Details

Time bar (total: 19.9s)

sample58.0ms

Algorithm
intervals
Results
22.0ms290×body80valid
6.0ms89×body80nan

simplify247.0ms

Counts
1 → 1
Iterations
IterNodes
done193
6193
5189
4179
3143
279
139
020

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize171.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite97.0ms

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×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sum-log sqrt-pow1 pow1/2 diff-log neg-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×associate--l- +-commutative sub-neg flip3-+ associate-+l- flip-+
Counts
4 → 151
Calls
4 calls:
28.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
33.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series450.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
107.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
129.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts
163 → 163
Iterations
IterNodes
done5001
21817
1441
0179

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.6b

localize200.0ms

Local error

Found 4 expressions with local error:

19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.3b
(cbrt (- (* b b) (* (* 4.0 a) c)))
20.3b
(cbrt (- (* b b) (* (* 4.0 a) c)))
20.3b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-div
5×pow1
4×expm1-log1p-u flip3-- add-cbrt-cube add-exp-log log1p-expm1-u flip-- add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 62
Calls
4 calls:
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series572.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
156.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
153.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
133.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify3.0s

Counts
74 → 74
Iterations
IterNodes
done5000
34267
2767
1224
094

prune923.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.6b

localize239.0ms

Local error

Found 4 expressions with local error:

19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity sqrt-div add-cube-cbrt
4×expm1-log1p-u rem-sqrt-square sqrt-pow1 flip3-- add-cbrt-cube pow1/2 add-exp-log log1p-expm1-u flip-- add-log-exp
Counts
4 → 68
Calls
4 calls:
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series432.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
95.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
102.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts
80 → 80
Iterations
IterNodes
done5000
33708
2585
1147
054

prune815.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.6b

localize164.0ms

Local error

Found 4 expressions with local error:

1.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.9b
(/ (fma 2.0 (/ (* a c) b) (* -2 b)) (* 2.0 a))
3.9b
(/ (* a c) b)
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-cbrt-cube add-exp-log
13×add-sqr-sqrt
12×add-cube-cbrt
10×fma-def
8×add-log-exp
6×times-frac
5×pow1
4×expm1-log1p-u cbrt-undiv associate-/r* distribute-rgt-neg-in div-exp log1p-expm1-u associate-/l*
3×distribute-lft-neg-in sqrt-prod
2×clear-num sum-log frac-2neg sqrt-div prod-exp cbrt-unprod div-inv distribute-lft-out
1×neg-sub0 +-commutative rem-sqrt-square neg-mul-1 sqrt-pow1 flip3-+ flip3-- pow1/2 neg-log associate-+l- flip-+ flip--
Counts
4 → 90
Calls
4 calls:
34.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(/ (fma 2.0 (/ (* a c) b) (* -2 b)) (* 2.0 a))
8.0ms
(/ (* a c) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series348.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
101.0ms
(/ (fma 2.0 (/ (* a c) b) (* -2 b)) (* 2.0 a))
35.0ms
(/ (* a c) b)
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
102 → 102
Iterations
IterNodes
done5000
22342
1472
0179

prune1.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.8b

regimes1.0s

Accuracy

94% (0.8b remaining)

Error of 7.0b against oracle of 6.2b and baseline of 19.9b

bsearch241.0ms

Steps
ItersRangePoint
8
2.072994944964499e+129
8.571507078369983e+131
1.4828322806133274e+130
7
-5.856362438573669e+138
-1.280729871585891e+137
-5.791348048249166e+138

simplify17.0ms

Iterations
IterNodes
done55
155
046

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.1s8727×body80valid
395.0ms2877×body80nan