Details

Time bar (total: 4.1s)

sample72.0ms

Algorithm
intervals
Results
14.0ms148×body160valid
14.0ms209×body80nan
13.0ms465×pre80true
7.0ms47×body320valid
3.0ms61×body80valid

simplify10.0ms

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: 43.3b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
37.2b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite27.0ms

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:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series65.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(- (* b b) (* (* 4.0 a) c))
28.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
15.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify45.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0396773
11550683
25001673

prune136.0ms

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

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New75782
Fresh000
Picked101
Done000
Total76783

Merged error: 0.2b

Counts
83 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* 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))
16.0ms
(/ (/ (+ 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)))))

series124.0ms

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))
44.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
56.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify112.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
06432667
132102408
250012396

prune310.0ms

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

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New15310163
Fresh516
Picked101
Done000
Total15911170

Merged error: 0b

Counts
170 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (* 2.0 a) (* 4.0 (* a c)))
0.3b
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
152×add-exp-log
92×add-cbrt-cube
73×prod-exp
46×div-exp
41×cbrt-unprod
26×cbrt-undiv
14×add-sqr-sqrt
12×*-un-lft-identity
9×pow1
8×add-cube-cbrt rec-exp 1-exp
7×associate-*r*
6×add-log-exp
5×flip3-- times-frac associate-*l* associate-/r/ flip--
4×frac-times associate-*r/ associate-/l*
3×sub-neg div-inv
2×distribute-rgt-in pow-flip frac-2neg distribute-lft-in pow-prod-down associate-*l/ clear-num associate-/r* distribute-lft-out-- difference-of-squares
1×distribute-rgt-neg-in diff-log sqrt-prod *-commutative inv-pow unswap-sqr
Counts
4 → 139
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
17.0ms
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
18.0ms
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series82.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
3.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
45.0ms
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
26.0ms
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify40.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08162127
150011586

prune174.0ms

Filtered
72 candidates to 151 candidates (-109.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1492151
Fresh3710
Picked101
Done000
Total1539162

Merged error: 0b

Counts
162 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ 1 (* (/ 0.5 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b
(* (/ 0.5 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log
27×add-sqr-sqrt
22×*-un-lft-identity
18×add-cbrt-cube
14×add-cube-cbrt
13×times-frac associate-*l*
10×div-exp add-log-exp
9×pow1
8×prod-exp
7×associate-*r*
6×flip3-- flip--
5×cbrt-undiv associate-/r/
4×frac-times sub-neg associate-*r/ cbrt-unprod distribute-lft-out-- difference-of-squares
3×rec-exp diff-log 1-exp associate-/l*
2×distribute-rgt-in pow-flip distribute-rgt-neg-in distribute-lft-in pow-prod-down associate-*l/ sqrt-prod div-inv unswap-sqr
1×associate--l- neg-sub0 frac-2neg neg-log clear-num associate-/r* *-commutative inv-pow
Counts
4 → 111
Calls
4 calls:
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(/ 1 (* (/ 0.5 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
14.0ms
(* (/ 0.5 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series107.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms
(- (* b b) (* (* 4.0 a) c))
48.0ms
(/ 1 (* (/ 0.5 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
34.0ms
(* (/ 0.5 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify65.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05701340
125531151
250011138

prune152.0ms

Filtered
80 candidates to 123 candidates (-53.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1212123
Fresh268
Picked011
Done000
Total1239132

Merged error: 0b

Counts
132 → 9

regimes211.0ms

Accuracy

0% (0.1b 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
0169
1169

end0.0ms

sample2.2s

Algorithm
intervals
Results
479.0ms4883×body160valid
445.0ms16195×pre80true
399.0ms8195×body80nan
196.0ms1334×body320valid
91.0ms1783×body80valid

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