Details

Time bar (total: 47.8s)

sample77.0ms

Algorithm
intervals
Results
44.0ms290×body80valid
11.0ms103×body80nan

simplify123.0ms

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: 24.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
4.1b
(* (* x y) z)
9.9b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.3b
(sqrt (- (* z z) (* t a)))

rewrite84.0ms

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:
14.0ms
(- (* z z) (* t a))
29.0ms
(* (* x y) z)
32.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
7.0ms
(sqrt (- (* z z) (* t a)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* z z) (* t a))
32.0ms
(* (* x y) z)
96.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
107.0ms
(sqrt (- (* z z) (* t a)))

simplify763.0ms

Counts
92 → 92
Iterations
IterNodes
done2001
21429
1362
0138

prune465.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.6b
(- (* z z) (* t a))
3.6b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.3b
(sqrt (- (* z z) (* t a)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
47×add-sqr-sqrt
46×*-un-lft-identity add-cube-cbrt
33×sqrt-prod
25×associate-/r*
18×add-cbrt-cube add-exp-log
7×cbrt-undiv div-exp associate-/l*
6×add-log-exp
5×pow1
4×sqrt-div insert-posit16 div-inv
3×flip3-- flip--
2×clear-num frac-2neg prod-exp cbrt-unprod associate-/l/
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log associate-/r/
Counts
4 → 136
Calls
4 calls:
18.0ms
(/ (sqrt (- (* z z) (* t a))) z)
7.0ms
(- (* z z) (* t a))
22.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
10.0ms
(sqrt (- (* z z) (* t a)))

series376.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ (sqrt (- (* z z) (* t a))) z)
50.0ms
(- (* z z) (* t a))
117.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
99.0ms
(sqrt (- (* z z) (* t a)))

simplify1.0s

Counts
148 → 148
Iterations
IterNodes
done2002
21928
1558
0214

prune831.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.6b

localize62.0ms

Local error

Found 4 expressions with local error:

1.5b
(/ (/ (* x y) (/ (cbrt (sqrt (- (* z z) (* t a)))) (cbrt z))) (/ (cbrt (sqrt (- (* z z) (* t a)))) (cbrt z)))
23.3b
(sqrt (- (* z z) (* t a)))
23.3b
(sqrt (- (* z z) (* t a)))
23.3b
(sqrt (- (* z z) (* t a)))

rewrite450.0ms

Algorithm
rewrite-expression-head
Rules
13718×times-frac
7749×cbrt-prod
4620×add-sqr-sqrt
4617×*-un-lft-identity add-cube-cbrt
2223×sqrt-prod
183×div-inv
63×associate-/l*
60×associate-/r/
58×associate-/r*
45×add-exp-log
27×cbrt-undiv add-cbrt-cube div-exp
7×pow1
6×sqrt-div
4×prod-exp cbrt-unprod insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip--
1×clear-num frac-2neg associate-/l/
Counts
4 → 3856
Calls
4 calls:
68.0ms
(/ (/ (* x y) (/ (cbrt (sqrt (- (* z z) (* t a)))) (cbrt z))) (/ (cbrt (sqrt (- (* z z) (* t a)))) (cbrt z)))
15.0ms
(sqrt (- (* z z) (* t a)))
15.0ms
(sqrt (- (* z z) (* t a)))
15.0ms
(sqrt (- (* z z) (* t a)))

series465.0ms

Counts
4 → 12
Calls
4 calls:
222.0ms
(/ (/ (* x y) (/ (cbrt (sqrt (- (* z z) (* t a)))) (cbrt z))) (/ (cbrt (sqrt (- (* z z) (* t a)))) (cbrt z)))
86.0ms
(sqrt (- (* z z) (* t a)))
81.0ms
(sqrt (- (* z z) (* t a)))
75.0ms
(sqrt (- (* z z) (* t a)))

simplify5.1s

Counts
3868 → 3868
Iterations
IterNodes
done3961
03961

prune31.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.6b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.6b
(- (* z z) (* t a))
3.6b
(/ (* x y) (/ 1 (/ z (sqrt (- (* z z) (* t a))))))
23.3b
(sqrt (- (* z z) (* t a)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
347×times-frac
149×add-sqr-sqrt
148×*-un-lft-identity add-cube-cbrt
83×associate-/r*
69×sqrt-prod
51×add-exp-log
29×div-exp
27×add-cbrt-cube
17×associate-/r/
16×sqrt-div
13×cbrt-undiv
10×div-inv
9×flip3-- flip--
7×prod-exp
6×add-log-exp
5×pow1
4×rec-exp 1-exp insert-posit16 associate-/l*
3×cbrt-unprod
2×clear-num frac-2neg
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log
Counts
4 → 258
Calls
4 calls:
13.0ms
(/ z (sqrt (- (* z z) (* t a))))
7.0ms
(- (* z z) (* t a))
27.0ms
(/ (* x y) (/ 1 (/ z (sqrt (- (* z z) (* t a))))))
7.0ms
(sqrt (- (* z z) (* t a)))

series299.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(/ z (sqrt (- (* z z) (* t a))))
51.0ms
(- (* z z) (* t a))
115.0ms
(/ (* x y) (/ 1 (/ z (sqrt (- (* z z) (* t a))))))
72.0ms
(sqrt (- (* z z) (* t a)))

simplify997.0ms

Counts
270 → 270
Iterations
IterNodes
done2025
11399
0479

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.6b

regimes1.1s

Accuracy

82.5% (3.4b remaining)

Error of 6.7b against oracle of 3.3b and baseline of 22.8b

bsearch223.0ms

Steps
ItersRangePoint
9
3.0793339614790758e+57
6.511477481037166e+66
4.540039934470349e+59
9
-3139973514407996.0
-13790401.520460634
-3078949553883556.0

simplify13.0ms

Iterations
IterNodes
done41
241
138
031

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.4s8878×body80valid
355.0ms2989×body80nan