Details

Time bar (total: 15.2s)

sample62.0ms

Algorithm
intervals
Results
26.0ms275×body80valid
8.0ms95×body80nan

simplify81.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
3.7b
(* (* x y) z)
8.6b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.8b
(sqrt (- (* z z) (* t a)))

rewrite110.0ms

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:
18.0ms
(- (* z z) (* t a))
39.0ms
(* (* x y) z)
40.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
9.0ms
(sqrt (- (* z z) (* t a)))

series353.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(- (* z z) (* t a))
29.0ms
(* (* x y) z)
156.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
109.0ms
(sqrt (- (* z z) (* t a)))

simplify1.6s

Counts
92 → 92
Iterations
IterNodes
done5000
21429
1362
0138

prune613.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.4b
(- (* z z) (* t a))
3.6b
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
22.8b
(sqrt (- (* z z) (* t a)))

rewrite121.0ms

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:
17.0ms
(/ z (sqrt (- (* z z) (* t a))))
17.0ms
(- (* z z) (* t a))
67.0ms
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
17.0ms
(sqrt (- (* z z) (* t a)))

series385.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(/ z (sqrt (- (* z z) (* t a))))
64.0ms
(- (* z z) (* t a))
134.0ms
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
101.0ms
(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts
128 → 128
Iterations
IterNodes
done5003
21661
1476
0171

prune598.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
1.4b
(* x (/ z (sqrt (- (* z z) (* t a)))))
2.5b
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
22.8b
(sqrt (- (* z z) (* t a)))

rewrite136.0ms

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 insert-posit16
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 → 96
Calls
4 calls:
8.0ms
(- (* z z) (* t a))
51.0ms
(* x (/ z (sqrt (- (* z z) (* t a)))))
65.0ms
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
9.0ms
(sqrt (- (* z z) (* t a)))

series348.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(- (* z z) (* t a))
81.0ms
(* x (/ z (sqrt (- (* z z) (* t a)))))
118.0ms
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
93.0ms
(sqrt (- (* z z) (* t a)))

simplify1.9s

Counts
108 → 108
Iterations
IterNodes
done5001
21400
1430
0166

prune599.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 2.8b

localize74.0ms

Local error

Found 4 expressions with local error:

3.6b
(* (* y x) (* (* (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
22.8b
(sqrt (- (* z z) (* t a)))
22.8b
(sqrt (- (* z z) (* t a)))
22.8b
(sqrt (- (* z z) (* t a)))

rewrite539.0ms

Algorithm
rewrite-expression-head
Rules
121×add-exp-log
69×add-cbrt-cube prod-exp cbrt-unprod
28×pow1
26×cbrt-undiv div-exp
15×pow-prod-down
10×add-sqr-sqrt associate-*r/
9×sqrt-prod
7×*-un-lft-identity add-cube-cbrt
6×sqrt-div
5×frac-times associate-*l/
4×insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip--
1×associate-*r* associate-*l* *-commutative
Counts
4 → 116
Calls
4 calls:
497.0ms
(* (* y x) (* (* (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
10.0ms
(sqrt (- (* z z) (* t a)))
16.0ms
(sqrt (- (* z z) (* t a)))
9.0ms
(sqrt (- (* z z) (* t a)))

series415.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(* (* y x) (* (* (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a))))) (/ (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)))
95.0ms
(sqrt (- (* z z) (* t a)))

simplify2.0s

Counts
128 → 128
Iterations
IterNodes
done5000
21836
1503
0180

prune702.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 2.8b

regimes986.0ms

Accuracy

86.3% (2.7b remaining)

Error of 6.1b against oracle of 3.4b and baseline of 23.2b

bsearch324.0ms

Steps
ItersRangePoint
9
5.011112315551321e+98
1.162298132228303e+106
9.659251240846705e+99
7
9.55261584131615e-251
2.312145188529779e-248
4.2013669449125285e-250
10
-5.1804348181252644e-228
-3.4330926237021946e-245
-1.0059935812111571e-240
9
-9.077327646451038e+154
-3.733798037926972e+148
-5.667193347780096e+153

simplify10.0ms

Iterations
IterNodes
done41
241
138
031

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.0s8817×body80valid
221.0ms2853×body80nan