Details

Time bar (total: 19.6s)

sample104.0ms

Algorithm
intervals
Results
54.0ms282×body80valid
11.0ms92×body80nan

simplify246.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
02038
13538
26637
311637
415037
516437
616637
done16637

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.5b

localize168.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (* b b) (* (* 4.0 a) c))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 54
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series360.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (* b b) (* (* 4.0 a) c))
72.0ms
(- (* b b) (* (* 4.0 a) c))
100.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
121.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.1s

Counts
66 → 66
Iterations

Useful iterations: 2 (103.0ms)

IterNodesCost
0621010
1165930
2739834
34972834
done5001834

prune433.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.4b

localize182.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
2.7b
(/ (- (- (* 2.0 (/ (* a c) b)) b) b) (* 2.0 a))
5.5b
(/ (* a c) b)
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite400.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-sqr-sqrt add-cbrt-cube
13×*-un-lft-identity
9×add-cube-cbrt
8×times-frac
6×associate-/l* add-log-exp
5×pow1
4×cbrt-undiv div-exp associate-/r*
3×flip3-- sqrt-prod flip--
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod div-inv associate-/l/ distribute-lft-out-- difference-of-squares
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-sub
Counts
4 → 76
Calls
4 calls:
16.0ms
(- (* b b) (* (* 4.0 a) c))
360.0ms
(/ (- (- (* 2.0 (/ (* a c) b)) b) b) (* 2.0 a))
11.0ms
(/ (* a c) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series310.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(- (* b b) (* (* 4.0 a) c))
121.0ms
(/ (- (- (* 2.0 (/ (* a c) b)) b) b) (* 2.0 a))
22.0ms
(/ (* a c) b)
108.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
88 → 88
Iterations

Useful iterations: 2 (348.0ms)

IterNodesCost
01641344
14471286
222581122
done50001122

prune614.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.6b

localize165.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.8b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/r*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
61.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
39.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms
(- (* b b) (* (* 4.0 a) c))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series586.0ms

Counts
4 → 12
Calls
4 calls:
263.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
129.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms
(- (* b b) (* (* 4.0 a) c))
115.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
88 → 88
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01491693
13861585
218861419
done50001399

prune484.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

localize148.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
2.5b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
2.7b
(/ (- (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b) b) (* 2.0 a))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
33×times-frac
30×add-exp-log
26×*-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×add-log-exp unswap-sqr
5×associate-/l*
3×flip3-- sqrt-prod flip-- div-inv
2×sqrt-div associate-/l/ distribute-lft-out-- difference-of-squares
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub associate-*r/ pow-prod-down associate-*l/ clear-num associate-/r* *-commutative
Counts
4 → 114
Calls
4 calls:
15.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
2.0s
(/ (- (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b) b) (* 2.0 a))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series452.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (* b b) (* (* 4.0 a) c))
90.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
174.0ms
(/ (- (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b) b) (* 2.0 a))
119.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.0s

Counts
126 → 126
Iterations

Useful iterations: done (3.0s)

IterNodesCost
02482456
17432367
241561857
done50021693

prune752.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.9b

regimes287.0ms

Accuracy

84.5% (2.3b remaining)

Error of 8.7b against oracle of 6.3b and baseline of 21.5b

bsearch267.0ms

Steps
ItersRangePoint
8
6412590.878131424
2116652649.122401
2098947641.3561494
9
-2.364746502264313e+125
-7.44056492395588e+118
-1.3675682634777099e+124

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
045124
152124
done52124

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.0s8674×body80valid
338.0ms2912×body80nan