Details

Time bar (total: 17.9s)

sample126.0ms

Algorithm
intervals
Results
78.0ms279×body80valid
19.0ms84×body80nan

simplify236.0ms

Counts
1 → 1
Iterations
IterNodes
done152
7152
6151
5144
4132
3101
262
135
020

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize137.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
20.8b
(sqrt (- (* b b) (* (* 4 a) c)))
20.8b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite77.0ms

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:
19.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
25.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series414.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
104.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
99.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
114.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.9s

Counts
79 → 79
Iterations
IterNodes
done5000
32698
2773
1250
0102

prune624.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.9b

localize151.0ms

Local error

Found 4 expressions with local error:

8.1b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
20.8b
(sqrt (- (* b b) (* (* 4 a) c)))
20.8b
(sqrt (- (* b b) (* (* 4 a) c)))
20.8b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite36.0ms

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))))))
8.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series429.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
105.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
109.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
100.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.5s

Counts
74 → 74
Iterations
IterNodes
done5000
32806
2727
1232
087

prune681.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.9b

localize192.0ms

Local error

Found 4 expressions with local error:

9.7b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
20.8b
(sqrt (- (* b b) (* (* 4 a) c)))
20.8b
(sqrt (- (* b b) (* (* 4 a) c)))
20.8b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite36.0ms

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:
11.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
104.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
86.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
99.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.9s

Counts
76 → 76
Iterations
IterNodes
done5002
32322
2669
1226
091

prune689.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.9b

localize213.0ms

Local error

Found 4 expressions with local error:

20.8b
(sqrt (- (* b b) (* (* 4 a) c)))
21.5b
(cbrt (- (* b b) (* (* 4 a) c)))
21.5b
(cbrt (- (* b b) (* (* 4 a) c)))
21.5b
(cbrt (- (* b b) (* (* 4 a) c)))

rewrite46.0ms

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:
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
10.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
10.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
10.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

series589.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
158.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
137.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
170.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

simplify1.8s

Counts
70 → 70
Iterations
IterNodes
done5002
31931
2578
1202
089

prune769.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 6.9b

regimes399.0ms

Accuracy

90.3% (1.1b remaining)

Error of 8.5b against oracle of 7.4b and baseline of 18.8b

bsearch216.0ms

Steps
ItersRangePoint
7
5.455680955858941e+61
9.381769121995126e+63
3.5713846885333815e+62
7
-3.975131512634171e+119
-7.031908089210839e+117
-1.7246734819168266e+119

simplify10.0ms

Iterations
IterNodes
done50
150
042

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.3s8750×body80valid
568.0ms3007×body80nan