Details

Time bar (total: 14.1s)

sample39.0ms

Algorithm
intervals
Results
13.0ms276×body80valid
4.0ms95×body80nan

simplify74.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
12114
24514
36714
49214
510714
done10714

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* z z) (* t a))
4.2b
(* (* x y) z)
8.5b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.2b
(sqrt (- (* z z) (* t a)))

rewrite74.0ms

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:
8.0ms
(- (* z z) (* t a))
18.0ms
(* (* x y) z)
36.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
9.0ms
(sqrt (- (* z z) (* t a)))

series290.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(- (* z z) (* t a))
34.0ms
(* (* x y) z)
131.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
72.0ms
(sqrt (- (* z z) (* t a)))

simplify1.1s

Counts
88 → 88
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01341237
13411135
21495975
done5001974

prune310.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
1.2b
(- (* z z) (* t a))
2.8b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
25.2b
(sqrt (- (* z z) (* t a)))

rewrite137.0ms

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:
29.0ms
(/ z (sqrt (- (* z z) (* t a))))
16.0ms
(- (* z z) (* t a))
69.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
15.0ms
(sqrt (- (* z z) (* t a)))

series316.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(/ z (sqrt (- (* z z) (* t a))))
49.0ms
(- (* z z) (* t a))
110.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
78.0ms
(sqrt (- (* z z) (* t a)))

simplify2.1s

Counts
124 → 124
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01662031
14181847
215211643
done50001642

prune367.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.9b

localize37.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (* x y) (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))
25.2b
(sqrt (- (* z z) (* t a)))
25.2b
(sqrt (- (* z z) (* t a)))
25.2b
(sqrt (- (* z z) (* t a)))

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log
29×add-cbrt-cube
23×prod-exp cbrt-unprod
18×sqrt-div
13×associate-*r*
12×pow1 cbrt-div
11×add-sqr-sqrt
9×flip3-- sqrt-prod flip--
8×cbrt-undiv add-cube-cbrt *-un-lft-identity div-exp associate-/r/
4×frac-times add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down
2×associate-*l/
1×times-frac associate-*l* *-commutative div-inv
Counts
4 → 90
Calls
4 calls:
175.0ms
(* (* x y) (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))
9.0ms
(sqrt (- (* z z) (* t a)))
14.0ms
(sqrt (- (* z z) (* t a)))
26.0ms
(sqrt (- (* z z) (* t a)))

series544.0ms

Counts
4 → 12
Calls
4 calls:
249.0ms
(* (* x y) (/ (* (cbrt z) (cbrt z)) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))
97.0ms
(sqrt (- (* z z) (* t a)))
91.0ms
(sqrt (- (* z z) (* t a)))
106.0ms
(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts
102 → 102
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01572541
14652310
220631763
done50001643

prune550.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.9b

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b
(* y (/ z (sqrt (- (* z z) (* t a)))))
1.2b
(- (* z z) (* t a))
1.7b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
25.2b
(sqrt (- (* z z) (* t a)))

rewrite151.0ms

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×sqrt-div pow-prod-down
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 diff-log div-inv
Counts
4 → 92
Calls
4 calls:
68.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
9.0ms
(- (* z z) (* t a))
47.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
22.0ms
(sqrt (- (* z z) (* t a)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
38.0ms
(- (* z z) (* t a))
137.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
72.0ms
(sqrt (- (* z z) (* t a)))

simplify2.8s

Counts
104 → 104
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
01611572
13951453
211621241
338541240
done50001240

prune399.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.9b

regimes524.0ms

Accuracy

84.5% (2.9b remaining)

Error of 6.3b against oracle of 3.5b and baseline of 21.9b

bsearch114.0ms

Steps
ItersRangePoint
7
7.763235271532398e+95
1.3510080551639932e+97
1.1719295172753232e+97
9
-7.754247409175047e+159
-6.278022273170321e+153
-1.3401354470987563e+154

simplify15.0ms

Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
02658
13158
23257
33857
done3857

end0.0ms

sample1.9s

Algorithm
intervals
Results
719.0ms8875×body80valid
208.0ms2953×body80nan