Details

Time bar (total: 46.9s)

sample114.0ms

Algorithm
intervals
Results
53.0ms282×body80valid
38.0ms91×body80nan

simplify160.0ms

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize162.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* (* 4 a) c))
2.5b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
22.7b
(sqrt (- (* b b) (* (* 4 a) c)))
22.7b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity add-log-exp
8×add-sqr-sqrt
6×pow1 add-cube-cbrt sqrt-prod
4×add-cbrt-cube sqrt-div add-exp-log insert-posit16
3×flip3-- flip--
2×rem-sqrt-square sum-log sqrt-pow1 pow1/2 distribute-lft-out
1×neg-sub0 +-commutative sub-neg distribute-rgt-neg-in flip3-+ diff-log neg-log associate-+l- flip-+
Counts
4 → 61
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4 a) c))
25.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series349.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(- (* b b) (* (* 4 a) c))
105.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
80.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
102.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.6s

Counts
73 → 73
Iterations
IterNodes
32749
2795
1247
095

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.5b

localize194.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* (* 4 a) c))
3.7b
(/ a (/ b c))
4.1b
(/ (* 2 c) (* 2 (- (/ a (/ b c)) b)))
22.7b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
48×add-sqr-sqrt
47×*-un-lft-identity add-cube-cbrt
21×add-cbrt-cube add-exp-log
14×associate-/r*
7×cbrt-undiv div-exp
6×div-inv add-log-exp
5×pow1
4×prod-exp cbrt-unprod insert-posit16 associate-/l*
3×flip3-- associate-/r/ sqrt-prod flip--
2×clear-num frac-2neg sqrt-div associate-*r/
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log
Counts
4 → 124
Calls
4 calls:
16.0ms
(- (* b b) (* (* 4 a) c))
12.0ms
(/ a (/ b c))
40.0ms
(/ (* 2 c) (* 2 (- (/ a (/ b c)) b)))
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series343.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (* b b) (* (* 4 a) c))
36.0ms
(/ a (/ b c))
86.0ms
(/ (* 2 c) (* 2 (- (/ a (/ b c)) b)))
137.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.8s

Counts
136 → 136
Iterations
IterNodes
22585
1667
0260

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.4b

localize198.0ms

Local error

Found 4 expressions with local error:

4.1b
(/ (* 2 c) (* 2 (- (/ a (/ b c)) b)))
11.5b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
22.7b
(sqrt (- (* b b) (* (* 4 a) c)))
22.7b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite51.0ms

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-*r/ 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:
21.0ms
(/ (* 2 c) (* 2 (- (/ a (/ b c)) b)))
13.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
8.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series432.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ (* 2 c) (* 2 (- (/ a (/ b c)) b)))
105.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
110.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
117.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify29.2s

Counts
84 → 84
Iterations
IterNodes
310754
21767
1415
0150

prune1.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.4b

localize171.0ms

Local error

Found 4 expressions with local error:

7.9b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
22.7b
(sqrt (- (* b b) (* (* 4 a) c)))
22.7b
(sqrt (- (* b b) (* (* 4 a) c)))
22.7b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite54.0ms

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:
16.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
13.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series480.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
105.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
127.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
130.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify921.0ms

Counts
74 → 74
Iterations
IterNodes
32296
2718
1232
087

prune1.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.4b

regimes513.0ms

Accuracy

89.5% (1.6b remaining)

Error of 8.0b against oracle of 6.5b and baseline of 21.3b

bsearch364.0ms

Steps
ItersRangePoint
9
2.1762368803982262e+45
1.3534154308951418e+51
2.0167317209326723e+50
8
-1.7996802595953755e+64
-1.2634430355867738e+61
-2.5394590287515435e+63

simplify11.0ms

Iterations
IterNodes
254
154
045

end0.0ms

sample3.1s

Algorithm
intervals
Results
2.2s8723×body80valid
543.0ms2878×body80nan