Details

Time bar (total: 27.9s)

sample86.0ms

Algorithm
intervals
Results
51.0ms507×body80valid

simplify4.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
011245
119245
249245
3156245
4303245
5420245
6930245
72357245
83719245
94506245
done5000245

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.1b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (* x x) (* (* y 4.0) (- (* z z) t)))
4.7b
(* (* y 4.0) (- (* z z) t))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-cbrt-cube add-exp-log
5×sub-neg
4×distribute-rgt-in add-sqr-sqrt distribute-lft-in associate-*r* associate--r+ add-log-exp
3×*-un-lft-identity pow-prod-down prod-exp add-cube-cbrt cbrt-unprod
2×flip3-- associate-*r/ flip--
1×diff-log associate-*l* *-commutative difference-of-squares
Counts
2 → 41
Calls
2 calls:
8.0ms
(- (* x x) (* (* y 4.0) (- (* z z) t)))
35.0ms
(* (* y 4.0) (- (* z z) t))

series200.0ms

Counts
2 → 6
Calls
2 calls:
92.0ms
(- (* x x) (* (* y 4.0) (- (* z z) t)))
108.0ms
(* (* y 4.0) (- (* z z) t))

simplify4.2s

Counts
47 → 47
Iterations

Useful iterations: 2 (335.0ms)

IterNodesCost
09313893
127711735
299811455
3464111455
done502911455

prune261.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* y 4.0) (sqrt (- (* z z) t)))
0.2b
(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
4.7b
(sqrt (- (* z z) t))
4.7b
(sqrt (- (* z z) t))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1
18×add-cbrt-cube sqrt-div add-exp-log
16×add-sqr-sqrt sqrt-prod
14×associate-*r*
10×*-un-lft-identity associate-*r/ add-cube-cbrt
9×flip3-- pow-prod-down prod-exp cbrt-unprod flip--
4×frac-times add-log-exp difference-of-squares
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* associate-*l/ *-commutative
Counts
4 → 89
Calls
4 calls:
58.0ms
(* (* y 4.0) (sqrt (- (* z z) t)))
105.0ms
(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
8.0ms
(sqrt (- (* z z) t))
12.0ms
(sqrt (- (* z z) t))

series334.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(* (* y 4.0) (sqrt (- (* z z) t)))
86.0ms
(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
61.0ms
(sqrt (- (* z z) t))
84.0ms
(sqrt (- (* z z) t))

simplify2.9s

Counts
101 → 101
Iterations

Useful iterations: done (2.8s)

IterNodesCost
013631333
137725005
2138824485
done500024205

prune657.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 2.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (* y 4.0) (sqrt (sqrt (- (* z z) t)))) (sqrt (sqrt (- (* z z) t))))
4.7b
(sqrt (- (* z z) t))
4.7b
(sqrt (- (* z z) t))
4.7b
(sqrt (- (* z z) t))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
30×sqrt-div
23×sqrt-prod
17×add-sqr-sqrt
16×pow1
13×add-cbrt-cube add-exp-log
10×*-un-lft-identity associate-*r* add-cube-cbrt
9×flip3-- flip--
8×associate-*r/
6×pow-prod-down prod-exp cbrt-unprod
4×frac-times add-log-exp difference-of-squares
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-*l/
1×associate-*l* *-commutative
Counts
4 → 84
Calls
4 calls:
160.0ms
(* (* (* y 4.0) (sqrt (sqrt (- (* z z) t)))) (sqrt (sqrt (- (* z z) t))))
16.0ms
(sqrt (- (* z z) t))
22.0ms
(sqrt (- (* z z) t))
16.0ms
(sqrt (- (* z z) t))

series343.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(* (* (* y 4.0) (sqrt (sqrt (- (* z z) t)))) (sqrt (sqrt (- (* z z) t))))
65.0ms
(sqrt (- (* z z) t))
81.0ms
(sqrt (- (* z z) t))
68.0ms
(sqrt (- (* z z) t))

simplify5.7s

Counts
96 → 96
Iterations

Useful iterations: 3 (3.4s)

IterNodesCost
013731665
135225428
2123825068
3481524868
done500224868

prune683.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 2.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* y (* 4.0 (sqrt (- (* z z) t)))) (fabs (cbrt (- (* z z) t))))
4.7b
(sqrt (- (* z z) t))
5.3b
(cbrt (- (* z z) t))
5.3b
(cbrt (- (* z z) t))

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1
13×add-cbrt-cube add-exp-log
12×add-sqr-sqrt
8×cbrt-prod *-un-lft-identity add-cube-cbrt
6×pow-prod-down prod-exp cbrt-unprod
4×cbrt-div flip3-- sqrt-div associate-*r/ sqrt-prod flip-- add-log-exp
3×associate-*r* difference-of-squares
2×pow1/3 associate-*l/
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative
Counts
4 → 67
Calls
4 calls:
166.0ms
(* (* y (* 4.0 (sqrt (- (* z z) t)))) (fabs (cbrt (- (* z z) t))))
16.0ms
(sqrt (- (* z z) t))
10.0ms
(cbrt (- (* z z) t))
10.0ms
(cbrt (- (* z z) t))

series515.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(* (* y (* 4.0 (sqrt (- (* z z) t)))) (fabs (cbrt (- (* z z) t))))
67.0ms
(sqrt (- (* z z) t))
162.0ms
(cbrt (- (* z z) t))
143.0ms
(cbrt (- (* z z) t))

simplify2.6s

Counts
79 → 79
Iterations

Useful iterations: done (2.6s)

IterNodesCost
015428242
138224971
2123624653
done500124093

prune663.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 2.0b

regimes1.2s

Accuracy

85.1% (0.5b remaining)

Error of 3.1b against oracle of 2.6b and baseline of 6.1b

bsearch1.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
020616
125616
done25616

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.3s15701×body80valid