Details

Time bar (total: 15.6s)

sample70.0ms

Algorithm
intervals
Results
34.0ms282×body80valid
8.0ms94×body80nan

simplify127.0ms

Counts
1 → 1
Iterations
IterNodes
done103
6103
597
470
353
236
121
012

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* z z) (* t a))
3.5b
(* (* x y) z)
7.6b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite96.0ms

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 insert-posit16
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 → 80
Calls
4 calls:
17.0ms
(- (* z z) (* t a))
20.0ms
(* (* x y) z)
46.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
10.0ms
(sqrt (- (* z z) (* t a)))

series334.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(- (* z z) (* t a))
45.0ms
(* (* x y) z)
137.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
91.0ms
(sqrt (- (* z z) (* t a)))

simplify1.5s

Counts
92 → 92
Iterations
IterNodes
done5000
21429
1362
0138

prune585.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.2b
(- (* z z) (* t a))
2.2b
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite126.0ms

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/ insert-posit16 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 → 116
Calls
4 calls:
14.0ms
(/ z (sqrt (- (* z z) (* t a))))
9.0ms
(- (* z z) (* t a))
80.0ms
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
18.0ms
(sqrt (- (* z z) (* t a)))

series346.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ z (sqrt (- (* z z) (* t a))))
47.0ms
(- (* z z) (* t a))
125.0ms
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
98.0ms
(sqrt (- (* z z) (* t a)))

simplify1.8s

Counts
128 → 128
Iterations
IterNodes
done5003
21661
1476
0171

prune600.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.5b

localize33.0ms

Local error

Found 4 expressions with local error:

1.7b
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
3.6b
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
24.8b
(sqrt (- (* z z) (* t a)))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
63×sqrt-prod
48×add-sqr-sqrt times-frac
35×*-un-lft-identity add-cube-cbrt
33×associate-*r*
30×add-cbrt-cube add-exp-log
16×sqrt-div
15×associate-*l*
9×cbrt-undiv associate-/r* div-exp prod-exp cbrt-unprod
8×pow1
6×associate-/r/
5×flip3-- flip--
4×insert-posit16 add-log-exp unswap-sqr
3×div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l*
Counts
4 → 145
Calls
4 calls:
22.0ms
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
140.0ms
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
9.0ms
(sqrt (- (* z z) (* t a)))
24.0ms
(sqrt (- (* z z) (* t a)))

series405.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
114.0ms
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
74.0ms
(sqrt (- (* z z) (* t a)))
95.0ms
(sqrt (- (* z z) (* t a)))

simplify2.3s

Counts
157 → 157
Iterations
IterNodes
done5001
22566
1675
0227

prune954.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (/ (sqrt (- (* z z) (* t a))) (* (* x y) z)))
3.5b
(* (* x y) z)
7.5b
(/ (sqrt (- (* z z) (* t a))) (* (* x y) z))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
52×add-exp-log
34×add-sqr-sqrt
33×*-un-lft-identity add-cube-cbrt
32×add-cbrt-cube
21×sqrt-prod
20×div-exp
15×prod-exp
11×pow1 associate-/r*
10×cbrt-undiv
9×cbrt-unprod associate-/l*
6×div-inv
4×rec-exp sqrt-div 1-exp insert-posit16 add-log-exp
3×associate-*r* pow-prod-down
2×clear-num frac-2neg flip3-- flip-- associate-/l/
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* associate-/r/ *-commutative pow-flip inv-pow
Counts
4 → 140
Calls
4 calls:
53.0ms
(/ 1 (/ (sqrt (- (* z z) (* t a))) (* (* x y) z)))
31.0ms
(* (* x y) z)
36.0ms
(/ (sqrt (- (* z z) (* t a))) (* (* x y) z))
19.0ms
(sqrt (- (* z z) (* t a)))

series489.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(/ 1 (/ (sqrt (- (* z z) (* t a))) (* (* x y) z)))
44.0ms
(* (* x y) z)
192.0ms
(/ (sqrt (- (* z z) (* t a))) (* (* x y) z))
106.0ms
(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts
152 → 152
Iterations
IterNodes
done5144
22084
1570
0222

prune655.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.5b

regimes1.1s

Accuracy

84.6% (2.9b remaining)

Error of 6.5b against oracle of 3.6b and baseline of 22.6b

bsearch146.0ms

Steps
ItersRangePoint
9
6.876815347956334e+134
1.292919298649766e+143
3.471068194478418e+142
9
-9.351864464929311e+91
-3.3514666867395575e+86
-3.962990925915687e+91

simplify5.0ms

Iterations
IterNodes
done28
228
125
021

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.1s8811×body80valid
293.0ms3007×body80nan