Details

Time bar (total: 15.7s)

sample248.0ms

Algorithm
intervals
Results
57.0ms101×body160valid
36.0ms115×body320valid
23.0ms259×body80nan
21.0ms515×pre80true
4.0ms10×body640valid
3.0ms30×body80valid

simplify721.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
014365
124365
244325
378325
4102325
5111325
done111325

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
0.1b
(- (* b b) (* (* 4.0 a) c))
27.5b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite243.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
121×add-sqr-sqrt
94×*-un-lft-identity
68×add-cube-cbrt
26×difference-of-squares
22×associate-/l*
16×sqrt-prod
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
8×add-log-exp
5×pow1 div-inv
3×cbrt-undiv associate-/r* flip3-- div-exp flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 149
Calls
4 calls:
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
119.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
13.0ms
(- (* b b) (* (* 4.0 a) c))
94.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series494.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
170.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
82.0ms
(- (* b b) (* (* 4.0 a) c))
138.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify2.4s

Counts
161 → 161
Iterations

Useful iterations: 2 (947.0ms)

IterNodesCost
028087734
169082980
2305882259
done500082259

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.7b

localize12.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune93.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 2.7b

localize25.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
0.3b
(/ (* a c) b)

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
27×add-cbrt-cube add-exp-log
20×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×cbrt-undiv div-exp
8×associate-/l*
6×associate-/r* div-inv
5×prod-exp cbrt-unprod
2×pow1 clear-num frac-2neg add-log-exp
1×associate-/l/
Counts
2 → 73
Calls
2 calls:
31.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
15.0ms
(/ (* a c) b)

series57.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
28.0ms
(/ (* a c) b)

simplify1.9s

Counts
79 → 79
Iterations

Useful iterations: done (1.9s)

IterNodesCost
016723274
146421513
2300821072
done500020952

prune599.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 2.7b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* c c) c)
0.3b
(/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))
0.3b
(* (* (* a a) a) (* (* c c) c))
0.7b
(cbrt (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b)))

rewrite435.0ms

Algorithm
rewrite-expression-head
Rules
216×add-cbrt-cube add-exp-log
147×pow1
141×prod-exp cbrt-unprod
55×pow-prod-down
46×pow-plus pow-prod-up
30×cbrt-undiv div-exp
10×pow2 pow-sqr
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt
5×cbrt-prod
4×associate-*r* add-log-exp
3×pow3
2×times-frac associate-*l* *-commutative div-inv
1×cbrt-div clear-num associate-/r* frac-2neg pow1/3 associate-/l* unswap-sqr
Counts
4 → 177
Calls
4 calls:
29.0ms
(* (* c c) c)
142.0ms
(/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))
134.0ms
(* (* (* a a) a) (* (* c c) c))
108.0ms
(cbrt (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b)))

series343.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (* c c) c)
154.0ms
(/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))
78.0ms
(* (* (* a a) a) (* (* c c) c))
44.0ms
(cbrt (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b)))

simplify1.5s

Counts
189 → 189
Iterations

Useful iterations: done (1.4s)

IterNodesCost
016666697
161955153
done500149986

prune525.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 2.6b

regimes714.0ms

Accuracy

0% (3.5b remaining)

Error of 6.2b against oracle of 2.7b and baseline of 6.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0583
1683
done683

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.1s2975×body160valid
1.0s3639×body320valid
844.0ms8315×body80nan
616.0ms16315×pre80true
143.0ms493×body640valid
62.0ms893×body80valid