Details

Time bar (total: 7.1s)

sample54.0ms

Algorithm
intervals
Results
11.0ms143×body160valid
9.0ms559×pre80true
9.0ms303×body80nan
3.0ms113×body80valid

simplify64.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01217
12117
24116
37516
48816
59616
done9616

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0)
0.2b
(/ (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0) a)
0.3b
(* (* 3.0 a) c)
27.2b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

rewrite216.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
147×add-sqr-sqrt
113×*-un-lft-identity
79×add-cube-cbrt
34×difference-of-squares
28×associate-/l*
17×sqrt-prod distribute-lft-out--
16×add-exp-log add-cbrt-cube
9×pow1
6×associate-/r* div-inv add-log-exp
4×cbrt-undiv div-exp
3×div-sub associate-*r* pow-prod-down prod-exp cbrt-unprod associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg diff-log associate-*l* *-commutative
Counts
4 → 182
Calls
4 calls:
77.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0)
71.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0) a)
16.0ms
(* (* 3.0 a) c)
42.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

series322.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0)
117.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0) a)
20.0ms
(* (* 3.0 a) c)
90.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)

simplify1.2s

Counts
194 → 194
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02874775
16894627
219844417
done50004407

prune496.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 9.4b

localize3.0ms

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

prune66.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 9.4b

localize6.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (* -0.5 (/ (* a c) b)) a)
0.2b
(/ (* a c) b)

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
21×add-exp-log add-cbrt-cube
8×cbrt-undiv div-exp
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac associate-/r*
5×prod-exp cbrt-unprod
2×pow1 frac-2neg clear-num div-inv associate-/l* add-log-exp
1×associate-*r/ associate-/l/
Counts
2 → 47
Calls
2 calls:
19.0ms
(/ (* -0.5 (/ (* a c) b)) a)
12.0ms
(/ (* a c) b)

series42.0ms

Counts
2 → 6
Calls
2 calls:
21.0ms
(/ (* -0.5 (/ (* a c) b)) a)
20.0ms
(/ (* a c) b)

simplify918.0ms

Counts
53 → 53
Iterations

Useful iterations: done (917.0ms)

IterNodesCost
097568
1253547
21093427
done5000353

prune161.0ms

Pruning

35 alts after pruning (34 fresh and 1 done)

Merged error: 9.3b

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* -0.5 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) a)
0.2b
(/ (* a c) b)
0.2b
(/ (* a c) b)
0.6b
(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt sqrt-prod
25×add-exp-log add-cbrt-cube
22×add-cube-cbrt *-un-lft-identity
21×times-frac
19×pow1
12×swap-sqr
10×associate-*r* associate-*l*
9×associate-/r*
8×sqrt-pow1 pow1/2 sqrt-div
7×cbrt-undiv div-exp div-inv
6×prod-exp cbrt-unprod
5×associate-*r/ pow-prod-up
4×add-log-exp unswap-sqr
3×frac-2neg pow-prod-down clear-num pow-sqr associate-/l/ associate-/l*
2×frac-times associate-*l/
1×pow2 pow-plus sqrt-unprod rem-square-sqrt *-commutative
Counts
4 → 132
Calls
4 calls:
80.0ms
(/ (* -0.5 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) a)
9.0ms
(/ (* a c) b)
9.0ms
(/ (* a c) b)
37.0ms
(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

series149.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ (* -0.5 (* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))) a)
20.0ms
(/ (* a c) b)
20.0ms
(/ (* a c) b)
61.0ms
(* (sqrt (/ (* a c) b)) (sqrt (/ (* a c) b)))

simplify1.1s

Counts
144 → 144
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01642008
13381295
214021109
done50001060

prune223.0ms

Pruning

38 alts after pruning (37 fresh and 1 done)

Merged error: 9.3b

regimes540.0ms

Accuracy

46.3% (7.5b remaining)

Error of 16.3b against oracle of 8.8b and baseline of 22.8b

bsearch2.0ms

Steps
ItersRangePoint
0
639.0355759811072
657.6396111444685
648.3375935627878

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02039
12439
done2439

end0.0ms

sample1.3s

Algorithm
intervals
Results
270.0ms16319×pre80true
266.0ms4444×body160valid
239.0ms8319×body80nan
112.0ms3556×body80valid