Details

Time bar (total: 9.8s)

sample34.0ms

Algorithm
intervals
Results
15.0ms285×body80valid
4.0ms87×body80nan

simplify92.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
02038
13938
27937
314337
416937
517837
618137
done18137

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.2b

localize116.0ms

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)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
11×add-sqr-sqrt
10×fma-def add-log-exp
9×add-cube-cbrt
6×pow1 sqrt-prod
4×add-exp-log expm1-log1p-u distribute-rgt-neg-in sqrt-div add-cbrt-cube log1p-expm1-u
3×distribute-lft-neg-in flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 sum-log distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg flip3-+ fma-neg diff-log prod-diff neg-log flip-+
Counts
4 → 77
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(+ (- b) (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)))

series265.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* (* 4.0 a) c))
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts
89 → 89
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01041247
12621114
29001017
338571006
done50001005

prune351.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.2b

localize118.0ms

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)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
10×fma-neg prod-diff
9×sqrt-prod
8×add-log-exp
7×pow1
6×distribute-lft-neg-in distribute-rgt-neg-in sqrt-div
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×neg-mul-1 diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 88
Calls
4 calls:
8.0ms
(- (- 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)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts
100 → 100
Iterations

Useful iterations: 3 (696.0ms)

IterNodesCost
01152639
12811649
28841574
338421538
done50011538

prune405.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.2b

localize119.0ms

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)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
10×fma-neg prod-diff
8×add-log-exp
6×cbrt-prod distribute-lft-neg-in distribute-rgt-neg-in
5×pow1
4×add-exp-log expm1-log1p-u cbrt-div flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×sqrt-prod
2×neg-mul-1 pow1/3 sqrt-div diff-log
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 83
Calls
4 calls:
8.0ms
(- (- 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)))

series355.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(- (- 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)))
96.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
96.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify501.0ms

Counts
95 → 95
Iterations

Useful iterations: done (498.0ms)

IterNodesCost
01782699
14272590
213822248
done50002247

prune510.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.2b

localize125.0ms

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)))

rewrite10.0ms

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 expm1-log1p-u flip3-- pow1/3 add-cbrt-cube flip-- log1p-expm1-u add-log-exp
Counts
4 → 60
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)))
3.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
94.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
95.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
98.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify792.0ms

Counts
72 → 72
Iterations

Useful iterations: 3 (211.0ms)

IterNodesCost
0671268
11621216
25111100
320381076
done50001076

prune438.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.2b

regimes163.0ms

Accuracy

88.9% (1.3b remaining)

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

bsearch202.0ms

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
046158
156158
done56158

end0.0ms

sample848.0ms

Algorithm
intervals
Results
441.0ms8712×body80valid
149.0ms2998×body80nan