Details

Time bar (total: 10.2s)

sample32.0ms

Algorithm
intervals
Results
10.0ms286×body80valid
3.0ms91×body80nan

simplify67.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
12214
24614
37214
49714
511214
done11214

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
4.1b
(* (* x y) z)
10.1b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.5b
(sqrt (- (* z z) (* t a)))

rewrite69.0ms

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×expm1-log1p-u sqrt-div log1p-expm1-u
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 fma-neg diff-log associate-*l* prod-diff clear-num *-commutative div-inv associate-/l*
Counts
4 → 86
Calls
4 calls:
8.0ms
(- (* z z) (* t a))
17.0ms
(* (* x y) z)
31.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
11.0ms
(sqrt (- (* z z) (* t a)))

series252.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(- (* z z) (* t a))
29.0ms
(* (* x y) z)
106.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
76.0ms
(sqrt (- (* z z) (* t a)))

simplify1.0s

Counts
98 → 98
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01461331
13611220
215601062
done50011060

prune284.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

localize11.0ms

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)))))
25.5b
(sqrt (- (* z z) (* t a)))

rewrite83.0ms

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×expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u
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 fma-neg diff-log associate-*r/ associate-*l* prod-diff clear-num *-commutative
Counts
4 → 122
Calls
4 calls:
13.0ms
(/ z (sqrt (- (* z z) (* t a))))
8.0ms
(- (* z z) (* t a))
43.0ms
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
11.0ms
(sqrt (- (* z z) (* t a)))

series281.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(/ z (sqrt (- (* z z) (* t a))))
41.0ms
(- (* z z) (* t a))
112.0ms
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
67.0ms
(sqrt (- (* z z) (* t a)))

simplify1.3s

Counts
134 → 134
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01792135
14381941
215821740
done50001738

prune375.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* z z) (* t a))
1.0b
(* x (/ z (sqrt (- (* z z) (* t a)))))
2.1b
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
25.5b
(sqrt (- (* z z) (* t a)))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
25×associate-*r*
20×add-cube-cbrt *-un-lft-identity times-frac
18×add-exp-log add-cbrt-cube
13×sqrt-prod
12×pow1
7×prod-exp cbrt-unprod
6×associate-*l* add-log-exp
4×expm1-log1p-u sqrt-div pow-prod-down log1p-expm1-u
3×flip3-- associate-*r/ flip-- unswap-sqr
2×cbrt-undiv div-exp associate-/r/ *-commutative
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff div-inv
Counts
4 → 102
Calls
4 calls:
9.0ms
(- (* z z) (* t a))
41.0ms
(* x (/ z (sqrt (- (* z z) (* t a)))))
44.0ms
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
15.0ms
(sqrt (- (* z z) (* t a)))

series311.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* z z) (* t a))
74.0ms
(* x (/ z (sqrt (- (* z z) (* t a)))))
113.0ms
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
79.0ms
(sqrt (- (* z z) (* t a)))

simplify2.0s

Counts
114 → 114
Iterations

Useful iterations: 3 (957.0ms)

IterNodesCost
01741680
14141552
212151342
340541340
done50001340

prune309.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.7b

localize16.0ms

Local error

Found 4 expressions with local error:

11.4b
(cbrt (* y (* x (/ z (sqrt (- (* z z) (* t a)))))))
25.5b
(sqrt (- (* z z) (* t a)))
25.5b
(sqrt (- (* z z) (* t a)))
25.5b
(sqrt (- (* z z) (* t a)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
2×associate-*r/
1×cbrt-prod cbrt-div pow1/3
Counts
4 → 63
Calls
4 calls:
37.0ms
(cbrt (* y (* x (/ z (sqrt (- (* z z) (* t a)))))))
11.0ms
(sqrt (- (* z z) (* t a)))
13.0ms
(sqrt (- (* z z) (* t a)))
11.0ms
(sqrt (- (* z z) (* t a)))

series493.0ms

Counts
4 → 12
Calls
4 calls:
267.0ms
(cbrt (* y (* x (/ z (sqrt (- (* z z) (* t a)))))))
71.0ms
(sqrt (- (* z z) (* t a)))
75.0ms
(sqrt (- (* z z) (* t a)))
80.0ms
(sqrt (- (* z z) (* t a)))

simplify1.4s

Counts
75 → 75
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01171065
1277966
2747882
32092873
done5000856

prune315.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.7b

regimes432.0ms

Accuracy

84% (3.1b remaining)

Error of 6.1b against oracle of 3.1b and baseline of 22.3b

bsearch130.0ms

Steps
ItersRangePoint
8
2.5834036296097543e+93
1.0947755062948554e+98
9.942908350064873e+94
8
3.8683726044958085e-236
1.1504173315589242e-231
1.1329867395911508e-234
7
-3.457830478277447e+77
-5.613235761893359e+75
-1.9461830837188635e+77

simplify7.0ms

Iterations

Useful iterations: 2 (4.0ms)

IterNodesCost
02950
13750
23849
34449
done4449

end0.0ms

sample899.0ms

Algorithm
intervals
Results
321.0ms8857×body80valid
91.0ms2872×body80nan