Details

Time bar (total: 18.5s)

sample59.0ms

Algorithm
intervals
Results
24.0ms269×body80valid
6.0ms75×body80nan

simplify291.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
02038
13938
27937
314237
417137
518137
618537
done18537

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.0b

localize133.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
1.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
37×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 neg-log
Counts
4 → 140
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
47.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series434.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (* b b) (* (* 4.0 a) c))
122.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
122.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.9s

Counts
152 → 152
Iterations

Useful iterations: 3 (1.8s)

IterNodesCost
01816137
14044128
211473279
348422634
done50002634

prune712.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.1b

localize137.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
4.1b
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
5.9b
(/ (* a c) b)
24.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite131.0ms

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
7×associate-/l*
6×add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp associate-/r* log1p-expm1-u distribute-lft-out--
3×flip3-- sqrt-prod flip--
2×distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num cbrt-unprod div-inv associate-/l/ difference-of-squares
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff
Counts
4 → 88
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
76.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
20.0ms
(/ (* a c) b)
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series266.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
22.0ms
(/ (* a c) b)
80.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
100 → 100
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01791531
14471455
217061277
done50021244

prune645.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.6b

localize131.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 4.0 a) c)
0.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.0b
(- (* b b) (* (* 4.0 a) c))
24.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
19×prod-diff
16×sqrt-prod
10×pow1
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
4×expm1-log1p-u log1p-expm1-u
3×flip3-- associate-*r* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 94
Calls
4 calls:
23.0ms
(* (* 4.0 a) c)
90.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series302.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (* 4.0 a) c)
106.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
67.0ms
(- (* b b) (* (* 4.0 a) c))
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.0s

Counts
106 → 106
Iterations

Useful iterations: 3 (2.3s)

IterNodesCost
01611863
13671562
211281333
345011245
done50001245

prune460.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.6b

localize151.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
4.1b
(/ (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))) (* 2.0 a))
4.3b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
24.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite245.0ms

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-/l* add-log-exp unswap-sqr
4×expm1-log1p-u log1p-expm1-u distribute-lft-out--
3×flip3-- sqrt-prod flip-- div-inv
2×distribute-rgt-neg-in sqrt-div associate-/l/ difference-of-squares
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num associate-/r* *-commutative
Counts
4 → 126
Calls
4 calls:
18.0ms
(- (* b b) (* (* 4.0 a) c))
96.0ms
(/ (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))) (* 2.0 a))
97.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(- (* b b) (* (* 4.0 a) c))
126.0ms
(/ (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))) (* 2.0 a))
62.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
108.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts
138 → 138
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02642685
17262565
229182023
done50011787

prune696.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.6b

regimes285.0ms

Accuracy

86.9% (1.9b remaining)

Error of 8.4b against oracle of 6.5b and baseline of 20.7b

bsearch258.0ms

Steps
ItersRangePoint
9
5.30600492772346e+88
5.894388948599132e+93
5.087167594777058e+91
8
-5.7211821970331905e+156
-1.4082798590396656e+153
-1.3283483556924014e+154

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
049135
157135
done57135

end0.0ms

sample1.3s

Algorithm
intervals
Results
591.0ms8741×body80valid
176.0ms2982×body80nan