Details

Time bar (total: 4.9s)

sample35.0ms

Algorithm
intervals
Results
14.0ms277×body80valid
5.0ms111×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03918
18018
214318
317718
418918
519318
619318

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

localize114.0ms

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)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square 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 → 151
Calls
4 calls:
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
76.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify66.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04183056
114712008
250011917

prune385.0ms

Filtered
163 candidates to 92 candidates (56.4%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1567163
Fresh000
Picked101
Done000
Total1577164

Merged error: 7.6b

Counts
164 → 7

localize113.0ms

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)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
55×add-sqr-sqrt
54×*-un-lft-identity
50×add-cube-cbrt
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
14×add-exp-log add-cbrt-cube
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×times-frac associate-/r*
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
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 sqrt-pow1 pow1/2 neg-log
Counts
4 → 155
Calls
4 calls:
10.0ms
(- (- 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)))

series226.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
65.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
18.0ms
(/ (* a c) b)
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify86.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
06203085
126922005
250021927

prune378.0ms

Filtered
167 candidates to 88 candidates (52.7%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1634167
Fresh336
Picked101
Done000
Total1677174

Merged error: 7.1b

Counts
174 → 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 (* (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)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
84×add-sqr-sqrt
67×*-un-lft-identity
63×add-cube-cbrt
60×prod-diff
34×sqrt-prod
31×times-frac
30×add-exp-log
23×add-cbrt-cube
22×distribute-rgt-neg-in associate-*r*
21×distribute-lft-neg-in
11×cbrt-prod
10×fma-neg
9×cbrt-undiv div-exp prod-exp cbrt-unprod
8×add-log-exp
7×pow1 neg-mul-1 associate-*l*
6×unswap-sqr
4×expm1-log1p-u log1p-expm1-u
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 frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 193
Calls
4 calls:
13.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
14.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series286.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
95.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
46.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify121.0ms

Algorithm
egg-herbie
Counts
205 → 205
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
09173793
142782579
250022578

prune628.0ms

Filtered
205 candidates to 128 candidates (62.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2032205
Fresh066
Picked101
Done000
Total2048212

Merged error: 7.1b

Counts
212 → 8

localize118.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* 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)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
6×times-frac associate-/r* add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×flip3-- sqrt-prod flip--
2×frac-2neg sqrt-div prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l*
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 81
Calls
4 calls:
4.0ms
(- (* 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)))

series210.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(- (* b b) (* (* 4.0 a) c))
65.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
18.0ms
(/ (* a c) b)
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0423634
12069555
25001550

prune305.0ms

Filtered
93 candidates to 70 candidates (75.3%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New93093
Fresh077
Picked011
Done000
Total938101

Merged error: 7.1b

Counts
101 → 8

regimes190.0ms

Accuracy

89.3% (1.6b remaining)

Error of 8.3b against oracle of 6.7b and baseline of 21.5b

bsearch173.0ms

Steps
ItersRangePoint
8
2.8028278488416225e+79
7.17624026241226e+82
7.042361471685654e+82
9
-2.772945999025709e+91
-2.403350477946658e+83
-2.3902069305449856e+91

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05665
15665

end0.0ms

sample843.0ms

Algorithm
intervals
Results
448.0ms8716×body80valid
150.0ms3046×body80nan