Details

sample34.0ms

Algorithm

intervals

Results

14.0ms	280×	body	80	valid
5.0ms	83×	body	80	nan

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	18
1	66	18
2	116	18
3	144	18
4	159	18
5	161	18
6	161	18

prune7.0ms

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: 17.8b

Counts

2 → 1

localize121.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.9b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
49×	`sqrt-prod`
38×	`*-un-lft-identity`
36×	`unswap-sqr`
32×	`difference-of-squares`
18×	`associate-l`
14×	`distribute-lft-out--`
12×	`add-log-exp`
6×	`pow1` `add-cube-cbrt` `swap-sqr` `*-commutative`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `sum-log` `distribute-lft-out`
1×	`+-commutative` `associate--l-` `associate-+l-` `sub-neg` `flip3-+` `flip-+`

Counts

4 → 105

Calls

4 calls:

35.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
33.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
26.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
83.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
78.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify143.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 3 (131.0ms)

Iter	Nodes	Cost
0	313	1102
1	1029	1062
2	4175	1047
3	5001	1031

prune299.0ms

Filtered

117 candidates to 72 candidates (61.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	110	7	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	7	118

Merged error: 6.4b

Counts

118 → 7

localize124.0ms

Local error

Found 4 expressions with local error:

6.7b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

203×	`add-sqr-sqrt`
108×	`sqrt-prod`
66×	`difference-of-squares`
63×	`unswap-sqr`
51×	`*-un-lft-identity`
29×	`associate-l`
22×	`distribute-lft-out--`
18×	`swap-sqr`
10×	`*-commutative`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`distribute-rgt-neg-in` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log`

Counts

4 → 147

Calls

4 calls:

127.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
27.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
78.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
80.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify150.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 3 (131.0ms)

Iter	Nodes	Cost
0	303	1829
1	1018	1703
2	4227	1681
3	5001	1643

prune370.0ms

Filtered

159 candidates to 77 candidates (48.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	159	7	166

Merged error: 6.4b

Counts

166 → 7

localize128.0ms

Local error

Found 4 expressions with local error:

11.1b	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
20.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

143×	`add-sqr-sqrt`
54×	`unswap-sqr`
51×	`*-un-lft-identity`
48×	`cbrt-prod`
45×	`difference-of-squares`
29×	`associate-l`
24×	`sqrt-prod`
18×	`distribute-lft-out--`
9×	`swap-sqr` `*-commutative`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`add-exp-log` `cbrt-div` `add-cbrt-cube` `distribute-lft-out`
3×	`flip3--` `flip--`
2×	`distribute-rgt-neg-in` `pow1/3` `sqrt-div` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 121

Calls

4 calls:

48.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series508.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
237.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
107.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify60.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	449	1549
1	1576	1470
2	5001	1441

prune420.0ms

Filtered

133 candidates to 78 candidates (58.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	132	8	140

Merged error: 6.4b

Counts

140 → 8

localize124.0ms

Local error

Found 4 expressions with local error:

11.1b	(+ (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) (- b))
20.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

143×	`add-sqr-sqrt`
54×	`unswap-sqr`
51×	`*-un-lft-identity`
48×	`cbrt-prod`
45×	`difference-of-squares`
29×	`associate-l`
24×	`sqrt-prod`
18×	`distribute-lft-out--`
9×	`swap-sqr` `*-commutative`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`add-exp-log` `cbrt-div` `add-cbrt-cube` `distribute-lft-out`
3×	`flip3--` `flip--`
2×	`distribute-rgt-neg-in` `pow1/3` `sqrt-div` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+r-` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `unsub-neg` `neg-log` `flip-+`

Counts

4 → 123

Calls

4 calls:

53.0ms	(+ (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) (- b))
26.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(+ (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))) (- b))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
100.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
101.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify58.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	450	1558
1	1638	1479
2	5002	1438

prune395.0ms

Filtered

135 candidates to 78 candidates (57.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	135	8	143

Merged error: 6.4b

Counts

143 → 8

regimes169.0ms

Accuracy

91.2% (1.1b remaining)

Error of 8.8b against oracle of 7.8b and baseline of 20.0b

bsearch174.0ms

Steps

Iters	Range		Point
7	8.70788314804275e+92	3.0899898012220906e+94	1.214024031535037e+94
10	-2.7851241427016145e+159	-9.354797223898085e+144	-1.024958645589419e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	58
1	48	58

end0.0ms

sample846.0ms

Algorithm

intervals

Results

458.0ms	8711×	body	80	valid
144.0ms	2987×	body	80	nan