Details

Time bar (total: 36.4s)

sample108.0ms

Algorithm
intervals
Results
63.0ms279×body80valid
20.0ms89×body80nan

simplify252.0ms

Counts
1 → 1
Iterations
IterNodes
8168
7168
6166
5160
4151
3125
275
138
020

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.6b

localize159.0ms

Local error

Found 4 expressions with local error:

1.3b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.4b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
26.8b
(sqrt (- (* b b) (* (* 4 a) c)))
26.8b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-sqr-sqrt add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-cbrt-cube sqrt-div add-exp-log insert-posit16
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sum-log distribute-rgt-neg-in 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 → 67
Calls
4 calls:
14.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
25.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series460.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
99.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
121.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
105.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify857.0ms

Counts
79 → 79
Iterations
IterNodes
32441
2760
1248
0102

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.5b

localize175.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
4.3b
(* (/ a b) c)
4.5b
(/ (* 2 c) (* (- (* (/ a b) c) b) 2))
26.8b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cbrt-cube add-exp-log
17×*-un-lft-identity
13×associate-*l* add-cube-cbrt
11×times-frac
8×add-log-exp
7×pow1
6×prod-exp cbrt-unprod
5×cbrt-undiv div-exp
4×sqrt-prod insert-posit16
3×flip3-- associate-*r* associate-*l/ flip--
2×sqrt-div diff-log associate-/r/ div-inv distribute-lft-out-- difference-of-squares unswap-sqr
1×associate--l- neg-sub0 rem-sqrt-square clear-num associate-/r* sub-neg distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 pow-prod-down neg-log *-commutative associate-/l*
Counts
4 → 92
Calls
4 calls:
15.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
12.0ms
(* (/ a b) c)
21.0ms
(/ (* 2 c) (* (- (* (/ a b) c) b) 2))
11.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series277.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
35.0ms
(* (/ a b) c)
60.0ms
(/ (* 2 c) (* (- (* (/ a b) c) b) 2))
78.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify888.0ms

Counts
104 → 104
Iterations
IterNodes
22113
1523
0202

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.5b

localize227.0ms

Local error

Found 4 expressions with local error:

4.5b
(/ (* 2 c) (* (- (* (/ a b) c) b) 2))
14.1b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
26.8b
(sqrt (- (* b b) (* (* 4 a) c)))
26.8b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
16×add-cbrt-cube add-exp-log
9×add-sqr-sqrt
8×add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×cbrt-undiv flip3-- sqrt-div div-exp prod-exp cbrt-unprod insert-posit16 flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-*l/ associate-/r/
1×associate--l- neg-sub0 clear-num associate-/r* sub-neg frac-2neg times-frac neg-log div-inv associate-/l* difference-of-squares
Counts
4 → 72
Calls
4 calls:
30.0ms
(/ (* 2 c) (* (- (* (/ a b) c) b) 2))
9.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
8.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series425.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ (* 2 c) (* (- (* (/ a b) c) b) 2))
115.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
95.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
117.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify20.2s

Counts
84 → 84
Iterations
IterNodes
39109
21755
1415
0150

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.5b

localize134.0ms

Local error

Found 4 expressions with local error:

4.3b
(* (/ a b) c)
4.3b
(/ (* a c) b)
4.5b
(/ (* 2 c) (* (- (* (/ a b) c) b) 2))
4.5b
(/ (* (- (/ (* a c) b) b) 2) (* 2 a))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
38×add-cbrt-cube add-exp-log
19×add-sqr-sqrt
15×times-frac
14×*-un-lft-identity add-cube-cbrt
13×associate-*l*
11×cbrt-undiv div-exp prod-exp cbrt-unprod
6×pow1
5×associate-/r* associate-*l/
4×insert-posit16 div-inv add-log-exp
3×clear-num frac-2neg associate-*r* associate-/l*
2×flip3-- associate-/r/ flip-- unswap-sqr associate-/l/
1×pow-prod-down *-commutative
Counts
4 → 103
Calls
4 calls:
20.0ms
(* (/ a b) c)
17.0ms
(/ (* a c) b)
38.0ms
(/ (* 2 c) (* (- (* (/ a b) c) b) 2))
29.0ms
(/ (* (- (/ (* a c) b) b) 2) (* 2 a))

series223.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (/ a b) c)
22.0ms
(/ (* a c) b)
84.0ms
(/ (* 2 c) (* (- (* (/ a b) c) b) 2))
77.0ms
(/ (* (- (/ (* a c) b) b) 2) (* 2 a))

simplify2.3s

Counts
115 → 115
Iterations
IterNodes
22898
1582
0202

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.5b

regimes487.0ms

Accuracy

87.1% (1.9b remaining)

Error of 7.5b against oracle of 5.6b and baseline of 20.4b

bsearch324.0ms

Steps
ItersRangePoint
9
2.662790715355376e+61
3.00977400694497e+66
2.9270846490810628e+66
9
-5.249771667565015e+21
-3971786699263373.5
-5.155933750194025e+21

simplify13.0ms

Iterations
IterNodes
253
153
044

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.9s8711×body80valid
1.1s2970×body80nan