Details

Time bar (total: 4.6s)

sample495.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 5.867564%

Guaranteed chance to sample good point: 42.561965%

Results
11.0ms34×body2560valid
9.0ms182×body80valid
9.0ms38×body1280valid
4.0ms84×body80nan
2.0ms10×body640valid
1.0ms4×body5120valid
1.0ms7×body320valid
0.0ms2×body160valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0219
1429
2769
3949
41029
51029

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 35.1b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.6b
(- (* b b) (* (* 3.0 a) c))
24.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite30.0ms

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-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
14.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series64.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
15.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms
(- (* b b) (* (* 3.0 a) c))
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0391774
11518684
25001674

prune172.0ms

Filtered
63 candidates to 82 candidates (-30.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New721082
Fresh000
Picked101
Done000
Total731083

Merged error: 6.7b

Counts
83 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.2b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
10.1b
(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 154
Calls
4 calls:
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
13.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series136.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
46.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
56.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
17.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify114.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
06442693
131432447
250012434

prune304.0ms

Filtered
111 candidates to 166 candidates (-49.5%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1633166
Fresh189
Picked101
Done000
Total16511176

Merged error: 6.6b

Counts
176 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.2b
(/ (* 1 (/ 3.0 (/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
10.1b
(/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
24.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
86×add-exp-log
54×add-cbrt-cube
40×div-exp
30×prod-exp
22×cbrt-undiv
20×add-sqr-sqrt
19×*-un-lft-identity
16×cbrt-unprod
8×times-frac 1-exp associate-/l* add-log-exp
7×add-cube-cbrt
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
3×flip3-- distribute-rgt-neg-in flip-- associate-/l/
2×frac-2neg sqrt-div diff-log clear-num associate-/r* div-inv
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 div-sub associate-*r/ neg-log
Counts
4 → 107
Calls
4 calls:
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
18.0ms
(/ (* 1 (/ 3.0 (/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
12.0ms
(/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series88.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
33.0ms
(/ (* 1 (/ 3.0 (/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
24.0ms
(/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify93.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
07781660
140841318
250021306

prune167.0ms

Filtered
68 candidates to 119 candidates (-75.0%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1190119
Fresh01010
Picked011
Done000
Total11911130

Merged error: 6.6b

Counts
130 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (* 3.0 a))
0.6b
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.6b
(- (* b b) (* (* 3.0 a) c))
24.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
15×add-exp-log
11×*-un-lft-identity
10×add-log-exp
9×add-cbrt-cube
8×pow1 add-sqr-sqrt
7×add-cube-cbrt
4×div-exp
3×times-frac prod-exp sqrt-prod associate-/l*
2×cbrt-undiv rec-exp flip3-- pow-flip sqrt-div 1-exp sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log pow-prod-down neg-log clear-num associate-/r* cbrt-unprod flip-+ div-inv inv-pow
Counts
4 → 70
Calls
4 calls:
5.0ms
(/ 1 (* 3.0 a))
8.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series40.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(/ 1 (* 3.0 a))
15.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms
(- (* b b) (* (* 3.0 a) c))
15.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify43.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0333489
11378443
25002427

prune95.0ms

Filtered
54 candidates to 82 candidates (-51.9%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New82082
Fresh099
Picked011
Done011
Total821193

Merged error: 6.6b

Counts
93 → 11

regimes661.0ms

Accuracy

83.6% (4.5b remaining)

Error of 10.1b against oracle of 5.6b and baseline of 32.8b

bsearch68.0ms

Steps
ItersRangePoint
9
1.289478017848784e-92
3.0960733146221547e-84
1.4688196011974082e-89
9
-7.696959026980834e+156
-1.7883696058631366e+151
-1.279354543327107e+154

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03817
13817

end0.0ms

sample1.8s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 5.867564%

Guaranteed chance to sample good point: 42.561965%

Results
338.0ms1097×body2560valid
307.0ms5776×body80valid
221.0ms907×body1280valid
111.0ms2202×body80nan
85.0ms443×body640valid
42.0ms262×body320valid
42.0ms110×body5120valid
11.0ms116×body160valid

Profiling

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