Details

Time bar (total: 30.6s)

sample71.0ms

Algorithm
intervals
Results
24.0ms281×body80valid
7.0ms93×body80nan

simplify124.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
12114
24514
36814
49314
511414
done11414

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
3.7b
(* (* x y) z)
8.1b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
27.7b
(sqrt (- (* z z) (* t a)))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
11×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
sqrt-prod
times-frac prod-exp associate-/r* cbrt-unprod add-log-exp
sqrt-div
cbrt-undiv flip3-- div-exp associate-*r* pow-prod-down flip--
associate-/r/
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:
15.0ms
(- (* z z) (* t a))
37.0ms
(* (* x y) z)
62.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
17.0ms
(sqrt (- (* z z) (* t a)))

series430.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (* z z) (* t a))
49.0ms
(* (* x y) z)
190.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
116.0ms
(sqrt (- (* z z) (* t a)))

simplify2.2s

Counts
88 → 88
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01341237
13691135
22350989
done5001987

prune827.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.2b

localize48.0ms

Local error

Found 4 expressions with local error:

1.1b
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
5.4b
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
27.7b
(sqrt (- (* z z) (* t a)))
27.7b
(sqrt (- (* z z) (* t a)))

rewrite312.0ms

Algorithm
rewrite-expression-head
Rules
63×sqrt-prod
48×add-sqr-sqrt times-frac
35×add-cube-cbrt *-un-lft-identity
33×associate-*r*
30×add-exp-log add-cbrt-cube
16×sqrt-div
15×associate-*l*
cbrt-undiv div-exp prod-exp associate-/r* cbrt-unprod
pow1
associate-/r/
flip3-- flip--
add-log-exp unswap-sqr
div-inv
rem-sqrt-square sqrt-pow1 pow1/2
frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 141
Calls
4 calls:
44.0ms
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
218.0ms
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
19.0ms
(sqrt (- (* z z) (* t a)))
19.0ms
(sqrt (- (* z z) (* t a)))

series605.0ms

Counts
4 → 12
Calls
4 calls:
185.0ms
(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
172.0ms
(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
129.0ms
(sqrt (- (* z z) (* t a)))
118.0ms
(sqrt (- (* z z) (* t a)))

simplify4.1s

Counts
153 → 153
Iterations

Useful iterations: done (4.1s)

IterNodesCost
02243682
16783347
242102978
done50002952

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize55.0ms

Local error

Found 4 expressions with local error:

3.6b
(/ (* (* x y) (/ z (sqrt (sqrt (- (* z z) (* t a)))))) (sqrt (sqrt (- (* z z) (* t a)))))
3.6b
(* (* x y) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
27.7b
(sqrt (- (* z z) (* t a)))
27.7b
(sqrt (- (* z z) (* t a)))

rewrite256.0ms

Algorithm
rewrite-expression-head
Rules
51×sqrt-prod
36×times-frac
34×add-exp-log add-cbrt-cube
33×add-sqr-sqrt associate-*r*
31×add-cube-cbrt *-un-lft-identity
12×sqrt-div prod-exp cbrt-unprod
11×pow1
cbrt-undiv div-exp associate-/r*
flip3-- associate-/r/ flip-- add-log-exp
pow-prod-down
rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ div-inv
frac-2neg associate-*l* clear-num *-commutative associate-/l/ associate-/l*
Counts
4 → 125
Calls
4 calls:
97.0ms
(/ (* (* x y) (/ z (sqrt (sqrt (- (* z z) (* t a)))))) (sqrt (sqrt (- (* z z) (* t a)))))
111.0ms
(* (* x y) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
18.0ms
(sqrt (- (* z z) (* t a)))
19.0ms
(sqrt (- (* z z) (* t a)))

series680.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(/ (* (* x y) (/ z (sqrt (sqrt (- (* z z) (* t a)))))) (sqrt (sqrt (- (* z z) (* t a)))))
244.0ms
(* (* x y) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
129.0ms
(sqrt (- (* z z) (* t a)))
119.0ms
(sqrt (- (* z z) (* t a)))

simplify4.0s

Counts
137 → 137
Iterations

Useful iterations: done (4.0s)

IterNodesCost
02113083
16482710
242242143
done50002126

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.2b

localize55.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (/ x (sqrt (sqrt 1))) (* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
6.0b
(* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
27.7b
(sqrt (- (* z z) (* t a)))
27.7b
(sqrt (- (* z z) (* t a)))

rewrite451.0ms

Algorithm
rewrite-expression-head
Rules
121×add-sqr-sqrt
111×sqrt-prod
105×times-frac
64×associate-*l*
63×add-cube-cbrt *-un-lft-identity
57×add-exp-log add-cbrt-cube
34×associate-*r*
22×prod-exp cbrt-unprod
17×cbrt-undiv div-exp
16×unswap-sqr
13×pow1
12×sqrt-div
frac-times associate-*r/
flip3-- pow-prod-down associate-*l/ associate-/r/ flip-- add-log-exp
div-inv
rem-sqrt-square sqrt-pow1 pow1/2 *-commutative
Counts
4 → 201
Calls
4 calls:
199.0ms
(* (/ x (sqrt (sqrt 1))) (* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
187.0ms
(* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
17.0ms
(sqrt (- (* z z) (* t a)))
27.0ms
(sqrt (- (* z z) (* t a)))

series531.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(* (/ x (sqrt (sqrt 1))) (* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
111.0ms
(* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
124.0ms
(sqrt (- (* z z) (* t a)))
112.0ms
(sqrt (- (* z z) (* t a)))

simplify768.0ms

Counts
213 → 213
Iterations

Useful iterations: done (757.0ms)

IterNodesCost
02976393
19075826
done50015034

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.2b

regimes1.3s

Accuracy

81.8% (3.7b remaining)

Error of 7.2b against oracle of 3.6b and baseline of 23.8b

bsearch138.0ms

Steps
ItersRangePoint
4
2.635805807203389e+81
5.223125367879209e+81
3.396669184341053e+81
9
-6.215183965753672e+74
-1.5421164969392891e+69
-2.8045670485597684e+72

simplify6.4s

Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
02537
13433
23829
35729
48029
58529
68929
79329
89729
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done500129

end0.0ms

sample2.8s

Algorithm
intervals
Results
960.0ms8842×body80valid
313.0ms2877×body80nan