Details

Time bar (total: 10.9s)

sample20.0ms

Algorithm
intervals
Results
9.0ms349×body80valid

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0911
12711
27411
315811
424311
529911
635111
747911
899011
9360011
done500011

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (* z z) (+ z 1.0))
13.7b
(/ (* x y) (* (* z z) (+ z 1.0)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log add-cbrt-cube
12×prod-exp cbrt-unprod
7×pow1
6×cbrt-undiv div-exp
5×*-un-lft-identity
4×add-sqr-sqrt associate-*r/ associate-*r*
3×add-cube-cbrt pow-prod-down
2×flip3-+ associate-/r/ flip-+ add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in times-frac associate-*l* clear-num associate-/r* *-commutative div-inv distribute-lft-out associate-/l* unswap-sqr
Counts
2 → 51
Calls
2 calls:
14.0ms
(* (* z z) (+ z 1.0))
17.0ms
(/ (* x y) (* (* z z) (+ z 1.0)))

series131.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(* (* z z) (+ z 1.0))
77.0ms
(/ (* x y) (* (* z z) (+ z 1.0)))

simplify917.0ms

Counts
57 → 57
Iterations

Useful iterations: 2 (254.0ms)

IterNodesCost
0112858
1369788
21986626
done5000626

prune120.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (+ z 1.0) (/ (* z z) y))
7.0b
(/ x (* (+ z 1.0) (/ (* z z) y)))
7.3b
(/ (* z z) y)

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log add-cbrt-cube
14×add-sqr-sqrt
12×*-un-lft-identity
10×cbrt-undiv add-cube-cbrt times-frac div-exp
9×prod-exp cbrt-unprod
7×associate-*r*
5×pow1 associate-/r/
4×frac-times flip3-+ associate-*l* associate-*l/ associate-/r* flip-+ associate-/l*
3×div-inv add-log-exp
2×frac-2neg associate-*r/ clear-num unswap-sqr
1×pow-prod-down *-commutative distribute-lft-out
Counts
3 → 84
Calls
3 calls:
17.0ms
(* (+ z 1.0) (/ (* z z) y))
10.0ms
(/ x (* (+ z 1.0) (/ (* z z) y)))
4.0ms
(/ (* z z) y)

series129.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(* (+ z 1.0) (/ (* z z) y))
63.0ms
(/ x (* (+ z 1.0) (/ (* z z) y)))
22.0ms
(/ (* z z) y)

simplify722.0ms

Counts
93 → 93
Iterations

Useful iterations: done (719.0ms)

IterNodesCost
01561250
14211195
216871003
done5000989

prune216.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (+ z 1.0) (/ z (/ y z)))
0.1b
(/ z (/ y z))
7.0b
(/ x (* (+ z 1.0) (/ z (/ y z))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
147×times-frac
92×add-sqr-sqrt
85×*-un-lft-identity
83×add-cube-cbrt
44×associate-*r*
31×add-exp-log add-cbrt-cube
14×associate-/r*
13×cbrt-undiv div-exp
10×div-inv
7×associate-/r/
6×prod-exp cbrt-unprod associate-/l*
5×pow1
4×frac-times flip3-+ associate-*l* associate-*l/ flip-+
3×add-log-exp unswap-sqr
2×frac-2neg associate-*r/ clear-num
1×pow-prod-down *-commutative distribute-lft-out
Counts
3 → 171
Calls
3 calls:
30.0ms
(* (+ z 1.0) (/ z (/ y z)))
5.0ms
(/ z (/ y z))
10.0ms
(/ x (* (+ z 1.0) (/ z (/ y z))))

series129.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(* (+ z 1.0) (/ z (/ y z)))
21.0ms
(/ z (/ y z))
63.0ms
(/ x (* (+ z 1.0) (/ z (/ y z))))

simplify1.6s

Counts
180 → 180
Iterations

Useful iterations: 2 (602.0ms)

IterNodesCost
02932462
17522287
231122023
done50012023

prune451.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
1.5b
(* (/ (cbrt x) z) y)
3.2b
(* (/ (* (cbrt x) (cbrt x)) (+ z 1.0)) (/ (* (/ (cbrt x) z) y) z))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
63×add-exp-log
51×add-cbrt-cube
36×add-sqr-sqrt
32×associate-*l*
28×times-frac
26×*-un-lft-identity
24×add-cube-cbrt prod-exp cbrt-unprod
21×cbrt-undiv div-exp
16×cbrt-prod
10×associate-*r*
8×pow1
5×unswap-sqr
4×add-log-exp
3×div-inv
2×pow1/3 pow-prod-down associate-*l/ associate-/r/ *-commutative
1×frac-times flip3-+ associate-*r/ flip-+ distribute-lft-out
Counts
4 → 119
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
11.0ms
(* (/ (cbrt x) z) y)
37.0ms
(* (/ (* (cbrt x) (cbrt x)) (+ z 1.0)) (/ (* (/ (cbrt x) z) y) z))

series614.0ms

Counts
4 → 12
Calls
4 calls:
199.0ms
(cbrt x)
197.0ms
(cbrt x)
129.0ms
(* (/ (cbrt x) z) y)
87.0ms
(* (/ (* (cbrt x) (cbrt x)) (+ z 1.0)) (/ (* (/ (cbrt x) z) y) z))

simplify1.3s

Counts
131 → 131
Iterations

Useful iterations: 2 (543.0ms)

IterNodesCost
02182081
16601988
229071424
done50001424

prune387.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes224.0ms

Accuracy

12.5% (2.7b remaining)

Error of 2.8b against oracle of 0.1b and baseline of 3.2b

bsearch76.0ms

Steps
ItersRangePoint
10
8.121476410325186e-188
4.551464151430799e-174
2.1377599442065233e-181

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02338
12938
done2938

end0.0ms

sample529.0ms

Algorithm
intervals
Results
298.0ms10718×body80valid