Details

Time bar (total: 13.8s)

sample43.0ms

Algorithm
intervals
Results
14.0ms291×body80valid
4.0ms96×body80nan

simplify67.0ms

Counts
1 → 1
Iterations
IterNodes
done114
5114
493
368
245
121
012

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* a t))
2.1b
(/ (* x y) (sqrt (- (* z z) (* a t))))
5.8b
(* (/ (* x y) (sqrt (- (* z z) (* a t)))) z)
23.1b
(sqrt (- (* z z) (* a t)))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube add-exp-log
16×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
12×times-frac associate-*l* sqrt-prod
7×pow1
6×associate-/r* sqrt-div add-log-exp
5×prod-exp cbrt-unprod
4×cbrt-undiv flip3-- div-exp associate-/r/ flip--
3×associate-*r*
2×div-inv
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log pow-prod-down associate-*l/ *-commutative associate-/l* unswap-sqr
Counts
4 → 88
Calls
4 calls:
7.0ms
(- (* z z) (* a t))
16.0ms
(/ (* x y) (sqrt (- (* z z) (* a t))))
45.0ms
(* (/ (* x y) (sqrt (- (* z z) (* a t)))) z)
18.0ms
(sqrt (- (* z z) (* a t)))

series389.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* z z) (* a t))
119.0ms
(/ (* x y) (sqrt (- (* z z) (* a t))))
139.0ms
(* (/ (* x y) (sqrt (- (* z z) (* a t)))) z)
85.0ms
(sqrt (- (* z z) (* a t)))

simplify1.4s

Counts
100 → 100
Iterations
IterNodes
done5000
22100
1392
0144

prune800.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* a t))))
0.2b
(- (* z z) (* a t))
2.7b
(* (* x y) (/ z (sqrt (- (* z z) (* a t)))))
23.1b
(sqrt (- (* z z) (* a t)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt
33×*-un-lft-identity add-cube-cbrt
24×associate-*r* sqrt-prod
18×add-cbrt-cube add-exp-log
10×pow1
6×associate-/r* sqrt-div prod-exp cbrt-unprod add-log-exp
4×flip3-- associate-/r/ flip--
3×cbrt-undiv div-exp pow-prod-down associate-/l*
2×div-inv
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log associate-*l* associate-*r/ *-commutative
Counts
4 → 112
Calls
4 calls:
13.0ms
(/ z (sqrt (- (* z z) (* a t))))
6.0ms
(- (* z z) (* a t))
52.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* a t)))))
7.0ms
(sqrt (- (* z z) (* a t)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(/ z (sqrt (- (* z z) (* a t))))
65.0ms
(- (* z z) (* a t))
142.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* a t)))))
77.0ms
(sqrt (- (* z z) (* a t)))

simplify1.7s

Counts
124 → 124
Iterations
IterNodes
done5001
22991
1475
0166

prune886.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (fabs (cbrt (- (* z z) (* a t))))) (/ z (sqrt (cbrt (- (* z z) (* a t))))))
2.7b
(* (* x y) (* (/ 1 (fabs (cbrt (- (* z z) (* a t))))) (/ z (sqrt (cbrt (- (* z z) (* a t)))))))
23.8b
(cbrt (- (* z z) (* a t)))
23.8b
(cbrt (- (* z z) (* a t)))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
99×add-exp-log
69×add-sqr-sqrt
57×add-cbrt-cube
53×times-frac
51×prod-exp
36×*-un-lft-identity
34×associate-*r*
32×add-cube-cbrt
27×cbrt-unprod
24×div-exp sqrt-prod
18×cbrt-prod pow1
14×associate-*l*
12×cbrt-undiv unswap-sqr
9×pow-prod-down
6×rec-exp cbrt-div 1-exp
5×associate-*r/
4×add-log-exp
3×flip3-- flip--
2×frac-times pow1/3 sqrt-div associate-*l/ associate-/r/ *-commutative div-inv
Counts
4 → 153
Calls
4 calls:
65.0ms
(* (/ 1 (fabs (cbrt (- (* z z) (* a t))))) (/ z (sqrt (cbrt (- (* z z) (* a t))))))
74.0ms
(* (* x y) (* (/ 1 (fabs (cbrt (- (* z z) (* a t))))) (/ z (sqrt (cbrt (- (* z z) (* a t)))))))
5.0ms
(cbrt (- (* z z) (* a t)))
5.0ms
(cbrt (- (* z z) (* a t)))

series822.0ms

Counts
4 → 12
Calls
4 calls:
197.0ms
(* (/ 1 (fabs (cbrt (- (* z z) (* a t))))) (/ z (sqrt (cbrt (- (* z z) (* a t))))))
335.0ms
(* (* x y) (* (/ 1 (fabs (cbrt (- (* z z) (* a t))))) (/ z (sqrt (cbrt (- (* z z) (* a t)))))))
160.0ms
(cbrt (- (* z z) (* a t)))
130.0ms
(cbrt (- (* z z) (* a t)))

simplify543.0ms

Counts
165 → 165
Iterations
IterNodes
done5001
1983
0304

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* a t))
1.6b
(* x (/ (* y z) (sqrt (- (* z z) (* a t)))))
9.5b
(/ (* y z) (sqrt (- (* z z) (* a t))))
23.1b
(sqrt (- (* z z) (* a t)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube add-exp-log
16×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
12×times-frac associate-*r* sqrt-prod
7×pow1
6×associate-/r* sqrt-div add-log-exp
5×prod-exp cbrt-unprod
4×cbrt-undiv flip3-- div-exp associate-/r/ flip--
3×associate-*l*
2×div-inv
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log pow-prod-down associate-*r/ *-commutative associate-/l* unswap-sqr
Counts
4 → 88
Calls
4 calls:
6.0ms
(- (* z z) (* a t))
42.0ms
(* x (/ (* y z) (sqrt (- (* z z) (* a t)))))
15.0ms
(/ (* y z) (sqrt (- (* z z) (* a t))))
7.0ms
(sqrt (- (* z z) (* a t)))

series297.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* z z) (* a t))
113.0ms
(* x (/ (* y z) (sqrt (- (* z z) (* a t)))))
66.0ms
(/ (* y z) (sqrt (- (* z z) (* a t))))
74.0ms
(sqrt (- (* z z) (* a t)))

simplify903.0ms

Counts
100 → 100
Iterations
IterNodes
done5001
22008
1395
0143

prune592.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.4b

regimes1.1s

Accuracy

78.5% (4.3b remaining)

Error of 7.8b against oracle of 3.5b and baseline of 23.3b

bsearch52.0ms

Steps
ItersRangePoint
0
7.590712924645989e+117
7.695838515569772e+117
7.64327572010788e+117
7
-6.499354134947939e+42
-2.420896724821489e+41
-6.395336884503867e+42

simplify14.0ms

Iterations
IterNodes
done47
347
245
134
025

end0.0ms

sample2.0s

Algorithm
intervals
Results
945.0ms8830×body80valid
208.0ms2961×body80nan