Details

Time bar (total: 15.7s)

sample112.0ms

Algorithm
intervals
Results
27.0ms86×body80nan
25.0ms36×body2560valid
21.0ms187×body80valid
14.0ms25×body1280valid
7.0ms17×body640valid
3.0ms8×body320valid
1.0ms4×body160valid

simplify96.0ms

Counts
1 → 1
Iterations
IterNodes
893
793
692
590
482
366
240
121
012

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3 a) c)
0.8b
(- (* b b) (* (* 3 a) c))
0.9b
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
23.5b
(sqrt (- (* b b) (* (* 3 a) c)))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-cbrt-cube add-exp-log
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod insert-posit16
3×flip3-- associate-*r* pow-prod-down prod-exp cbrt-unprod flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
13.0ms
(* (* 3 a) c)
7.0ms
(- (* b b) (* (* 3 a) c))
57.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
15.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

series261.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (* 3 a) c)
49.0ms
(- (* b b) (* (* 3 a) c))
88.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
100.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.9s

Counts
76 → 76
Iterations
IterNodes
33323
2951
1295
0123

prune375.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* a c) 3)
0.8b
(- (* b b) (* (* a c) 3))
0.9b
(- (sqrt (- (* b b) (* (* a c) 3))) b)
23.5b
(sqrt (- (* b b) (* (* a c) 3)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-cbrt-cube add-exp-log
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod insert-posit16
3×flip3-- associate-*r* pow-prod-down prod-exp cbrt-unprod flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
15.0ms
(* (* a c) 3)
9.0ms
(- (* b b) (* (* a c) 3))
49.0ms
(- (sqrt (- (* b b) (* (* a c) 3))) b)
7.0ms
(sqrt (- (* b b) (* (* a c) 3)))

series321.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (* a c) 3)
69.0ms
(- (* b b) (* (* a c) 3))
109.0ms
(- (sqrt (- (* b b) (* (* a c) 3))) b)
124.0ms
(sqrt (- (* b b) (* (* a c) 3)))

simplify1.8s

Counts
76 → 76
Iterations
IterNodes
33341
2922
1296
0123

prune418.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.6b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (* a c) (* (cbrt 3) (cbrt 3))) (cbrt 3))
0.8b
(- (* b b) (* (* (* a c) (* (cbrt 3) (cbrt 3))) (cbrt 3)))
0.9b
(- (sqrt (- (* b b) (* (* (* a c) (* (cbrt 3) (cbrt 3))) (cbrt 3)))) b)
23.5b
(sqrt (- (* b b) (* (* (* a c) (* (cbrt 3) (cbrt 3))) (cbrt 3))))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
23×pow1
22×add-exp-log
13×add-cbrt-cube pow-prod-down prod-exp cbrt-unprod
12×add-sqr-sqrt
9×*-un-lft-identity
8×add-log-exp
7×add-cube-cbrt
6×associate-*r*
4×sqrt-prod insert-posit16
3×cbrt-prod flip3-- flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 76
Calls
4 calls:
80.0ms
(* (* (* a c) (* (cbrt 3) (cbrt 3))) (cbrt 3))
7.0ms
(- (* b b) (* (* (* a c) (* (cbrt 3) (cbrt 3))) (cbrt 3)))
36.0ms
(- (sqrt (- (* b b) (* (* (* a c) (* (cbrt 3) (cbrt 3))) (cbrt 3)))) b)
7.0ms
(sqrt (- (* b b) (* (* (* a c) (* (cbrt 3) (cbrt 3))) (cbrt 3))))

series572.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(* (* (* a c) (* (cbrt 3) (cbrt 3))) (cbrt 3))
125.0ms
(- (* b b) (* (* (* a c) (* (cbrt 3) (cbrt 3))) (cbrt 3)))
193.0ms
(- (sqrt (- (* b b) (* (* (* a c) (* (cbrt 3) (cbrt 3))) (cbrt 3)))) b)
169.0ms
(sqrt (- (* b b) (* (* (* a c) (* (cbrt 3) (cbrt 3))) (cbrt 3))))

simplify2.6s

Counts
88 → 88
Iterations
IterNodes
35506
21217
1380
0153

prune311.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 13.6b

localize40.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 3 a) c))
11.4b
(- (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))) b)
23.5b
(sqrt (- (* b b) (* (* 3 a) c)))
23.5b
(sqrt (- (* b b) (* (* 3 a) c)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip--
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log
1×difference-of-squares
Counts
4 → 59
Calls
4 calls:
8.0ms
(- (* b b) (* (* 3 a) c))
40.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))) b)
7.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

series350.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(- (* b b) (* (* 3 a) c))
120.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))) b)
93.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
74.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.1s

Counts
71 → 71
Iterations
IterNodes
32753
2743
1230
096

prune299.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 13.6b

regimes477.0ms

Accuracy

85.9% (3.0b remaining)

Error of 14.8b against oracle of 11.9b and baseline of 32.9b

bsearch171.0ms

Steps
ItersRangePoint
8
5.833527798943191e-77
3.6732813120885656e-72
6.235673785124529e-73
7
-2.005420514903704e+154
-2.9230384601346835e+152
-1.3376190644449892e+154

simplify5.0ms

Iterations
IterNodes
232
132
027

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.2s1025×body2560valid
1.1s5891×body80valid
495.0ms882×body1280valid
348.0ms2952×body80nan
185.0ms462×body640valid
118.0ms96×body5120valid
70.0ms238×body320valid
24.0ms104×body160valid