Details

Time bar (total: 5.3s)

sample35.0ms

Algorithm
intervals
Results
13.0ms279×body80valid
4.0ms83×body80nan

simplify15.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03918
18018
214318
317718
418918
519318
619318
done19318

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.5b

localize85.0ms

Local error

Found 4 expressions with local error:

1.8b
(- (* b b) (* (* 4.0 a) c))
2.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite60.0ms

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:
8.0ms
(- (* b b) (* (* 4.0 a) c))
22.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series287.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* (* 4.0 a) c))
86.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify132.0ms

Counts
89 → 89
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0264600
11046558
24657542
35001542
done5001542

prune385.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.9b

localize91.0ms

Local error

Found 4 expressions with local error:

7.5b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite53.0ms

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:
14.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series311.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
78.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify179.0ms

Counts
100 → 100
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
02831391
19981121
247231013
350011013
done50011013

prune461.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.9b

localize97.0ms

Local error

Found 4 expressions with local error:

24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
25.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log expm1-log1p-u cbrt-div flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 64
Calls
4 calls:
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series358.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
101.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
102.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify81.0ms

Counts
76 → 76
Iterations

Useful iterations: 3 (75.0ms)

IterNodesCost
0215636
1688602
22689596
35001594
done5001594

prune496.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.9b

localize95.0ms

Local error

Found 4 expressions with local error:

24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log expm1-log1p-u rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- log1p-expm1-u add-log-exp
Counts
4 → 68
Calls
4 calls:
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series299.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify70.0ms

Counts
80 → 80
Iterations

Useful iterations: 3 (64.0ms)

IterNodesCost
0139588
1510568
22129564
35001560
done5001560

prune397.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 10.9b

regimes213.0ms

Accuracy

91.8% (1.0b remaining)

Error of 8.6b against oracle of 7.6b and baseline of 19.7b

bsearch137.0ms

Steps
ItersRangePoint
6
9.002760019060421e+93
3.662435776182418e+94
3.1052531941342384e+94
7
-2.7712805237551144e+157
-1.011647758169582e+156
-1.02783867982226e+156

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05867
15867
done5867

end0.0ms

sample912.0ms

Algorithm
intervals
Results
439.0ms8745×body80valid
129.0ms2851×body80nan