Details

Time bar (total: 11.9s)

sample24.0ms

Algorithm
intervals
Results
12.0ms349×body80valid

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0911
12711
27611
316711
425311
531711
638411
751811
8103311
9368711
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)))

rewrite28.0ms

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×expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u 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 → 55
Calls
2 calls:
14.0ms
(* (* z z) (+ z 1.0))
12.0ms
(/ (* x y) (* (* z z) (+ z 1.0)))

series150.0ms

Counts
2 → 6
Calls
2 calls:
59.0ms
(* (* z z) (+ z 1.0))
90.0ms
(/ (* x y) (* (* z z) (+ z 1.0)))

simplify988.0ms

Counts
61 → 61
Iterations

Useful iterations: 2 (265.0ms)

IterNodesCost
0116898
1377826
22037663
done5000663

prune140.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (+ z 1.0) (/ (pow z 2) y))
7.0b
(/ x (* (+ z 1.0) (/ (pow z 2) y)))
7.3b
(/ (pow z 2) y)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
55×times-frac
50×add-sqr-sqrt
40×*-un-lft-identity
38×add-cube-cbrt
34×add-exp-log
28×associate-*r*
22×unpow-prod-down
19×add-cbrt-cube
14×div-exp
11×associate-/l*
8×prod-exp unpow2 sqr-pow
6×cbrt-undiv
5×pow1 associate-/r/ unswap-sqr
4×frac-times flip3-+ associate-*l* associate-*l/ associate-/r* cbrt-unprod flip-+
3×expm1-log1p-u pow-to-exp pow-exp log1p-expm1-u div-inv add-log-exp
2×frac-2neg associate-*r/ clear-num
1×pow-prod-down *-commutative distribute-lft-out
Counts
3 → 142
Calls
3 calls:
24.0ms
(* (+ z 1.0) (/ (pow z 2) y))
8.0ms
(/ x (* (+ z 1.0) (/ (pow z 2) y)))
4.0ms
(/ (pow z 2) y)

series142.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(* (+ z 1.0) (/ (pow z 2) y))
70.0ms
(/ x (* (+ z 1.0) (/ (pow z 2) y)))
24.0ms
(/ (pow z 2) y)

simplify1.0s

Counts
151 → 151
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02311944
15521813
222301584
done50011575

prune435.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.5b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
73×add-exp-log
57×add-cbrt-cube
32×prod-exp cbrt-unprod
22×cbrt-undiv div-exp
11×*-un-lft-identity
10×associate-*l*
9×pow1 cbrt-prod add-sqr-sqrt add-cube-cbrt
5×frac-times associate-*r/
4×expm1-log1p-u times-frac log1p-expm1-u add-log-exp
3×pow1/3 pow-prod-down associate-*l/
2×associate-/r/
1×flip3-+ associate-*r* *-commutative flip-+ div-inv distribute-lft-out
Counts
4 → 99
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)
42.0ms
(* (/ (* (cbrt x) (cbrt x)) (+ z 1.0)) (* (/ (cbrt x) z) (/ y z)))

series713.0ms

Counts
4 → 12
Calls
4 calls:
205.0ms
(cbrt x)
199.0ms
(cbrt x)
204.0ms
(cbrt x)
104.0ms
(* (/ (* (cbrt x) (cbrt x)) (+ z 1.0)) (* (/ (cbrt x) z) (/ y z)))

simplify838.0ms

Counts
111 → 111
Iterations

Useful iterations: 2 (250.0ms)

IterNodesCost
01731910
15611813
221551176
done50011176

prune329.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (pow (cbrt x) 3) (+ z 1.0)) z)
0.6b
(cbrt x)
0.7b
(pow (cbrt x) 3)
3.4b
(* (/ (/ (pow (cbrt x) 3) (+ z 1.0)) z) (/ y z))

rewrite224.0ms

Algorithm
rewrite-expression-head
Rules
1015×times-frac
700×*-un-lft-identity
512×add-sqr-sqrt
448×add-cube-cbrt
238×associate-*l*
181×cbrt-prod
178×unpow-prod-down cube-prod
126×distribute-lft-out
78×associate-/l*
52×add-exp-log
31×sqr-pow
30×add-cbrt-cube
29×cube-mult unpow3
26×div-exp
16×unswap-sqr
14×associate-/r/
13×associate-*r*
12×cbrt-undiv
10×prod-exp div-inv
7×pow1 flip3-+ flip-+
6×cbrt-unprod
4×expm1-log1p-u pow-to-exp pow-exp log1p-expm1-u add-log-exp
3×pow-unpow associate-/r*
2×pow-pow pow1/3
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/ rem-cube-cbrt
Counts
4 → 676
Calls
4 calls:
33.0ms
(/ (/ (pow (cbrt x) 3) (+ z 1.0)) z)
1.0ms
(cbrt x)
2.0ms
(pow (cbrt x) 3)
128.0ms
(* (/ (/ (pow (cbrt x) 3) (+ z 1.0)) z) (/ y z))

series651.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(/ (/ (pow (cbrt x) 3) (+ z 1.0)) z)
214.0ms
(cbrt x)
260.0ms
(pow (cbrt x) 3)
103.0ms
(* (/ (/ (pow (cbrt x) 3) (+ z 1.0)) z) (/ y z))

simplify768.0ms

Counts
688 → 688
Iterations

Useful iterations: done (738.0ms)

IterNodesCost
062012760
1184310080
done500010064

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes184.0ms

Accuracy

40.4% (1.9b remaining)

Error of 1.9b against oracle of 0.0b and baseline of 3.2b

bsearch48.0ms

Steps
ItersRangePoint
6
-2.0962939869438485e-131
-1.6515814557998607e-132
-1.544292488324377e-131

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02553
13053
done3053

end0.0ms

sample527.0ms

Algorithm
intervals
Results
305.0ms10718×body80valid