Details

Time bar (total: 5.2s)

sample42.0ms

Algorithm
intervals
Results
20.0ms279×body80valid
5.0ms79×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03818
17918
213618
316118
417318
517718
617718

prune4.0ms

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: 18.5b

Counts
2 → 1

localize120.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
0.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 distribute-rgt-neg-in neg-log
Counts
4 → 60
Calls
4 calls:
4.0ms
(- (* 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)))

series269.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* (* 4.0 a) c))
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify116.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (109.0ms)

IterNodesCost
0227581
1878551
23814541
35002538

prune256.0ms

Filtered
72 candidates to 55 candidates (76.4%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New66672
Fresh000
Picked101
Done000
Total67673

Merged error: 6.5b

Counts
73 → 6

localize119.0ms

Local error

Found 4 expressions with local error:

20.7b
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
21.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))
21.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))
21.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
60×cbrt-div
30×flip3-- flip--
28×frac-times
26×sqrt-div
24×pow1
15×sqrt-pow1
14×associate-*l/
12×pow1/3
9×cbrt-prod pow-prod-up
8×associate-*r/
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow-plus
5×pow-prod-down
4×add-exp-log add-cbrt-cube add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 89
Calls
4 calls:
22.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series399.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
121.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
96.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
108.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify185.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 3 (168.0ms)

IterNodesCost
03481856
19131805
241361785
350021704

prune380.0ms

Filtered
101 candidates to 65 candidates (64.4%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1010101
Fresh055
Picked011
Done000
Total1016107

Merged error: 6.5b

Counts
107 → 6

localize134.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
3.1b
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
4.8b
(/ (* a c) b)
20.7b
(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 add-log-exp
5×pow1
4×cbrt-undiv div-exp associate-/r* associate-/l*
3×flip3-- sqrt-prod flip--
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod div-inv associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-sub
Counts
4 → 72
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
10.0ms
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
4.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series214.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
19.0ms
(/ (* a c) b)
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify54.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0424597
11957520
25001518

prune305.0ms

Filtered
84 candidates to 61 candidates (72.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New81384
Fresh044
Picked101
Done011
Total82890

Merged error: 5.2b

Counts
90 → 8

localize115.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.6b
(- (* b b) (* (* 4.0 a) c))
20.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

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-/r*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv flip3-- flip3-+ sqrt-div div-exp sum-log associate-/r/ flip-- flip-+
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log neg-log prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 69
Calls
4 calls:
11.0ms
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
13.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series408.0ms

Counts
4 → 12
Calls
4 calls:
213.0ms
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(- (* b b) (* (* 4.0 a) c))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify43.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0368755
11530656
25001644

prune237.0ms

Filtered
81 candidates to 61 candidates (75.3%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New79281
Fresh246
Picked101
Done101
Total83689

Merged error: 5.0b

Counts
89 → 6

regimes155.0ms

Accuracy

89.6% (1.6b remaining)

Error of 7.8b against oracle of 6.3b and baseline of 21.3b

bsearch317.0ms

Steps
ItersRangePoint
7
3.0106008231332273e+28
3.853441604264477e+30
3.7841174599135035e+30
10
-4.721270821582062e-307
5.602029484535934e-299
4.464513229872e-311
10
-2.90407839199202e+158
-1.093530084538893e+147
-1.1894934445791155e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06171
16371
26371

end0.0ms

sample1.2s

Algorithm
intervals
Results
740.0ms8730×body80valid
186.0ms2863×body80nan