Details

sample38.0ms

Algorithm

intervals

Results

15.0ms	275×	body	80	valid
4.0ms	79×	body	80	nan

simplify15.0ms

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

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: 20.0b

Counts

2 → 1

localize114.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite121.0ms

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:

36.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
32.0ms	(+ (- 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)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify156.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 3 (140.0ms)

Iter	Nodes	Cost
0	320	1102
1	1096	1062
2	4653	1047
3	5001	1033

prune370.0ms

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: 7.3b

Counts

118 → 7

localize115.0ms

Local error

Found 4 expressions with local error:

8.4b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite209.0ms

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:

130.0ms	(- (- 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)))

series289.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify167.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	313	1829
1	1101	1703
2	4861	1681
3	5001	1681

prune462.0ms

Filtered

159 candidates to 82 candidates (51.6%)

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: 7.3b

Counts

166 → 7

localize121.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

32.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series352.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
90.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
100.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify143.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (130.0ms)

Iter	Nodes	Cost
0	291	1245
1	1012	1222
2	4226	1210
3	5001	1188

prune465.0ms

Filtered

135 candidates to 78 candidates (57.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	135	7	142

Merged error: 7.3b

Counts

142 → 7

localize119.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.8b	(/ (* a c) b)
5.0b	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

300×	`*-un-lft-identity`
178×	`add-sqr-sqrt`
156×	`times-frac`
136×	`distribute-lft-out--`
80×	`associate-l`
76×	`add-cube-cbrt`
45×	`associate-r`
40×	`distribute-rgt-neg-in`
33×	`unswap-sqr`
28×	`difference-of-squares`
24×	`sqrt-prod` `associate-/l*`
18×	`*-commutative`
14×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/r*`
8×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`swap-sqr`
2×	`flip3--` `frac-2neg` `sqrt-div` `prod-exp` `clear-num` `sum-log` `associate-/r/` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 274

Calls

4 calls:

36.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(/ (* a c) b)
39.0ms	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms	(/ (* a c) b)
180.0ms	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	879	2849
1	4002	2760
2	5001	2752

prune758.0ms

Filtered

286 candidates to 152 candidates (53.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	284	2	286
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	286	7	293

Merged error: 6.5b

Counts

293 → 7

regimes189.0ms

Accuracy

92.6% (1.1b remaining)

Error of 7.6b against oracle of 6.5b and baseline of 21.3b

bsearch193.0ms

Steps

Iters	Range		Point
9	4.546949039871578e+116	7.0067478635952275e+121	7.587411789834341e+119
9	-1.6289578644700005e+63	-1.5322109559450533e+54	-1.6048696542769354e+63

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	62
1	52	62

end0.0ms

sample883.0ms

Algorithm

intervals

Results

478.0ms	8700×	body	80	valid
153.0ms	2865×	body	80	nan