Details

Time bar (total: 20.7s)

sample65.0ms

Algorithm
intervals
Results
36.0ms283×body80valid
12.0ms108×body80nan

simplify208.0ms

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.0b

localize170.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4 a) c))
1.1b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
23.2b
(sqrt (- (* b b) (* (* 4 a) c)))
23.2b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip--
3×diff-log
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 distribute-rgt-neg-in neg-log
Counts
4 → 64
Calls
4 calls:
7.0ms
(- (* b b) (* (* 4 a) c))
31.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
16.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series406.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (* b b) (* (* 4 a) c))
122.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
114.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
119.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.1s

Counts
76 → 76
Iterations
IterNodes
32593
2742
1237
099

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.8b

localize156.0ms

Local error

Found 4 expressions with local error:

6.8b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
23.2b
(sqrt (- (* b b) (* (* 4 a) c)))
23.2b
(sqrt (- (* b b) (* (* 4 a) c)))
23.2b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite31.0ms

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))))))
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series470.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
132.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
116.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
102.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.1s

Counts
74 → 74
Iterations
IterNodes
32327
2716
1230
087

prune1.5s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 7.8b

localize219.0ms

Local error

Found 4 expressions with local error:

11.3b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
23.2b
(sqrt (- (* b b) (* (* 4 a) c)))
23.2b
(sqrt (- (* b b) (* (* 4 a) c)))
23.2b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
11×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 difference-of-squares
Counts
4 → 64
Calls
4 calls:
10.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series498.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
113.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
128.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
117.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify975.0ms

Counts
76 → 76
Iterations
IterNodes
32124
2658
1224
091

prune1.5s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 7.8b

localize197.0ms

Local error

Found 4 expressions with local error:

23.2b
(sqrt (- (* b b) (* (* 4 a) c)))
23.2b
(sqrt (- (* b b) (* (* 4 a) c)))
23.9b
(cbrt (- (* b b) (* (* 4 a) c)))
23.9b
(cbrt (- (* b b) (* (* 4 a) c)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-prod pow1 sqrt-prod
4×cbrt-div flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip-- add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 60
Calls
4 calls:
8.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
20.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

series479.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
120.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
138.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
124.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

simplify4.4s

Counts
72 → 72
Iterations
IterNodes
46322
31876
2580
1200
089

prune1.6s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 7.8b

regimes545.0ms

Accuracy

89.5% (1.3b remaining)

Error of 8.0b against oracle of 6.7b and baseline of 19.1b

bsearch319.0ms

Steps
ItersRangePoint
9
1.9710174875302874e+32
1.945305249879839e+37
1.9280516389664611e+37
8
-3.585760457965514e+97
-4.884785332531034e+94
-3.2137442760107994e+97

simplify34.0ms

Iterations
IterNodes
251
151
042

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.7s8739×body80valid
982.0ms2881×body80nan