Details

Time bar (total: 5.3s)

sample924.0ms

Algorithm
intervals
Results
13.0ms142×body160valid
8.0ms270×pre80true
6.0ms114×body80valid
1.0ms14×body80nan

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: 27.7b

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))
0.3b
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
27.7b
(+ (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:
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(- (* 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))))

series64.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(- (* b b) (* (* 4.0 a) c))
25.0ms
(/ (+ (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 (35.0ms)

IterNodesCost
0396773
11550683
25001673

prune129.0ms

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

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New76682
Fresh000
Picked101
Done000
Total77683

Merged error: 0.4b

Counts
83 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (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)))))

rewrite46.0ms

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))
15.0ms
(/ (/ (+ 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)))))

series123.0ms

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))
55.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify113.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
06432666
132102408
250012396

prune316.0ms

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

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New15310163
Fresh505
Picked101
Done000
Total15910169

Merged error: 0b

Counts
169 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
0.4b
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
0.4b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
118×pow1
66×pow-prod-down
64×add-sqr-sqrt
46×times-frac
44×add-exp-log *-un-lft-identity add-cbrt-cube
28×add-cube-cbrt
27×prod-exp cbrt-unprod
24×difference-of-squares
11×associate-/r*
9×pow-sqr pow-prod-up associate-/l*
8×sqrt-prod distribute-lft-out--
6×add-log-exp
4×unpow-prod-down distribute-rgt-neg-in associate-/r/ associate-/l/ sqr-pow
3×flip3-+ pow-plus flip-+
2×cbrt-undiv flip3-- frac-2neg div-exp clear-num flip-- div-inv
1×+-commutative pow2 div-sub swap-sqr associate-*r* associate-*l* sum-log *-commutative
Counts
4 → 166
Calls
4 calls:
4.0ms
(+ (* b b) (* (* 4.0 a) c))
23.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
10.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
11.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series110.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(+ (* b b) (* (* 4.0 a) c))
69.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
25.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
8.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify162.0ms

Algorithm
egg-herbie
Counts
178 → 178
Iterations

Useful iterations: 2 (137.0ms)

IterNodesCost
07312798
143602471
250032462

prune350.0ms

Filtered
100 candidates to 178 candidates (-78.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1771178
Fresh189
Picked101
Done000
Total1799188

Merged error: 0b

Counts
188 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

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:
10.0ms
(* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series94.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
17.0ms
(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
42.0ms
(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify87.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
05181106
13294871
25002864

prune123.0ms

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

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New94397
Fresh358
Picked011
Done000
Total979106

Merged error: 0b

Counts
106 → 9

regimes221.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02412
12612
22612

end0.0ms

sample2.2s

Algorithm
intervals
Results
419.0ms4375×body160valid
244.0ms8473×pre80true
178.0ms3625×body80valid
26.0ms473×body80nan

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