Details

Time bar (total: 9.0s)

sample34.0ms

Algorithm
intervals
Results
15.0ms285×body80valid
4.0ms87×body80nan

simplify88.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
02038
13838
27837
313637
415737
516637
616937
done16937

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.2b

localize117.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
1.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity add-log-exp
8×add-sqr-sqrt
6×pow1 add-cube-cbrt sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 sum-log distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg distribute-rgt-neg-in flip3-+ diff-log neg-log flip-+
Counts
4 → 57
Calls
4 calls:
2.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series273.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* (* 4.0 a) c))
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
69 → 69
Iterations

Useful iterations: 3 (323.0ms)

IterNodesCost
0931129
12441009
2838915
33453904
done5001904

prune279.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.2b

localize120.0ms

Local error

Found 4 expressions with local error:

12.2b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 60
Calls
4 calls:
10.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (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)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series300.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
72 → 72
Iterations

Useful iterations: 3 (296.0ms)

IterNodesCost
0901506
12271066
27821000
33100988
done5001988

prune333.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.2b

localize126.0ms

Local error

Found 4 expressions with local error:

6.1b
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
7×add-cube-cbrt *-un-lft-identity
6×cbrt-prod
5×pow1
4×add-exp-log cbrt-div flip3-- add-cbrt-cube flip--
3×sqrt-prod
2×pow1/3 sqrt-div diff-log
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 55
Calls
4 calls:
6.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series375.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
107.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
102.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify469.0ms

Counts
67 → 67
Iterations

Useful iterations: done (467.0ms)

IterNodesCost
01491566
13711475
213241275
done50001261

prune409.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.2b

localize134.0ms

Local error

Found 4 expressions with local error:

21.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
21.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity
4×pow1 add-exp-log flip3-- pow1/3 add-cbrt-cube flip-- add-log-exp
Counts
4 → 52
Calls
4 calls:
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series413.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
103.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
103.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
104.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify823.0ms

Counts
64 → 64
Iterations

Useful iterations: 3 (195.0ms)

IterNodesCost
0651180
11541144
24951024
319931004
done50001004

prune410.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.2b

regimes179.0ms

Accuracy

88.9% (1.3b remaining)

Error of 8.9b against oracle of 7.6b and baseline of 19.6b

bsearch205.0ms

Steps
ItersRangePoint
8
2.1878188410446244e+107
3.8616146939177386e+111
7.989761210864844e+108
10
-2.1502820188078274e+175
-2.227381996671495e+165
-2.2572095326645574e+165

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
047157
158157
done58157

end0.0ms

sample864.0ms

Algorithm
intervals
Results
453.0ms8712×body80valid
144.0ms2998×body80nan