Details

Time bar (total: 17.1s)

sample76.0ms

Algorithm
intervals
Results
40.0ms284×body80valid
10.0ms85×body80nan

simplify200.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize161.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.6b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite101.0ms

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:
22.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
37.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
18.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
22.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series380.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
113.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
84.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
89.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.1s

Counts
79 → 79
Iterations
IterNodes
done5000
32698
2773
1250
0102

prune773.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.7b

localize146.0ms

Local error

Found 4 expressions with local error:

11.8b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite58.0ms

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:
11.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
9.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
19.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
18.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series438.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
99.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
117.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
97.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.2s

Counts
74 → 74
Iterations
IterNodes
done5000
32806
2727
1232
087

prune730.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.7b

localize150.0ms

Local error

Found 4 expressions with local error:

9.3b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))
21.2b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite43.0ms

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:
16.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
9.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series424.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
91.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
102.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
106.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.7s

Counts
76 → 76
Iterations
IterNodes
done5002
32322
2669
1226
091

prune1.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.7b

localize197.0ms

Local error

Found 4 expressions with local error:

21.2b
(sqrt (- (* b b) (* (* 4 a) c)))
22.0b
(cbrt (- (* b b) (* (* 4 a) c)))
22.0b
(cbrt (- (* b b) (* (* 4 a) c)))
22.0b
(cbrt (- (* b b) (* (* 4 a) c)))

rewrite39.0ms

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:
20.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
6.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

series450.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
110.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
104.0ms
(cbrt (- (* b b) (* (* 4 a) c)))
111.0ms
(cbrt (- (* b b) (* (* 4 a) c)))

simplify1.7s

Counts
70 → 70
Iterations
IterNodes
done5002
31931
2578
1202
089

prune761.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.7b

regimes421.0ms

Accuracy

86% (1.7b remaining)

Error of 9.1b against oracle of 7.4b and baseline of 19.5b

bsearch272.0ms

Steps
ItersRangePoint
8
4.664337482673326e-05
0.17679972651571432
0.17389787404847717
8
-1.3198903247987554e+155
-1.1250773400730914e+152
-1.3122553888834108e+154

simplify10.0ms

Iterations
IterNodes
done45
145
038

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.6s8783×body80valid
475.0ms2988×body80nan