Details

Time bar (total: 5.3s)

sample1.1s

Algorithm
intervals
sampling

Space saved by range analysis: 25.512052%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 0%

Results
12.0ms174×body80valid
8.0ms28×body2560valid
8.0ms32×body1280valid
2.0ms12×body640valid
1.0ms4×body5120valid
1.0ms5×body320valid
1.0ms11×body80nan
0.0ms9×body80invalid
0.0ms1×body160valid

simplify9.0ms

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: 33.0b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

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:
11.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(+ (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)))

series66.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
15.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0396773
11550683
25001673

prune161.0ms

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

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New73982
Fresh000
Picked101
Done000
Total74983

Merged error: 7.1b

Counts
83 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
3.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.9b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 148
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms
(/ (+ 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:
9.0ms
(- (* b b) (* (* 4.0 a) c))
45.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
61.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify110.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
06372580
131842341
250012328

prune282.0ms

Filtered
106 candidates to 160 candidates (-50.9%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1564160
Fresh268
Picked011
Done000
Total15811169

Merged error: 7.0b

Counts
169 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
14.4b
(/ (* 2.0 a) (* 4.0 (* a c)))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt add-log-exp
9×*-un-lft-identity prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 70
Calls
4 calls:
11.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series41.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
3.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify60.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0426636
12470542
25003534

prune130.0ms

Filtered
55 candidates to 82 candidates (-49.1%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New81182
Fresh189
Picked101
Done011
Total831093

Merged error: 7.0b

Counts
93 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (* (/ 0.5 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.7b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
13×add-cbrt-cube
12×add-sqr-sqrt
11×*-un-lft-identity
10×add-log-exp
9×div-exp
8×pow1
7×add-cube-cbrt
6×prod-exp
5×flip3-- associate-/r/ flip--
4×cbrt-undiv sqrt-prod
3×rec-exp times-frac diff-log 1-exp associate-/l*
2×frac-times sub-neg pow-flip sqrt-div associate-*r/ cbrt-unprod distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 pow-prod-down neg-log associate-*l/ clear-num associate-/r* div-inv inv-pow
Counts
4 → 82
Calls
4 calls:
13.0ms
(/ 1 (* (/ 0.5 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms
(- (neg 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)))

series91.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ 1 (* (/ 0.5 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
18.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify49.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0439925
11879796
25003783

prune106.0ms

Filtered
61 candidates to 94 candidates (-54.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New93194
Fresh178
Picked101
Done011
Total959104

Merged error: 7.0b

Counts
104 → 9

regimes364.0ms

Accuracy

95% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 29.1b

bsearch128.0ms

Steps
ItersRangePoint
8
9.049369841653771e+105
1.7990151859052157e+109
5.99443458367034e+107
7
-4.98599761618103e-177
-1.1552942326503213e-178
-1.1682840951803057e-178
8
-4.359177875849184e+67
-4.3643220836244786e+64
-3.467672019600625e+67

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04425
14425

end0.0ms

sample2.3s

Algorithm
intervals
sampling

Space saved by range analysis: 25.512052%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 0%

Results
312.0ms1011×body2560valid
269.0ms5121×body80valid
227.0ms941×body1280valid
94.0ms482×body640valid
42.0ms111×body5120valid
34.0ms236×body320valid
21.0ms332×body80invalid
18.0ms365×body80nan
10.0ms98×body160valid

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