Details

Time bar (total: 25.8s)

sample107.0ms

Algorithm
intervals
Results
36.0ms47×body1280valid
21.0ms43×body640valid
12.0ms160×body80valid
7.0ms25×body320valid
6.0ms109×body80nan
3.0ms16×body160valid

simplify2.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
08302
115302
224302
352302
4151302
5506302
62074302
done5000302

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize35.0ms

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)))

rewrite157.0ms

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:
17.0ms
(/ x (+ x y))
63.0ms
(/ (exp (* x (log (/ x (+ x y))))) x)
32.0ms
(* x (log (/ x (+ x y))))
10.0ms
(log (/ x (+ x y)))

series458.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(/ x (+ x y))
203.0ms
(/ (exp (* x (log (/ x (+ x y))))) x)
111.0ms
(* x (log (/ x (+ x y))))
76.0ms
(log (/ x (+ x y)))

simplify3.5s

Counts
308 → 308
Iterations

Useful iterations: done (3.5s)

IterNodesCost
0478156937
1907146435
23235143683
done5000143658

prune2.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize112.0ms

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)))))

rewrite120.0ms

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:
17.0ms
(* (cbrt x) (cbrt x))
59.0ms
(* (cbrt (+ x y)) (cbrt (+ x y)))
8.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
22.0ms
(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

series777.0ms

Counts
4 → 12
Calls
4 calls:
304.0ms
(* (cbrt x) (cbrt x))
260.0ms
(* (cbrt (+ x y)) (cbrt (+ x y)))
104.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
108.0ms
(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

simplify2.2s

Counts
199 → 199
Iterations

Useful iterations: 2 (827.0ms)

IterNodesCost
029886805
166175597
2343474905
done500074905

prune1.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize75.0ms

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))))

rewrite46.0ms

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))))
10.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
19.0ms
(log (/ (cbrt x) (cbrt (+ x y))))

series691.0ms

Counts
4 → 12
Calls
4 calls:
311.0ms
(cbrt x)
134.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
133.0ms
(log (/ (cbrt x) (cbrt (+ x y))))
113.0ms
(log (/ (cbrt x) (cbrt (+ x y))))

simplify2.1s

Counts
208 → 208
Iterations

Useful iterations: 3 (847.0ms)

IterNodesCost
0177122639
1325113006
2799112658
33163112498
done5001112498

prune1.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize72.0ms

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 (* (cbrt (+ x y)) (cbrt (+ x y))))) (log (/ x (cbrt (+ x y)))))

rewrite270.0ms

Algorithm
rewrite-expression-head
Rules
80×*-un-lft-identity
55×log-prod
52×cbrt-prod add-sqr-sqrt
44×add-cube-cbrt
42×times-frac
38×pow1
28×fma-def
27×associate-+r+ log-pow
21×distribute-lft-out
19×pow1/3
18×cbrt-div distribute-rgt-neg-in
12×distribute-lft-neg-in
10×flip3-+ flip-+
9×swap-sqr add-exp-log
8×pow-prod-down
7×associate-*r* associate-*l*
6×pow-sqr pow-prod-up
5×add-log-exp
4×expm1-log1p-u frac-times add-cbrt-cube associate-/r/ log1p-expm1-u unswap-sqr
3×pow2 pow-plus
2×log-div sum-log rem-log-exp associate-*l/ associate-*r/ div-inv
1×neg-sub0 +-commutative associate-+l+ distribute-neg-in associate-+r- neg-mul-1 div-exp neg-log prod-exp *-commutative associate-+l- cbrt-unprod
Counts
4 → 191
Calls
4 calls:
3.0ms
(cbrt (+ x y))
51.0ms
(* (cbrt (+ x y)) (cbrt (+ x y)))
6.0ms
(log (/ x (cbrt (+ x y))))
201.0ms
(+ (- (log (* (cbrt (+ x y)) (cbrt (+ x y))))) (log (/ x (cbrt (+ x y)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
204.0ms
(cbrt (+ x y))
209.0ms
(* (cbrt (+ x y)) (cbrt (+ x y)))
243.0ms
(log (/ x (cbrt (+ x y))))
391.0ms
(+ (- (log (* (cbrt (+ x y)) (cbrt (+ x y))))) (log (/ x (cbrt (+ x y)))))

simplify1.8s

Counts
203 → 203
Iterations

Useful iterations: done (1.8s)

IterNodesCost
027876527
164365425
2242362341
done500161139

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes127.0ms

Accuracy

97.4% (0.2b remaining)

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

bsearch101.0ms

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

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0231064
1291064
done291064

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.1s1478×body1280valid
1.0s1550×body640valid
418.0ms4791×body80valid
227.0ms2943×body80nan
221.0ms826×body320valid
78.0ms480×body160valid