Details

Time bar (total: 3.9s)

sample313.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 5.867564%

Guaranteed chance to sample good point: 42.561744%

Results
10.0ms34×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
0249
1459
2799
3979
41059
51059

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

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.6b
(- (* b b) (* 4.0 (* a c)))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite26.0ms

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:
10.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series63.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
16.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms
(- (* b b) (* 4.0 (* a c)))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0394773
11501683
25002673

prune151.0ms

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

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New74882
Fresh000
Picked101
Done000
Total75883

Merged error: 6.7b

Counts
83 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.1b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
10.1b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite45.0ms

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:
9.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series130.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
55.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify99.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
06352693
129742447
250012434

prune275.0ms

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

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1633166
Fresh167
Picked101
Done000
Total1659174

Merged error: 6.6b

Counts
174 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.6b
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.6b
(- (* b b) (* 4.0 (* a c)))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
16×*-un-lft-identity
13×add-cbrt-cube
11×add-sqr-sqrt
10×prod-exp add-log-exp
8×add-cube-cbrt
7×pow1 associate-*r*
5×associate-*l*
4×div-exp cbrt-unprod distribute-lft-out
3×flip3-+ times-frac sqrt-prod flip-+
2×cbrt-undiv frac-times rec-exp flip3-- distribute-rgt-neg-in sqrt-div 1-exp associate-*l/ sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 80
Calls
4 calls:
14.0ms
(* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series63.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
15.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms
(- (* b b) (* 4.0 (* a c)))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify55.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0470914
12126788
25001776

prune137.0ms

Filtered
66 candidates to 92 candidates (-39.4%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New91192
Fresh178
Picked011
Done000
Total929101

Merged error: 6.6b

Counts
101 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.6b
(- (* b b) (* 4.0 (* a c)))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
53×times-frac
45×*-un-lft-identity
26×add-sqr-sqrt
25×add-exp-log add-cube-cbrt
13×add-cbrt-cube
12×div-exp
11×associate-/r*
10×distribute-lft-out add-log-exp
9×associate-/r/
6×pow1
5×cbrt-undiv distribute-rgt-neg-in flip3-+ flip-+ div-inv
3×rec-exp 1-exp prod-exp sqrt-prod associate-/l*
2×flip3-- sqrt-div sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 diff-log neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 114
Calls
4 calls:
23.0ms
(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
14.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms
(- (* b b) (* 4.0 (* a c)))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series72.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
15.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms
(- (* b b) (* 4.0 (* a c)))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify64.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05251585
125501372
250011305

prune123.0ms

Filtered
71 candidates to 126 candidates (-77.5%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1260126
Fresh077
Picked011
Done011
Total1269135

Merged error: 6.6b

Counts
135 → 9

regimes307.0ms

Accuracy

84.6% (4.5b remaining)

Error of 10.1b against oracle of 5.6b and baseline of 34.6b

bsearch62.0ms

Steps
ItersRangePoint
9
1.289478017848784e-92
3.0960733146221547e-84
2.4464565658583153e-86
8
-8.382670411051464e+140
-3.442563917519272e+136
-7.018837578197459e+139

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03816
13816

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: 42.561744%

Results
333.0ms1094×body2560valid
304.0ms5776×body80valid
223.0ms911×body1280valid
111.0ms2204×body80nan
87.0ms442×body640valid
41.0ms110×body5120valid
40.0ms263×body320valid
11.0ms115×body160valid

Profiling

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