Details

Time bar (total: 27.0s)

sample86.0ms

Algorithm
intervals
Results
37.0ms272×body80valid
11.0ms90×body80nan

simplify293.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
02038
13638
26637
312237
416137
517437
617637
done17637

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.9b

localize186.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 151
Calls
4 calls:
45.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series582.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
152.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
132.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
150.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.9s

Counts
163 → 163
Iterations

Useful iterations: done (2.8s)

IterNodesCost
01796238
14414232
218173344
done50002696

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.4b

localize251.0ms

Local error

Found 4 expressions with local error:

8.9b
(- (- b) (* (sqrt (sqrt (fma (- 4.0) (* a c) (pow b 2)))) (sqrt (sqrt (fma (- 4.0) (* a c) (pow b 2))))))
22.8b
(sqrt (fma (- 4.0) (* a c) (pow b 2)))
22.8b
(sqrt (fma (- 4.0) (* a c) (pow b 2)))
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite68.0ms

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
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×neg-mul-1 flip3-- sqrt-div diff-log flip--
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 84
Calls
4 calls:
33.0ms
(- (- b) (* (sqrt (sqrt (fma (- 4.0) (* a c) (pow b 2)))) (sqrt (sqrt (fma (- 4.0) (* a c) (pow b 2))))))
3.0ms
(sqrt (fma (- 4.0) (* a c) (pow b 2)))
3.0ms
(sqrt (fma (- 4.0) (* a c) (pow b 2)))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series619.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(- (- b) (* (sqrt (sqrt (fma (- 4.0) (* a c) (pow b 2)))) (sqrt (sqrt (fma (- 4.0) (* a c) (pow b 2))))))
150.0ms
(sqrt (fma (- 4.0) (* a c) (pow b 2)))
166.0ms
(sqrt (fma (- 4.0) (* a c) (pow b 2)))
132.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts
96 → 96
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01322443
13161485
212351422
done50011407

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.4b

localize259.0ms

Local error

Found 4 expressions with local error:

22.8b
(sqrt (fma (- 4.0) (* a c) (pow b 2)))
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite68.0ms

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 add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3 sqrt-div
Counts
4 → 62
Calls
4 calls:
3.0ms
(sqrt (fma (- 4.0) (* a c) (pow b 2)))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
25.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series719.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(sqrt (fma (- 4.0) (* a c) (pow b 2)))
139.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
197.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
205.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify4.7s

Counts
74 → 74
Iterations

Useful iterations: done (4.7s)

IterNodesCost
01101150
12461067
2805976
34340964
done5000963

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.4b

localize295.0ms

Local error

Found 4 expressions with local error:

23.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite51.0ms

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:
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series729.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
177.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
181.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
192.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify4.2s

Counts
72 → 72
Iterations

Useful iterations: 3 (1.9s)

IterNodesCost
0671268
11691224
26101100
333741076
done50001076

prune1.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.4b

regimes596.0ms

Accuracy

92.4% (1.0b remaining)

Error of 8.6b against oracle of 7.6b and baseline of 20.1b

bsearch408.0ms

Steps
ItersRangePoint
8
4.049254448328916e+76
2.3057443967677173e+80
2.2766902918844874e+80
8
-1.7982126770691641e+158
-3.251690204975706e+154
-3.316762893443504e+154

simplify13.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
047131
156131
done56131

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.5s8711×body80valid
591.0ms2982×body80nan