Details

Time bar (total: 6.2s)

sample30.0ms

Algorithm
intervals
Results
10.0ms282×body80valid
3.0ms103×body80nan

simplify44.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01214
12214
24514
36814
49214
510514
done10514

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
2.9b
(* (* x y) z)
11.4b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.6b
(sqrt (- (* z z) (* t a)))

rewrite28.0ms

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:
3.0ms
(- (* z z) (* t a))
7.0ms
(* (* x y) z)
12.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
5.0ms
(sqrt (- (* z z) (* t a)))

series210.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* z z) (* t a))
24.0ms
(* (* x y) z)
86.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify573.0ms

Counts
98 → 98
Iterations

Useful iterations: 2 (153.0ms)

IterNodesCost
01461331
13631220
216651062
done50011062

prune281.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.6b
(- (* z z) (* t a))
2.5b
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
23.6b
(sqrt (- (* z z) (* t a)))

rewrite37.0ms

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:
6.0ms
(/ z (sqrt (- (* z z) (* t a))))
3.0ms
(- (* z z) (* t a))
19.0ms
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
5.0ms
(sqrt (- (* z z) (* t a)))

series233.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ z (sqrt (- (* z z) (* t a))))
34.0ms
(- (* z z) (* t a))
86.0ms
(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify652.0ms

Counts
134 → 134
Iterations

Useful iterations: 2 (191.0ms)

IterNodesCost
01792135
14491941
217771740
done50011740

prune359.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
1.3b
(* x (/ z (sqrt (- (* z z) (* t a)))))
1.5b
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
23.6b
(sqrt (- (* z z) (* t a)))

rewrite51.0ms

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:
3.0ms
(- (* z z) (* t a))
20.0ms
(* x (/ z (sqrt (- (* z z) (* t a)))))
20.0ms
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
5.0ms
(sqrt (- (* z z) (* t a)))

series242.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* z z) (* t a))
58.0ms
(* x (/ z (sqrt (- (* z z) (* t a)))))
86.0ms
(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
64.0ms
(sqrt (- (* z z) (* t a)))

simplify595.0ms

Counts
114 → 114
Iterations

Useful iterations: 2 (143.0ms)

IterNodesCost
01741680
14201552
214721342
done50001342

prune293.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.1b

localize13.0ms

Local error

Found 4 expressions with local error:

1.3b
(* x (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
1.5b
(* y (* x (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
23.6b
(sqrt (- (* z z) (* t a)))
23.6b
(sqrt (- (* z z) (* t a)))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
28×sqrt-div
27×add-exp-log add-cbrt-cube
16×add-sqr-sqrt associate-*r*
13×pow1
12×prod-exp cbrt-unprod
10×add-cube-cbrt *-un-lft-identity
8×flip3-- associate-/r/ flip--
6×associate-*l* sqrt-prod
5×associate-*r/
4×cbrt-undiv expm1-log1p-u frac-times times-frac div-exp pow-prod-down log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ *-commutative unswap-sqr
1×div-inv
Counts
4 → 97
Calls
4 calls:
54.0ms
(* x (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
103.0ms
(* y (* x (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
5.0ms
(sqrt (- (* z z) (* t a)))
5.0ms
(sqrt (- (* z z) (* t a)))

series269.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* x (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
87.0ms
(* y (* x (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
59.0ms
(sqrt (- (* z z) (* t a)))
63.0ms
(sqrt (- (* z z) (* t a)))

simplify537.0ms

Counts
109 → 109
Iterations

Useful iterations: 2 (141.0ms)

IterNodesCost
01712530
14141641
214721386
done50011386

prune341.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.1b

regimes301.0ms

Accuracy

83.8% (3.1b remaining)

Error of 6.6b against oracle of 3.5b and baseline of 22.6b

bsearch94.0ms

Steps
ItersRangePoint
9
1.1514081473628363e+89
6.147715137559524e+97
8.840009572039548e+95
10
-2.167781788999652e+162
-1.4102566258715918e+152
-1.2137296334810365e+154

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02029
12829
23029
done3029

end0.0ms

sample779.0ms

Algorithm
intervals
Results
324.0ms8878×body80valid
101.0ms2953×body80nan