Details

Time bar (total: 20.9s)

sample63.0ms

Algorithm
intervals
Results
28.0ms278×body80valid
6.0ms100×body80nan

simplify109.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
012285
121285
236285
353285
470285
597285
6103285
done103285

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
5.0b
(* (* x y) z)
11.2b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
27.2b
(sqrt (- (* z z) (* t a)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube add-exp-log
11×add-sqr-sqrt
10×pow1 *-un-lft-identity add-cube-cbrt
9×sqrt-prod
6×associate-/r* times-frac prod-exp cbrt-unprod add-log-exp
4×sqrt-div
3×cbrt-undiv flip3-- div-exp associate-*r* pow-prod-down flip--
2×associate-/r/
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log associate-*l* *-commutative div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
13.0ms
(- (* z z) (* t a))
32.0ms
(* (* x y) z)
29.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
14.0ms
(sqrt (- (* z z) (* t a)))

series361.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* z z) (* t a))
49.0ms
(* (* x y) z)
153.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
110.0ms
(sqrt (- (* z z) (* t a)))

simplify2.1s

Counts
88 → 88
Iterations

Useful iterations: done (2.1s)

IterNodesCost
013424087
135921433
2140320873
done500120753

prune656.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.6b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.8b
(- (* z z) (* t a))
2.4b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
27.2b
(sqrt (- (* z z) (* t a)))

rewrite102.0ms

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:
22.0ms
(/ z (sqrt (- (* z z) (* t a))))
12.0ms
(- (* z z) (* t a))
47.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
14.0ms
(sqrt (- (* z z) (* t a)))

series399.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(/ z (sqrt (- (* z z) (* t a))))
41.0ms
(- (* z z) (* t a))
161.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
112.0ms
(sqrt (- (* z z) (* t a)))

simplify2.2s

Counts
124 → 124
Iterations

Useful iterations: done (2.2s)

IterNodesCost
016640386
147236543
2176236019
done500135739

prune697.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.4b

localize87.0ms

Local error

Found 4 expressions with local error:

1.4b
(* x (* y (* (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a))))))))
27.2b
(sqrt (- (* z z) (* t a)))
27.2b
(sqrt (- (* z z) (* t a)))
27.2b
(sqrt (- (* z z) (* t a)))

rewrite376.0ms

Algorithm
rewrite-expression-head
Rules
29×add-exp-log
21×add-cbrt-cube
16×pow1
15×prod-exp cbrt-unprod
11×add-sqr-sqrt
9×sqrt-prod
8×*-un-lft-identity add-cube-cbrt
7×associate-*r/
6×sqrt-div pow-prod-down
4×cbrt-undiv div-exp add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-*l* flip--
1×frac-times associate-*r* associate-*l/ *-commutative
Counts
4 → 75
Calls
4 calls:
350.0ms
(* x (* y (* (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a))))))))
10.0ms
(sqrt (- (* z z) (* t a)))
7.0ms
(sqrt (- (* z z) (* t a)))
7.0ms
(sqrt (- (* z z) (* t a)))

series551.0ms

Counts
4 → 12
Calls
4 calls:
292.0ms
(* x (* y (* (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a))))))))
88.0ms
(sqrt (- (* z z) (* t a)))
76.0ms
(sqrt (- (* z z) (* t a)))
94.0ms
(sqrt (- (* z z) (* t a)))

simplify6.1s

Counts
87 → 87
Iterations

Useful iterations: done (6.1s)

IterNodesCost
013231942
133628792
2116628272
3475128072
done500027792

prune714.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
1.2b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
1.4b
(* y (/ z (sqrt (- (* z z) (* t a)))))
27.2b
(sqrt (- (* z z) (* t a)))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
25×associate-*r*
20×*-un-lft-identity times-frac add-cube-cbrt
18×add-cbrt-cube add-exp-log
13×sqrt-prod
12×pow1
7×prod-exp cbrt-unprod
6×associate-*l* add-log-exp
4×sqrt-div pow-prod-down
3×flip3-- associate-*r/ flip-- unswap-sqr
2×cbrt-undiv div-exp associate-/r/ *-commutative
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log div-inv
Counts
4 → 92
Calls
4 calls:
6.0ms
(- (* z z) (* t a))
53.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
47.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
7.0ms
(sqrt (- (* z z) (* t a)))

series363.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(- (* z z) (* t a))
143.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
73.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
81.0ms
(sqrt (- (* z z) (* t a)))

simplify1.8s

Counts
104 → 104
Iterations

Useful iterations: done (1.8s)

IterNodesCost
016130418
142627358
2136627197
done500127037

prune616.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.4b

regimes1.0s

Accuracy

84.5% (3.0b remaining)

Error of 6.3b against oracle of 3.3b and baseline of 22.6b

bsearch87.0ms

Steps
ItersRangePoint
1
1.8047529537396908e+77
1.9106710751339173e+77
1.8841915447853606e+77
9
-1.5609492160219461e+159
-1.6646169640830922e+150
-1.0342362768199871e+154

simplify13.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
021667
127667
230667
done30667

end0.0ms

sample2.1s

Algorithm
intervals
Results
871.0ms8886×body80valid
635.0ms3063×body80nan