Details

Time bar (total: 4.5s)

sample79.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 99.998264%

Space saved by search: 99.998264%

Guaranteed chance to sample good point: 0%

Results
16.0ms554×pre80true
15.0ms157×body160valid
14.0ms298×body80nan
6.0ms46×body320valid
6.0ms53×body80valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 44.5b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
40.0b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite29.0ms

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:
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series66.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(- (* b b) (* (* 4.0 a) c))
26.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
18.0ms
(+ (neg b) (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

prune123.0ms

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

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New79382
Fresh000
Picked101
Done000
Total80383

Merged error: 0.2b

Counts
83 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
82×add-sqr-sqrt *-un-lft-identity
38×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
11×distribute-rgt-neg-in sqrt-prod
10×add-log-exp
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 151
Calls
4 calls:
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
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))
13.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series132.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
46.0ms
(/ (/ (+ 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)))))

simplify116.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
06432666
132102408
250012396

prune307.0ms

Filtered
106 candidates to 163 candidates (-53.8%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New15310163
Fresh112
Picked101
Done000
Total15511166

Merged error: 0.0b

Counts
166 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.3b
(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt
57×*-un-lft-identity
52×add-exp-log
45×times-frac
32×add-cbrt-cube
28×add-cube-cbrt
27×associate-*r*
18×div-exp
17×prod-exp
14×distribute-lft-out-- difference-of-squares
10×cbrt-undiv
9×cbrt-unprod
8×associate-/r*
7×pow1 distribute-rgt-neg-in sqrt-prod
6×associate-/l/ add-log-exp
4×frac-times rec-exp flip3-+ 1-exp associate-*l/ associate-/r/ flip-+ associate-/l*
3×flip3-- associate-*l* flip-- div-inv unswap-sqr
2×frac-2neg associate-*r/ clear-num un-div-inv
1×sub-neg pow-flip diff-log pow-prod-down *-commutative inv-pow
Counts
4 → 150
Calls
4 calls:
11.0ms
(/ 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
19.0ms
(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
19.0ms
(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series144.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
45.0ms
(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
63.0ms
(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify198.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
07292182
148731812
250011812

prune242.0ms

Filtered
93 candidates to 162 candidates (-74.2%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1602162
Fresh3710
Picked011
Done000
Total16310173

Merged error: 0.0b

Counts
173 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b
(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
27×add-exp-log add-cbrt-cube
16×add-sqr-sqrt
14×*-un-lft-identity
10×prod-exp cbrt-unprod add-log-exp
7×associate-*r*
6×pow1 cbrt-undiv add-cube-cbrt div-exp
4×sub-neg flip3-- associate-*r/ flip-- distribute-lft-out-- difference-of-squares
3×diff-log associate-*l*
2×distribute-rgt-in distribute-rgt-neg-in distribute-lft-in sqrt-prod associate-/r/
1×associate--l- neg-sub0 frac-2neg times-frac pow-prod-down neg-log clear-num associate-/r* *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 85
Calls
4 calls:
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
16.0ms
(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series104.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
32.0ms
(* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
46.0ms
(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify89.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
05181106
13294871
25002864

prune125.0ms

Filtered
62 candidates to 97 candidates (-56.5%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New91697
Fresh538
Picked101
Done011
Total9710107

Merged error: 0b

Counts
107 → 10

regimes345.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02613
12613

end0.0ms

sample2.1s

Algorithm
intervals
sampling

Space saved by range analysis: 99.998264%

Space saved by search: 99.998264%

Guaranteed chance to sample good point: 0%

Results
473.0ms4923×body160valid
468.0ms16315×pre80true
396.0ms8315×body80nan
198.0ms1359×body320valid
87.0ms1718×body80valid

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