Details

Time bar (total: 9.0s)

sample33.0ms

Algorithm
intervals
Results
14.0ms283×body80valid
4.0ms81×body80nan

simplify96.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
02038
13638
26637
312137
414937
516137
616237
done16237

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize118.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite43.0ms

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:
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(+ (- 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)))

series305.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
80.0ms
(+ (- b) (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)))

simplify1.3s

Counts
163 → 163
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01796238
14074208
211713343
done50003240

prune437.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.2b

localize122.0ms

Local error

Found 4 expressions with local error:

20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite19.0ms

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:
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)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series292.0ms

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

simplify1.3s

Counts
80 → 80
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0541228
11391080
24711004
318411004
done50011000

prune391.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.2b

localize121.0ms

Local error

Found 4 expressions with local error:

1.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.5b
(/ (* 2.0 c) (fma 2.0 (/ (* a c) b) (* -2 b)))
4.5b
(/ (* a c) b)
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-exp-log add-cbrt-cube
13×add-sqr-sqrt
12×add-cube-cbrt
10×fma-def
8×add-log-exp
6×times-frac associate-/r*
5×pow1
4×cbrt-undiv expm1-log1p-u distribute-rgt-neg-in div-exp log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×frac-2neg sqrt-div prod-exp clear-num sum-log cbrt-unprod div-inv distribute-lft-out associate-/l*
1×+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 neg-log flip-- flip-+
Counts
4 → 90
Calls
4 calls:
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(/ (* 2.0 c) (fma 2.0 (/ (* a c) b) (* -2 b)))
3.0ms
(/ (* a c) b)
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series237.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
67.0ms
(/ (* 2.0 c) (fma 2.0 (/ (* a c) b) (* -2 b)))
19.0ms
(/ (* a c) b)
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify801.0ms

Counts
102 → 102
Iterations

Useful iterations: 2 (153.0ms)

IterNodesCost
01761355
14361264
215651094
done50001094

prune415.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.2b

localize123.0ms

Local error

Found 4 expressions with local error:

1.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.5b
(/ (* 2.0 c) (fma 2.0 (/ a (/ b c)) (* -2 b)))
4.2b
(/ a (/ b c))
20.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
56×*-un-lft-identity
53×add-sqr-sqrt
52×add-cube-cbrt
16×associate-/r*
14×add-exp-log add-cbrt-cube
10×fma-def
8×add-log-exp
6×div-inv
5×pow1 cbrt-undiv div-exp
4×expm1-log1p-u distribute-rgt-neg-in log1p-expm1-u associate-/l*
3×distribute-lft-neg-in sqrt-prod
2×frac-2neg sqrt-div clear-num sum-log distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 neg-log prod-exp associate-/r/ flip-- cbrt-unprod flip-+
Counts
4 → 139
Calls
4 calls:
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(/ (* 2.0 c) (fma 2.0 (/ a (/ b c)) (* -2 b)))
5.0ms
(/ a (/ b c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series241.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
64.0ms
(/ (* 2.0 c) (fma 2.0 (/ a (/ b c)) (* -2 b)))
26.0ms
(/ a (/ b c))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify720.0ms

Counts
151 → 151
Iterations

Useful iterations: 2 (234.0ms)

IterNodesCost
02792049
16521898
221121718
done50011718

prune661.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.7b

regimes199.0ms

Accuracy

92% (1.3b remaining)

Error of 7.0b against oracle of 5.7b and baseline of 21.7b

bsearch161.0ms

Steps
ItersRangePoint
7
1.1889782913455773e+76
8.569650126343972e+77
5.0729377846831736e+76
9
-2.6633759314474964e+132
-4.540359937862506e+126
-4.7733545789625156e+131

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
042157
150157
done50157

end0.0ms

sample834.0ms

Algorithm
intervals
Results
446.0ms8726×body80valid
137.0ms2945×body80nan