Details

Time bar (total: 9.2s)

sample76.0ms

Algorithm
intervals
Results
15.0ms111×body320valid
14.0ms512×pre80true
12.0ms256×body80nan
9.0ms97×body160valid
5.0ms27×body80valid
4.0ms21×body640valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 52.2b

Counts
2 → 1

localize11.0ms

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))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
25.7b
(+ (- b) (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:
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series298.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
43.0ms
(- (* b b) (* (* 4.0 a) c))
105.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify47.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0405779
11563685
25002674

prune178.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New79382
Fresh000
Picked101
Done000
Total80383

Merged error: 0.1b

Counts
83 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- 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:
4.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series443.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b b) (* (* 4.0 a) c))
75.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
143.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
178.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify114.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
06422664
131752400
250032388

prune378.0ms

Filtered
163 candidates to 106 candidates (65.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1576163
Fresh112
Picked101
Done000
Total1597166

Merged error: 0.0b

Counts
166 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (+ 0 (* 4.0 (* a c))))
0.2b
(/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b
(/ (/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
0.4b
(* (/ (sqrt (+ 0 (* 4.0 (* a c)))) 2.0) (/ (/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
665×times-frac
530×add-sqr-sqrt
482×*-un-lft-identity
286×add-cube-cbrt
239×sqrt-prod
148×associate-*r*
98×distribute-lft-out-- difference-of-squares
54×associate-/l*
49×distribute-rgt-neg-in
32×add-exp-log add-cbrt-cube
22×associate-*l*
16×associate-/r/
13×cbrt-undiv div-exp
12×unswap-sqr
11×div-inv
10×associate-/r*
8×flip3-- flip--
7×pow1
6×prod-exp cbrt-unprod
4×sqrt-div add-log-exp
3×associate-/l/
2×frac-2neg flip3-+ clear-num flip-+
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 502
Calls
4 calls:
2.0ms
(sqrt (+ 0 (* 4.0 (* a c))))
13.0ms
(/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
20.0ms
(/ (/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
78.0ms
(* (/ (sqrt (+ 0 (* 4.0 (* a c)))) 2.0) (/ (/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series1.3s

Counts
4 → 12
Calls
4 calls:
116.0ms
(sqrt (+ 0 (* 4.0 (* a c))))
401.0ms
(/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
404.0ms
(/ (/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
404.0ms
(* (/ (sqrt (+ 0 (* 4.0 (* a c)))) 2.0) (/ (/ (sqrt (+ 0 (* 4.0 (* a c)))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify129.0ms

Algorithm
egg-herbie
Counts
514 → 514
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0154911246
1500110695

prune1.1s

Filtered
514 candidates to 257 candidates (50.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New5131514
Fresh066
Picked101
Done000
Total5147521

Merged error: 0b

Counts
521 → 7

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 4.0 (/ (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)) (* a c)))
0.3b
(* (/ 4.0 (/ (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)) (* a c))) (+ (* (- b) (- b)) (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
0.3b
(/ (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)) (* a c))
25.8b
(+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
543×times-frac
452×add-sqr-sqrt
267×*-un-lft-identity
216×difference-of-squares
198×unpow-prod-down cube-prod
128×associate-*l*
105×add-cube-cbrt
90×sqr-pow
81×distribute-lft-out--
72×sqrt-prod
42×associate-/r*
40×sqrt-div associate-/l*
36×distribute-rgt-neg-in
32×add-exp-log add-cbrt-cube
22×associate-*r/
21×flip3-- flip--
16×frac-add
12×cbrt-undiv div-exp
10×frac-times div-inv
9×difference-cubes
7×prod-exp cbrt-unprod
6×pow1 add-log-exp
5×associate-*l/
3×flip3-+ associate-*r* flip-+
2×distribute-lft-neg-out frac-2neg clear-num associate-/r/ associate-/l/ unswap-sqr
1×+-commutative distribute-rgt-in distribute-rgt-out distribute-lft-in div-sub unsub-neg pow-prod-down sum-log *-commutative
Counts
4 → 463
Calls
4 calls:
39.0ms
(/ 4.0 (/ (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)) (* a c)))
66.0ms
(* (/ 4.0 (/ (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)) (* a c))) (+ (* (- b) (- b)) (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
33.0ms
(/ (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)) (* a c))
13.0ms
(+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series967.0ms

Counts
4 → 12
Calls
4 calls:
252.0ms
(/ 4.0 (/ (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)) (* a c)))
355.0ms
(* (/ 4.0 (/ (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)) (* a c))) (+ (* (- b) (- b)) (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
241.0ms
(/ (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)) (* a c))
118.0ms
(+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify143.0ms

Algorithm
egg-herbie
Counts
475 → 475
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0186811817
1500111304

prune1.2s

Filtered
475 candidates to 234 candidates (49.3%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New4750475
Fresh066
Picked011
Done000
Total4757482

Merged error: 0b

Counts
482 → 7

regimes116.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify13.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04038
14838
25038
37138
48838
59338
610338
711338
812238
913138
1013938
1114738
1215438
1315638
1416438
1517638
1618538
1719538
1821938
1924338
2024838
2125338
2226038
2326038

end0.0ms

sample2.1s

Algorithm
intervals
Results
514.0ms3679×body320valid
453.0ms15963×pre80true
371.0ms7963×body80nan
272.0ms2922×body160valid
88.0ms485×body640valid
44.0ms914×body80valid

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