Details

Time bar (total: 5.2s)

sample36.0ms

Algorithm
intervals
Results
14.0ms277×body80valid
5.0ms111×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03818
17918
213618
316118
417318
517718
617718

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 19.7b

Counts
2 → 1

localize119.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.2b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-sqr-sqrt add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
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 distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 63
Calls
4 calls:
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series306.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
82.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify116.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (108.0ms)

IterNodesCost
0246646
1890606
23702588
35001584

prune284.0ms

Filtered
75 candidates to 60 candidates (80.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New68775
Fresh000
Picked101
Done000
Total69776

Merged error: 7.6b

Counts
76 → 7

localize120.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.7b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
4.2b
(/ (* a c) b)
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-sqr-sqrt add-cbrt-cube
13×*-un-lft-identity
9×add-cube-cbrt
8×add-log-exp
6×times-frac associate-/r*
5×pow1
4×cbrt-undiv div-exp sqrt-prod
3×flip3-- flip--
2×frac-2neg sqrt-div diff-log prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l* distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 neg-log
Counts
4 → 77
Calls
4 calls:
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
4.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series248.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
19.0ms
(/ (* a c) b)
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify57.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0450688
12176609
25001607

prune307.0ms

Filtered
89 candidates to 65 candidates (73.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New85489
Fresh336
Picked101
Done000
Total89796

Merged error: 7.1b

Counts
96 → 7

localize125.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.7b
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
3.7b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
31×times-frac
30×add-exp-log
26×*-un-lft-identity
23×add-cbrt-cube
22×add-cube-cbrt associate-*r*
11×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
8×add-log-exp
7×pow1 associate-*l*
6×unswap-sqr
4×sqrt-prod
3×flip3-- associate-/r* flip-- div-inv
2×sqrt-div diff-log associate-/r/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 115
Calls
4 calls:
13.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
15.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series309.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
104.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
54.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify94.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
07461376
137511199
250021152

prune511.0ms

Filtered
127 candidates to 91 candidates (71.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1243127
Fresh066
Picked101
Done000
Total1259134

Merged error: 7.1b

Counts
134 → 9

localize129.0ms

Local error

Found 4 expressions with local error:

5.3b
(cbrt (/ a (* (cbrt b) (cbrt b))))
5.3b
(cbrt (/ a (* (cbrt b) (cbrt b))))
5.3b
(cbrt (/ a (* (cbrt b) (cbrt b))))
21.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
12×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
9×times-frac
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 63
Calls
4 calls:
5.0ms
(cbrt (/ a (* (cbrt b) (cbrt b))))
5.0ms
(cbrt (/ a (* (cbrt b) (cbrt b))))
5.0ms
(cbrt (/ a (* (cbrt b) (cbrt b))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series555.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(cbrt (/ a (* (cbrt b) (cbrt b))))
200.0ms
(cbrt (/ a (* (cbrt b) (cbrt b))))
146.0ms
(cbrt (/ a (* (cbrt b) (cbrt b))))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify76.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (69.0ms)

IterNodesCost
0196592
1605553
22342546
35002544

prune407.0ms

Filtered
75 candidates to 66 candidates (88.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New75075
Fresh088
Picked011
Done000
Total75984

Merged error: 7.1b

Counts
84 → 9

regimes220.0ms

Accuracy

90.5% (1.4b remaining)

Error of 7.7b against oracle of 6.3b and baseline of 20.7b

bsearch164.0ms

Steps
ItersRangePoint
8
2.8028278488416225e+79
7.17624026241226e+82
7.042361471685654e+82
8
-1.0818597257815559e+95
-2.772945999025709e+91
-1.2226693456193597e+93

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06486
16486

end0.0ms

sample848.0ms

Algorithm
intervals
Results
434.0ms8716×body80valid
148.0ms3046×body80nan