Details

Time bar (total: 13.4s)

sample131.0ms

Algorithm
intervals
Results
30.0ms185×body80valid
28.0ms33×body2560valid
23.0ms32×body1280valid
13.0ms97×body80nan
6.0ms12×body640valid
6.0ms5×body5120valid
3.0ms8×body320valid
1.0ms3×body160valid

simplify135.0ms

Counts
1 → 1
Iterations
IterNodes
done98
798
697
595
487
370
243
124
014

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 4 a) c)
0.6b
(- (* b b) (* (* 4 a) c))
1.1b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
22.2b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 *-un-lft-identity add-log-exp
9×add-cbrt-cube add-exp-log
7×add-sqr-sqrt
6×add-cube-cbrt
4×insert-posit16
3×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×sum-log flip3-- sqrt-div flip-- distribute-lft-out
1×neg-sub0 +-commutative rem-sqrt-square sub-neg distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 diff-log associate-*l* neg-log *-commutative associate-+l- flip-+
Counts
4 → 64
Calls
4 calls:
31.0ms
(* (* 4 a) c)
15.0ms
(- (* b b) (* (* 4 a) c))
28.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series293.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (* 4 a) c)
63.0ms
(- (* b b) (* (* 4 a) c))
95.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
113.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.0s

Counts
76 → 76
Iterations
IterNodes
done2002
32002
21026
1324
0125

prune457.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
0.6b
(- (* b b) (* (* c a) 4))
1.1b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
22.2b
(sqrt (- (* b b) (* (* c a) 4)))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 88
Calls
4 calls:
70.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
7.0ms
(- (* b b) (* (* c a) 4))
47.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
7.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series410.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
64.0ms
(- (* b b) (* (* c a) 4))
118.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
80.0ms
(sqrt (- (* b b) (* (* c a) 4)))

simplify965.0ms

Counts
100 → 100
Iterations
IterNodes
done2001
32001
21108
1400
0161

prune445.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* (* 4 c) a))) b) a)
0.6b
(- (* b b) (* (* 4 c) a))
1.1b
(- (sqrt (- (* b b) (* (* 4 c) a))) b)
22.2b
(sqrt (- (* b b) (* (* 4 c) a)))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 88
Calls
4 calls:
83.0ms
(/ (- (sqrt (- (* b b) (* (* 4 c) a))) b) a)
15.0ms
(- (* b b) (* (* 4 c) a))
38.0ms
(- (sqrt (- (* b b) (* (* 4 c) a))) b)
12.0ms
(sqrt (- (* b b) (* (* 4 c) a)))

series351.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (- (sqrt (- (* b b) (* (* 4 c) a))) b) a)
53.0ms
(- (* b b) (* (* 4 c) a))
90.0ms
(- (sqrt (- (* b b) (* (* 4 c) a))) b)
104.0ms
(sqrt (- (* b b) (* (* 4 c) a)))

simplify795.0ms

Counts
100 → 100
Iterations
IterNodes
done2002
32002
21133
1397
0161

prune436.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.9b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4 c) a))) b)))
0.6b
(- (* b b) (* (* 4 c) a))
1.1b
(- (sqrt (- (* b b) (* (* 4 c) a))) b)
22.2b
(sqrt (- (* b b) (* (* 4 c) a)))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
123×add-sqr-sqrt
96×*-un-lft-identity
70×add-cube-cbrt
26×difference-of-squares
24×associate-/r*
16×sqrt-prod
15×add-exp-log
13×distribute-lft-out--
9×add-cbrt-cube associate-/r/
8×add-log-exp
7×flip3-- div-exp flip--
6×pow1
5×div-inv
4×insert-posit16
3×cbrt-undiv associate-/l*
2×rec-exp sub-neg sqrt-div diff-log 1-exp
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-flip inv-pow
Counts
4 → 166
Calls
4 calls:
64.0ms
(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4 c) a))) b)))
11.0ms
(- (* b b) (* (* 4 c) a))
46.0ms
(- (sqrt (- (* b b) (* (* 4 c) a))) b)
15.0ms
(sqrt (- (* b b) (* (* 4 c) a)))

series443.0ms

Counts
4 → 12
Calls
4 calls:
194.0ms
(/ 1 (/ a (- (sqrt (- (* b b) (* (* 4 c) a))) b)))
59.0ms
(- (* b b) (* (* 4 c) a))
104.0ms
(- (sqrt (- (* b b) (* (* 4 c) a))) b)
85.0ms
(sqrt (- (* b b) (* (* 4 c) a)))

simplify1.2s

Counts
178 → 178
Iterations
IterNodes
done2001
32001
21808
1649
0265

prune717.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.9b

regimes409.0ms

Accuracy

83.9% (4.4b remaining)

Error of 10.1b against oracle of 5.8b and baseline of 32.9b

bsearch177.0ms

Steps
ItersRangePoint
9
2.0671083276743448e-101
1.4914771383599542e-96
1.489031291672483e-98
5
-3.3440263710910746e+131
-9.921521910190385e+130
-1.7512236628315378e+131

simplify7.0ms

Iterations
IterNodes
done31
131
027

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.3s1106×body2560valid
869.0ms842×body1280valid
794.0ms5933×body80valid
532.0ms2940×body80nan
299.0ms437×body640valid
112.0ms120×body5120valid
99.0ms210×body320valid
26.0ms113×body160valid