10.0ms	(- (* 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 (34.0ms)

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

prune170.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	71	11	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	11	83

Merged error: 4.6b

Counts

83 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* 3.0 a) c)
1.0b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.6b	(- (* b b) (* (* 3.0 a) c))
20.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite21.0ms

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

series40.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 3.0 a) c)
14.0ms	(+ (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

72 → 72

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	302	468
1	1299	428
2	5002	417

prune127.0ms

Filtered

52 candidates to 72 candidates (-38.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	72	11	83

Merged error: 4.4b

Counts

83 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 3.0 (* a c))
1.0b	(+ (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
1.6b	(- (* b b) (* 3.0 (* a c)))
20.7b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite20.0ms

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:

5.0ms	(* 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))))

series40.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 3.0 (* a c))
14.0ms	(+ (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))))

simplify129.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (121.0ms)

Iter	Nodes	Cost
0	292	467
1	1079	427
2	4710	416
3	5001	415

prune116.0ms

Filtered

50 candidates to 72 candidates (-44.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	72	11	83

Merged error: 4.4b

Counts

83 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* 3.0 a))
1.0b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.6b	(- (* b b) (* (* 3.0 a) c))
20.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite19.0ms

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)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ 1 (* 3.0 a))
14.0ms	(+ (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)))

simplify40.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	333	489
1	1378	443
2	5002	427

prune94.0ms

Filtered

54 candidates to 82 candidates (-51.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	82	11	93

Merged error: 4.4b

Counts

93 → 11

regimes675.0ms

Accuracy

86.1% (3.9b remaining)

Error of 9.3b against oracle of 5.4b and baseline of 33.7b

bsearch111.0ms

Steps

Iters	Range	Point
9	1.4207218227508602e+125	1.7687561556963888e+130	6.126240493567788e+125
7	3.401319575465327e-151	3.421882355712698e-149	3.055688900930523e-150
10	-3.692428373978256e+65	-2.9514001404867553e+50	-6.741241628846222e+60

Iters

Range

Point

1.4207218227508602e+125

1.7687561556963888e+130

6.126240493567788e+125

3.401319575465327e-151

3.421882355712698e-149

3.055688900930523e-150

-3.692428373978256e+65

-2.9514001404867553e+50

-6.741241628846222e+60

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	29
1	51	29
2	51	29

end0.0ms

sample1.7s

Algorithm

intervals

Results

349.0ms	1064×	body	2560	valid
331.0ms	5894×	body	80	valid
233.0ms	887×	body	1280	valid
150.0ms	2829×	body	80	nan
101.0ms	444×	body	640	valid
38.0ms	99×	body	5120	valid
33.0ms	212×	body	320	valid
12.0ms	117×	body	160	valid

Details

sample58.0ms

simplify9.0ms

prune4.0ms

localize11.0ms

rewrite26.0ms

series63.0ms

simplify43.0ms

prune170.0ms

localize14.0ms

rewrite21.0ms

series40.0ms

simplify43.0ms

prune127.0ms

localize12.0ms

rewrite20.0ms

series40.0ms

simplify129.0ms

prune116.0ms

localize12.0ms

rewrite19.0ms

series38.0ms

simplify40.0ms

prune94.0ms

regimes675.0ms

bsearch111.0ms

simplify2.0ms

end0.0ms

sample1.7s

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