Details

Time bar (total: 16.4s)

sample79.0ms

Algorithm
intervals
Results
36.0ms273×body80valid
13.0ms97×body80nan

simplify161.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.0b

localize197.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.6b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite124.0ms

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:
34.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
44.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
19.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
23.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series467.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
121.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
114.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
111.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.0s

Counts
79 → 79
Iterations
IterNodes
done5000
32698
2773
1250
0102

prune604.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.0b

localize182.0ms

Local error

Found 4 expressions with local error:

11.1b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite81.0ms

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:
24.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
18.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
18.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
18.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series436.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
115.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
106.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
106.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.2s

Counts
74 → 74
Iterations
IterNodes
done5000
32806
2727
1232
087

prune701.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.0b

localize190.0ms

Local error

Found 4 expressions with local error:

9.2b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))
23.1b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite92.0ms

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:
25.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
20.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
25.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
20.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series423.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
108.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
100.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
97.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.9s

Counts
76 → 76
Iterations
IterNodes
done5002
32322
2669
1226
091

prune763.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 8.0b

localize134.0ms

Local error

Found 4 expressions with local error:

23.1b
(sqrt (- (* b b) (* (* 4 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4 a) c)))
23.8b
(cbrt (- (* b b) (* (* 4 a) c)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-div
5×pow1
4×flip3-- add-cbrt-cube add-exp-log insert-posit16 flip-- add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 58
Calls
4 calls:
23.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
13.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
12.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
7.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

series539.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
128.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
154.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
133.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

simplify2.2s

Counts
70 → 70
Iterations
IterNodes
done5002
31931
2578
1202
089

prune618.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 8.0b

regimes330.0ms

Accuracy

88.5% (1.3b remaining)

Error of 8.8b against oracle of 7.5b and baseline of 19.1b

bsearch235.0ms

Steps
ItersRangePoint
8
3.2407605759015045e+140
1.292919298649766e+143
5.9445047311226904e+140
8
-5.8501169415505e+41
-1.816545290760657e+37
-5.748232111683622e+41

simplify17.0ms

Iterations
IterNodes
done50
150
042

end0.0ms

sample1.5s

Algorithm
intervals
Results
990.0ms8736×body80valid
261.0ms3069×body80nan