Details

Time bar (total: 14.8s)

sample73.0ms

Algorithm
intervals
Results
26.0ms281×body80valid
6.0ms79×body80nan

simplify121.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
12114
24514
36814
49314
511414
done11414

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* z z) (* t a))
3.2b
(* (* x y) z)
7.6b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.4b
(sqrt (- (* z z) (* t a)))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
11×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×sqrt-prod
6×times-frac prod-exp associate-/r* cbrt-unprod add-log-exp
4×sqrt-div
3×cbrt-undiv flip3-- div-exp associate-*r* pow-prod-down flip--
2×associate-/r/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*l* clear-num *-commutative div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
14.0ms
(- (* z z) (* t a))
43.0ms
(* (* x y) z)
42.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
19.0ms
(sqrt (- (* z z) (* t a)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(- (* z z) (* t a))
38.0ms
(* (* x y) z)
136.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
84.0ms
(sqrt (- (* z z) (* t a)))

simplify2.0s

Counts
88 → 88
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01341237
13691135
22350989
done5001987

prune387.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* z z) (* t a))
0.1b
(/ z (sqrt (- (* z z) (* t a))))
2.1b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
23.4b
(sqrt (- (* z z) (* t a)))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
24×associate-*r* sqrt-prod
18×add-exp-log add-cbrt-cube
10×pow1
6×sqrt-div prod-exp associate-/r* cbrt-unprod add-log-exp
4×flip3-- associate-/r/ flip--
3×cbrt-undiv div-exp pow-prod-down associate-/l*
2×div-inv
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ associate-*l* clear-num *-commutative
Counts
4 → 112
Calls
4 calls:
9.0ms
(- (* z z) (* t a))
30.0ms
(/ z (sqrt (- (* z z) (* t a))))
73.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
18.0ms
(sqrt (- (* z z) (* t a)))

series355.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* z z) (* t a))
95.0ms
(/ z (sqrt (- (* z z) (* t a))))
136.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
79.0ms
(sqrt (- (* z z) (* t a)))

simplify2.0s

Counts
124 → 124
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01662031
14751855
229431657
done50021653

prune469.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* z z) (* t a))
0.1b
(/ (sqrt (- (* z z) (* t a))) z)
2.1b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.4b
(sqrt (- (* z z) (* t a)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
47×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
25×associate-/r*
18×add-exp-log add-cbrt-cube
7×cbrt-undiv div-exp associate-/l*
6×add-log-exp
5×pow1
4×sqrt-div div-inv
3×flip3-- flip--
2×frac-2neg prod-exp clear-num cbrt-unprod associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/r/
Counts
4 → 132
Calls
4 calls:
16.0ms
(- (* z z) (* t a))
27.0ms
(/ (sqrt (- (* z z) (* t a))) z)
25.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
9.0ms
(sqrt (- (* z z) (* t a)))

series358.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(- (* z z) (* t a))
99.0ms
(/ (sqrt (- (* z z) (* t a))) z)
108.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
97.0ms
(sqrt (- (* z z) (* t a)))

simplify2.2s

Counts
144 → 144
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02102654
15752439
236842239
done50022233

prune597.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a)))))
0.1b
(/ z (sqrt (- (* z z) (* t a))))
2.1b
(/ (* x y) (/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a))))))
23.4b
(sqrt (- (* z z) (* t a)))

rewrite214.0ms

Algorithm
rewrite-expression-head
Rules
941×times-frac
416×add-sqr-sqrt
415×add-cube-cbrt *-un-lft-identity
405×sqrt-prod
179×associate-/r*
44×associate-/r/
42×sqrt-div
32×add-exp-log add-cbrt-cube
24×div-inv
21×flip3-- flip--
16×cbrt-undiv div-exp
10×associate-/l*
5×pow1
4×add-log-exp
3×frac-2neg prod-exp clear-num cbrt-unprod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 567
Calls
4 calls:
27.0ms
(/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a)))))
18.0ms
(/ z (sqrt (- (* z z) (* t a))))
106.0ms
(/ (* x y) (/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a))))))
17.0ms
(sqrt (- (* z z) (* t a)))

series402.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a)))))
70.0ms
(/ z (sqrt (- (* z z) (* t a))))
144.0ms
(/ (* x y) (/ (sqrt 1) (/ z (sqrt (- (* z z) (* t a))))))
75.0ms
(sqrt (- (* z z) (* t a)))

simplify1.1s

Counts
579 → 579
Iterations

Useful iterations: done (1.0s)

IterNodesCost
063915804
1197212497
done500212180

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.9b

regimes568.0ms

Accuracy

84.4% (3.1b remaining)

Error of 6.8b against oracle of 3.7b and baseline of 23.4b

bsearch112.0ms

Steps
ItersRangePoint
8
8.123581701571455e+93
3.7790309889164093e+96
3.742227003601956e+96
10
-5.351987414543535e+167
-3.329626013588087e+149
-1.3146714561089265e+154

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02232
13031
23231
done3231

end0.0ms

sample2.0s

Algorithm
intervals
Results
707.0ms8824×body80valid
205.0ms2892×body80nan