Details

Time bar (total: 12.8s)

sample32.0ms

Algorithm
intervals
Results
15.0ms270×body80valid

simplify152.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
0911
12111
24010
36710
410210
513910
614410
done14410

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.1b

localize11.0ms

Local error

Found 2 expressions with local error:

3.4b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
5.4b
(* y (+ 1.0 (* z z)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
20×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
16×add-exp-log add-cbrt-cube
13×associate-/l*
6×cbrt-undiv div-exp
4×pow1 associate-*r/
3×associate-*r* associate-*l* prod-exp cbrt-unprod div-inv
2×expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num associate-/r* *-commutative associate-/l/ unswap-sqr
Counts
2 → 74
Calls
2 calls:
16.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
16.0ms
(* y (+ 1.0 (* z z)))

series150.0ms

Counts
2 → 6
Calls
2 calls:
80.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
70.0ms
(* y (+ 1.0 (* z z)))

simplify1.1s

Counts
80 → 80
Iterations

Useful iterations: 2 (428.0ms)

IterNodesCost
01601102
14461075
22244866
done5001866

prune265.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.9b

localize21.0ms

Local error

Found 2 expressions with local error:

2.7b
(* (/ (* (cbrt 1.0) (cbrt 1.0)) y) (/ (/ (cbrt 1.0) x) (fma z z 1.0)))
3.4b
(/ (/ (cbrt 1.0) x) (fma z z 1.0))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
275×times-frac
167×add-sqr-sqrt
141×add-cube-cbrt *-un-lft-identity
70×associate-*r*
65×cbrt-prod
43×add-exp-log
33×add-cbrt-cube
22×associate-/l*
18×cbrt-undiv div-exp
12×prod-exp cbrt-unprod
10×div-inv
8×unswap-sqr
7×associate-*l*
4×pow1
3×associate-/r*
2×expm1-log1p-u log1p-expm1-u add-log-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
2 → 225
Calls
2 calls:
90.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) y) (/ (/ (cbrt 1.0) x) (fma z z 1.0)))
21.0ms
(/ (/ (cbrt 1.0) x) (fma z z 1.0))

series319.0ms

Counts
2 → 6
Calls
2 calls:
177.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) y) (/ (/ (cbrt 1.0) x) (fma z z 1.0)))
142.0ms
(/ (/ (cbrt 1.0) x) (fma z z 1.0))

simplify574.0ms

Counts
231 → 231
Iterations

Useful iterations: done (565.0ms)

IterNodesCost
03694954
112394732
done50004416

prune854.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (sqrt (cbrt 1.0)) (sqrt (fma z z 1.0))) (/ (* (cbrt 1.0) (cbrt 1.0)) y))
1.7b
(* (* (/ (sqrt (cbrt 1.0)) (sqrt (fma z z 1.0))) (/ (* (cbrt 1.0) (cbrt 1.0)) y)) (/ (/ (sqrt (cbrt 1.0)) x) (sqrt (fma z z 1.0))))
15.7b
(sqrt (fma z z 1.0))
15.7b
(sqrt (fma z z 1.0))

rewrite325.0ms

Algorithm
rewrite-expression-head
Rules
424×times-frac
284×sqrt-prod
264×add-sqr-sqrt
222×add-cube-cbrt *-un-lft-identity
197×associate-*r*
133×add-exp-log
117×add-cbrt-cube
76×cbrt-prod
59×associate-*l*
53×prod-exp cbrt-unprod
49×cbrt-undiv div-exp
14×unswap-sqr
13×pow1
9×div-inv
6×frac-times associate-*l/
4×expm1-log1p-u associate-*r/ pow-prod-down log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 *-commutative
Counts
4 → 387
Calls
4 calls:
56.0ms
(* (/ (sqrt (cbrt 1.0)) (sqrt (fma z z 1.0))) (/ (* (cbrt 1.0) (cbrt 1.0)) y))
236.0ms
(* (* (/ (sqrt (cbrt 1.0)) (sqrt (fma z z 1.0))) (/ (* (cbrt 1.0) (cbrt 1.0)) y)) (/ (/ (sqrt (cbrt 1.0)) x) (sqrt (fma z z 1.0))))
2.0ms
(sqrt (fma z z 1.0))
2.0ms
(sqrt (fma z z 1.0))

series1.0s

Counts
4 → 12
Calls
4 calls:
712.0ms
(* (/ (sqrt (cbrt 1.0)) (sqrt (fma z z 1.0))) (/ (* (cbrt 1.0) (cbrt 1.0)) y))
169.0ms
(* (* (/ (sqrt (cbrt 1.0)) (sqrt (fma z z 1.0))) (/ (* (cbrt 1.0) (cbrt 1.0)) y)) (/ (/ (sqrt (cbrt 1.0)) x) (sqrt (fma z z 1.0))))
76.0ms
(sqrt (fma z z 1.0))
78.0ms
(sqrt (fma z z 1.0))

simplify1.3s

Counts
399 → 399
Iterations

Useful iterations: done (1.3s)

IterNodesCost
061712380
1226411335
done500010263

prune1.6s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (/ (* (cbrt 1.0) (cbrt 1.0)) y))
0.6b
(cbrt (/ (* (cbrt 1.0) (cbrt 1.0)) y))
2.4b
(* (* (cbrt (/ (* (cbrt 1.0) (cbrt 1.0)) y)) (cbrt (/ (* (cbrt 1.0) (cbrt 1.0)) y))) (* (cbrt (/ (* (cbrt 1.0) (cbrt 1.0)) y)) (/ (/ (cbrt 1.0) x) (fma z z 1.0))))
3.4b
(/ (/ (cbrt 1.0) x) (fma z z 1.0))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
83×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
50×cbrt-prod
41×add-exp-log
26×cbrt-div
24×add-cbrt-cube
22×associate-/l*
18×prod-exp cbrt-unprod
17×frac-times
16×pow1
11×associate-*r/ associate-*l/
9×cbrt-undiv div-exp
8×pow-prod-down
7×div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r*
2×pow1/3
1×frac-2neg associate-*r* associate-*l* clear-num *-commutative associate-/l/
Counts
4 → 191
Calls
4 calls:
5.0ms
(cbrt (/ (* (cbrt 1.0) (cbrt 1.0)) y))
5.0ms
(cbrt (/ (* (cbrt 1.0) (cbrt 1.0)) y))
119.0ms
(* (* (cbrt (/ (* (cbrt 1.0) (cbrt 1.0)) y)) (cbrt (/ (* (cbrt 1.0) (cbrt 1.0)) y))) (* (cbrt (/ (* (cbrt 1.0) (cbrt 1.0)) y)) (/ (/ (cbrt 1.0) x) (fma z z 1.0))))
19.0ms
(/ (/ (cbrt 1.0) x) (fma z z 1.0))

series1.2s

Counts
4 → 12
Calls
4 calls:
459.0ms
(cbrt (/ (* (cbrt 1.0) (cbrt 1.0)) y))
393.0ms
(cbrt (/ (* (cbrt 1.0) (cbrt 1.0)) y))
178.0ms
(* (* (cbrt (/ (* (cbrt 1.0) (cbrt 1.0)) y)) (cbrt (/ (* (cbrt 1.0) (cbrt 1.0)) y))) (* (cbrt (/ (* (cbrt 1.0) (cbrt 1.0)) y)) (/ (/ (cbrt 1.0) x) (fma z z 1.0))))
129.0ms
(/ (/ (cbrt 1.0) x) (fma z z 1.0))

simplify1.7s

Counts
203 → 203
Iterations

Useful iterations: done (1.7s)

IterNodesCost
03454780
19094388
239843655
done50013439

prune856.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.9b

regimes176.0ms

Accuracy

0% (1.7b remaining)

Error of 6.7b against oracle of 5.0b and baseline of 6.7b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01117
11217
done1217

end0.0ms

sample798.0ms

Algorithm
intervals
Results
419.0ms8610×body80valid