Details

Time bar (total: 11.6s)

sample79.0ms

Algorithm
intervals
Results
46.0ms281×body80valid
12.0ms84×body80nan

simplify215.0ms

Counts
1 → 1
Iterations
IterNodes
done168
7168
6166
5160
4151
3125
275
138
020

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.9b

localize170.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.7b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
23.4b
(sqrt (- (* b b) (* (* 4 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite58.0ms

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:
18.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
18.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
12.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series412.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
117.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
89.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
98.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify576.0ms

Counts
79 → 79
Iterations
IterNodes
done2000
2773
1250
0102

prune504.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.1b

localize137.0ms

Local error

Found 4 expressions with local error:

7.4b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
23.4b
(sqrt (- (* b b) (* (* 4 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div
4×add-cbrt-cube add-exp-log insert-posit16
3×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip--
2×sum-log
1×neg-sub0 +-commutative flip3-+ neg-log associate-+l- flip-+
Counts
4 → 62
Calls
4 calls:
8.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
9.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series418.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
100.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
104.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
113.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify754.0ms

Counts
74 → 74
Iterations
IterNodes
done2000
2727
1232
087

prune639.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.1b

localize174.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
4.5b
(/ (* 2 c) (* 2 (- (/ a (/ b c)) b)))
5.7b
(/ a (/ b c))
23.4b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
52×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
21×add-cbrt-cube add-exp-log
14×associate-/r*
8×add-log-exp
7×cbrt-undiv div-exp
6×div-inv
5×pow1
4×prod-exp sqrt-prod cbrt-unprod insert-posit16 associate-/l*
3×flip3-- associate-/r/ flip--
2×clear-num frac-2neg sqrt-div diff-log associate-*r/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square sub-neg distribute-rgt-neg-in sqrt-pow1 pow1/2 neg-log
Counts
4 → 130
Calls
4 calls:
31.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
35.0ms
(/ (* 2 c) (* 2 (- (/ a (/ b c)) b)))
6.0ms
(/ a (/ b c))
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series327.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
80.0ms
(/ (* 2 c) (* 2 (- (/ a (/ b c)) b)))
39.0ms
(/ a (/ b c))
84.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify617.0ms

Counts
142 → 142
Iterations
IterNodes
done2001
1746
0285

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize174.0ms

Local error

Found 4 expressions with local error:

14.9b
(- (- b) (* (* (cbrt (sqrt (- (* b b) (* (* 4 a) c)))) (cbrt (sqrt (- (* b b) (* (* 4 a) c))))) (cbrt (sqrt (- (* b b) (* (* 4 a) c))))))
23.4b
(sqrt (- (* b b) (* (* 4 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4 a) c)))
23.4b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div
4×flip3-- add-cbrt-cube add-exp-log insert-posit16 flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log
1×associate--l- neg-sub0 sub-neg neg-log
Counts
4 → 63
Calls
4 calls:
17.0ms
(- (- b) (* (* (cbrt (sqrt (- (* b b) (* (* 4 a) c)))) (cbrt (sqrt (- (* b b) (* (* 4 a) c))))) (cbrt (sqrt (- (* b b) (* (* 4 a) c))))))
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series389.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(- (- b) (* (* (cbrt (sqrt (- (* b b) (* (* 4 a) c)))) (cbrt (sqrt (- (* b b) (* (* 4 a) c))))) (cbrt (sqrt (- (* b b) (* (* 4 a) c))))))
102.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
92.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
98.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify528.0ms

Counts
75 → 75
Iterations
IterNodes
done2002
2713
1228
088

prune745.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.1b

regimes319.0ms

Accuracy

87.2% (2.0b remaining)

Error of 7.3b against oracle of 5.2b and baseline of 21.0b

bsearch369.0ms

Steps
ItersRangePoint
7
1.9723660647371773e+81
3.4101289177416236e+83
3.340270116328134e+83
6
-6.8156570572547095e-267
-1.1055728218964216e-267
-1.1253904323982412e-267
10
-2.64779304316231e+160
-6.749854855548698e+149
-1.4755018087753095e+152

simplify25.0ms

Iterations
IterNodes
done65
165
056

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.9s8781×body80valid
512.0ms2986×body80nan