Details

Time bar (total: 20.8s)

sample74.0ms

Algorithm
intervals
Results
23.0ms47×body1280valid
12.0ms43×body640valid
8.0ms160×body80valid
5.0ms25×body320valid
4.0ms109×body80nan
2.0ms16×body160valid

simplify1.4s

Counts
1 → 1
Iterations
IterNodes
done5000
62074
5506
4151
352
224
115
08

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (+ x y))
0.0b
(/ (exp (* x (log (/ x (+ x y))))) x)
0.1b
(* x (log (/ x (+ x y))))
8.6b
(log (/ x (+ x y)))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
261×times-frac
221×*-un-lft-identity
198×log-prod
149×add-sqr-sqrt
147×add-cube-cbrt
144×exp-sum
90×distribute-rgt-in distribute-lft-in
42×associate-/l*
37×distribute-lft-out
24×associate-/r/
13×div-inv
12×flip3-+ add-exp-log flip-+
10×add-cbrt-cube
8×pow1
7×associate-/r*
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
3×div-exp associate-*l*
2×cbrt-undiv clear-num frac-2neg rem-log-exp log-pow
1×log-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 296
Calls
4 calls:
16.0ms
(/ x (+ x y))
52.0ms
(/ (exp (* x (log (/ x (+ x y))))) x)
20.0ms
(* x (log (/ x (+ x y))))
5.0ms
(log (/ x (+ x y)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(/ x (+ x y))
162.0ms
(/ (exp (* x (log (/ x (+ x y))))) x)
92.0ms
(* x (log (/ x (+ x y))))
52.0ms
(log (/ x (+ x y)))

simplify2.1s

Counts
308 → 308
Iterations
IterNodes
done5000
23235
1907
0478

prune1.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt x) (cbrt x))
0.6b
(* (cbrt (+ x y)) (cbrt (+ x y)))
2.1b
(log (/ (cbrt x) (cbrt (+ x y))))
3.1b
(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
85×cbrt-prod
74×*-un-lft-identity
64×add-sqr-sqrt
61×log-prod
48×add-cube-cbrt
43×times-frac
26×cbrt-div
24×add-exp-log
20×pow1
15×swap-sqr
13×flip3-+ associate-*r* associate-*l* flip-+
12×pow1/3 distribute-lft-out
10×associate-/r/
8×frac-times unswap-sqr
7×rem-log-exp
6×prod-exp
5×div-exp
4×expm1-log1p-u add-cbrt-cube pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up log1p-expm1-u add-log-exp
2×pow2 log-div pow-plus log-pow *-commutative cbrt-unprod div-inv
Counts
4 → 187
Calls
4 calls:
9.0ms
(* (cbrt x) (cbrt x))
33.0ms
(* (cbrt (+ x y)) (cbrt (+ x y)))
7.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
16.0ms
(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

series788.0ms

Counts
4 → 12
Calls
4 calls:
293.0ms
(* (cbrt x) (cbrt x))
277.0ms
(* (cbrt (+ x y)) (cbrt (+ x y)))
106.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
113.0ms
(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

simplify1.9s

Counts
199 → 199
Iterations
IterNodes
done5000
23434
1661
0298

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt x)
2.1b
(log (/ (cbrt x) (cbrt (+ x y))))
2.1b
(log (/ (cbrt x) (cbrt (+ x y))))
2.1b
(log (/ (cbrt x) (cbrt (+ x y))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
144×log-prod
138×cbrt-prod
126×times-frac
122×*-un-lft-identity
86×add-sqr-sqrt add-cube-cbrt
18×distribute-lft-out
13×add-exp-log
7×pow1
6×cbrt-div rem-log-exp associate-/r/
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×log-div flip3-+ div-exp log-pow flip-+ div-inv
1×pow1/3
Counts
4 → 196
Calls
4 calls:
1.0ms
(cbrt x)
7.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
7.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
7.0ms
(log (/ (cbrt x) (cbrt (+ x y))))

series488.0ms

Counts
4 → 12
Calls
4 calls:
207.0ms
(cbrt x)
82.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
103.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
95.0ms
(log (/ (cbrt x) (cbrt (+ x y))))

simplify1.3s

Counts
208 → 208
Iterations
IterNodes
done5001
33163
2799
1325
0177

prune1.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ x y))
0.6b
(* (cbrt (+ x y)) (cbrt (+ x y)))
1.2b
(log (/ x (cbrt (+ x y))))
2.4b
(+ (log (/ 1 (* (cbrt (+ x y)) (cbrt (+ x y))))) (log (/ x (cbrt (+ x y)))))

rewrite283.0ms

Algorithm
rewrite-expression-head
Rules
76×*-un-lft-identity
69×log-prod
52×cbrt-prod add-sqr-sqrt
45×times-frac
44×add-cube-cbrt
30×cbrt-div
27×associate-+r+
25×pow1
17×distribute-lft-out
16×flip3-+ log-pow flip-+
15×associate-+l+
14×fma-def
13×pow1/3
12×associate-/r/
9×swap-sqr add-exp-log pow-flip
8×frac-times
7×associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up log1p-expm1-u add-log-exp unswap-sqr
3×log-div div-inv
2×pow2 pow-plus rem-log-exp
1×+-commutative associate-+r- sum-log div-exp prod-exp *-commutative associate-+l- cbrt-unprod inv-pow
Counts
4 → 186
Calls
4 calls:
5.0ms
(cbrt (+ x y))
48.0ms
(* (cbrt (+ x y)) (cbrt (+ x y)))
6.0ms
(log (/ x (cbrt (+ x y))))
211.0ms
(+ (log (/ 1 (* (cbrt (+ x y)) (cbrt (+ x y))))) (log (/ x (cbrt (+ x y)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
169.0ms
(cbrt (+ x y))
219.0ms
(* (cbrt (+ x y)) (cbrt (+ x y)))
232.0ms
(log (/ x (cbrt (+ x y))))
453.0ms
(+ (log (/ 1 (* (cbrt (+ x y)) (cbrt (+ x y))))) (log (/ x (cbrt (+ x y)))))

simplify1.5s

Counts
198 → 198
Iterations
IterNodes
done5003
22610
1685
0305

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes107.0ms

Accuracy

97.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 6.1b

bsearch89.0ms

Steps
ItersRangePoint
9
1.6675236871481135e-12
5.1798647897020696e-05
5.105764663642185e-05
6
-3.812236742374531e+23
-6.2573470230411204e+22
-3.381665497082661e+23

simplify5.0ms

Iterations
IterNodes
done29
129
023

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.0s1478×body1280valid
650.0ms1550×body640valid
504.0ms480×body160valid
376.0ms4791×body80valid
235.0ms826×body320valid
189.0ms2943×body80nan