Details

Time bar (total: 9.7s)

sample63.0ms

Algorithm
intervals
Results
33.0ms278×body80valid
10.0ms101×body80nan

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03518
16618
211618
314418
415918
516118
616118

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
0.9b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 distribute-rgt-neg-in neg-log
Counts
4 → 60
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series59.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify115.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (109.0ms)

IterNodesCost
0227581
1878551
23814541
35002538

prune876.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
3.6b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
4.9b
(/ (* a c) b)
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
14×add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt times-frac associate-/r*
6×add-log-exp
5×pow1
4×cbrt-undiv div-exp distribute-lft-out--
3×flip3-- sqrt-prod flip--
2×distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l* difference-of-squares
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 77
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
18.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
3.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series54.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
25.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
5.0ms
(/ (* a c) b)
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify48.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0397657
11995574
25001570

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
3.5b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.6b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
34×times-frac
30×add-exp-log *-un-lft-identity
23×add-cbrt-cube
22×add-cube-cbrt associate-*r*
11×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
7×pow1 associate-*l*
6×associate-/r* add-log-exp unswap-sqr
4×distribute-lft-out--
3×flip3-- sqrt-prod flip-- div-inv
2×distribute-rgt-neg-in sqrt-div associate-/r/ difference-of-squares
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 115
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
26.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
17.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series63.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
28.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify82.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
06931370
135581189
250011148

prune1.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
3.6b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))))))
4.0b
(* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))
24.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
74×add-exp-log
67×add-sqr-sqrt
64×times-frac
47×add-cbrt-cube
37×*-un-lft-identity
36×cbrt-prod
31×associate-*r*
29×cbrt-undiv add-cube-cbrt div-exp
25×prod-exp cbrt-unprod
12×unswap-sqr
11×associate-*l*
7×pow1
6×associate-/r* add-log-exp
4×div-inv distribute-lft-out--
3×flip3-- sqrt-prod flip--
2×distribute-rgt-neg-in sqrt-div associate-/r/ difference-of-squares
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 150
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))))))
49.0ms
(* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series65.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
31.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))))))
9.0ms
(* (/ (/ a (* (cbrt b) (cbrt b))) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify42.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
010052856
150012409

prune2.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.5b

regimes538.0ms

Accuracy

92.7% (1.1b remaining)

Error of 8.0b against oracle of 6.9b and baseline of 21.4b

bsearch91.0ms

Steps
ItersRangePoint
7
7.8930669794294e+68
1.794276654474529e+70
1.7701741483501238e+70
9
-4.2740907516194833e+155
-3.627510837665024e+149
-1.3386170315757073e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08190
18190

end0.0ms

sample1.5s

Algorithm
intervals
Results
958.0ms8734×body80valid
301.0ms2874×body80nan