Details

Time bar (total: 6.0s)

sample30.0ms

Algorithm
intervals
Results
11.0ms279×body80valid
3.0ms106×body80nan

simplify41.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01214
12114
24414
36514
48914
510214
done10214

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
3.0b
(* (* x y) z)
8.3b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite27.0ms

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×sqrt-div
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 diff-log associate-*l* clear-num *-commutative div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
6.0ms
(* (* x y) z)
12.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series201.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
82.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify552.0ms

Counts
88 → 88
Iterations

Useful iterations: 2 (140.0ms)

IterNodesCost
01341237
13431135
21608975
done5001975

prune228.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.8b
(- (* z z) (* t a))
1.6b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite34.0ms

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×flip3-- associate-/r/ flip--
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 diff-log associate-*r/ associate-*l* clear-num *-commutative
Counts
4 → 112
Calls
4 calls:
6.0ms
(/ z (sqrt (- (* z z) (* t a))))
3.0ms
(- (* z z) (* t a))
18.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ z (sqrt (- (* z z) (* t a))))
32.0ms
(- (* z z) (* t a))
84.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify641.0ms

Counts
124 → 124
Iterations

Useful iterations: 2 (178.0ms)

IterNodesCost
01662031
14291847
217261643
done50001643

prune292.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
1.6b
(* (* x y) (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
24.8b
(sqrt (- (* z z) (* t a)))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
28×sqrt-div
25×add-exp-log add-cbrt-cube
15×associate-*r*
11×pow1 prod-exp cbrt-unprod
10×add-sqr-sqrt
9×flip3-- flip--
8×add-cube-cbrt *-un-lft-identity associate-/r/
6×sqrt-prod add-log-exp
4×cbrt-undiv frac-times div-exp
3×times-frac associate-*r/ pow-prod-down
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/
1×sub-neg diff-log associate-*l* *-commutative div-inv
Counts
4 → 81
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
51.0ms
(* (* x y) (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series237.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* z z) (* t a))
84.0ms
(* (* x y) (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
56.0ms
(sqrt (- (* z z) (* t a)))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify566.0ms

Counts
93 → 93
Iterations

Useful iterations: 2 (157.0ms)

IterNodesCost
01572039
14171446
216721200
done50011200

prune291.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* z z) (* t a))
1.8b
(* x (* y (/ (* (cbrt z) (cbrt z)) (fabs (cbrt (- (* z z) (* t a)))))))
25.7b
(cbrt (- (* z z) (* t a)))
25.7b
(cbrt (- (* z z) (* t a)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
16×add-cbrt-cube
9×pow1
8×prod-exp cbrt-unprod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-prod add-log-exp
4×cbrt-div
3×flip3-- associate-*l* pow-prod-down flip--
2×cbrt-undiv pow1/3 associate-*r/ div-exp
1×sub-neg diff-log associate-*r* *-commutative
Counts
4 → 61
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
29.0ms
(* x (* y (/ (* (cbrt z) (cbrt z)) (fabs (cbrt (- (* z z) (* t a)))))))
2.0ms
(cbrt (- (* z z) (* t a)))
2.0ms
(cbrt (- (* z z) (* t a)))

series368.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* z z) (* t a))
166.0ms
(* x (* y (/ (* (cbrt z) (cbrt z)) (fabs (cbrt (- (* z z) (* t a)))))))
79.0ms
(cbrt (- (* z z) (* t a)))
87.0ms
(cbrt (- (* z z) (* t a)))

simplify488.0ms

Counts
73 → 73
Iterations

Useful iterations: 2 (113.0ms)

IterNodesCost
01401356
13801321
213061047
done50001047

prune277.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.8b

regimes433.0ms

Accuracy

87.7% (2.5b remaining)

Error of 5.7b against oracle of 3.2b and baseline of 23.6b

bsearch100.0ms

Steps
ItersRangePoint
10
8.756260439201689e+104
1.7016018298191544e+118
6.307442222943313e+112
7
-1.8239455871173137e+105
-7.060621971491881e+103
-3.308556132875522e+104

simplify5.0ms

Iterations

Useful iterations: 2 (3.0ms)

IterNodesCost
02950
13848
23947
35047
done5047

end0.0ms

sample800.0ms

Algorithm
intervals
Results
348.0ms8836×body80valid
98.0ms2919×body80nan