Details

Time bar (total: 2.8m)

sample278.0ms

Algorithm
intervals
Results
143.0ms1764×body80nan
19.0ms256×body80valid

simplify2.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
01516
12716
26115
315715
445915
5172515
done500115

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (+ (log (+ x y)) (log z)) t)
0.2b
(fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))
0.6b
(+ (log (+ x y)) (log z))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
49×*-un-lft-identity
28×pow1
25×log-pow distribute-lft-out
21×prod-diff
19×add-sqr-sqrt
17×add-cube-cbrt
7×log-prod fma-neg
6×add-log-exp
5×distribute-lft-out--
4×associate-+l- log-div associate-+l+ fma-def
3×add-exp-log expm1-log1p-u associate-+r+ flip3-+ add-cbrt-cube flip-+ log1p-expm1-u
2×associate--l- diff-log sum-log
1×+-commutative sub-neg flip3-- associate--l+ flip-- fma-udef difference-of-squares
Counts
3 → 92
Calls
3 calls:
81.0ms
(- (+ (log (+ x y)) (log z)) t)
1.0ms
(fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))
27.0ms
(+ (log (+ x y)) (log z))

series494.0ms

Counts
3 → 9
Calls
3 calls:
251.0ms
(- (+ (log (+ x y)) (log z)) t)
141.0ms
(fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))
101.0ms
(+ (log (+ x y)) (log z))

simplify933.0ms

Counts
101 → 101
Iterations

Useful iterations: done (929.0ms)

IterNodesCost
01701568
14051344
213941147
done50011084

prune523.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t)
0.2b
(fma (- a 0.5) (log t) (- (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t))
0.4b
(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))
0.5b
(+ (log (sqrt (+ x y))) (log z))

rewrite625.0ms

Algorithm
rewrite-expression-head
Rules
138×*-un-lft-identity
114×distribute-lft-out
90×pow1
88×log-pow
39×prod-diff
30×add-sqr-sqrt
28×add-cube-cbrt
17×log-prod
14×associate-+l+
13×fma-neg
12×fma-def
11×distribute-lft-out--
10×associate-+l- log-div sqrt-div add-log-exp
8×sqrt-prod
7×flip3-+ sum-log flip-+
4×add-exp-log associate--l- expm1-log1p-u associate-+r- associate-+r+ add-cbrt-cube log1p-expm1-u
3×diff-log
2×+-commutative sqrt-pow1 pow1/2
1×sub-neg flip3-- associate--l+ flip-- fma-udef difference-of-squares
Counts
4 → 172
Calls
4 calls:
540.0ms
(- (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t)
0.0ms
(fma (- a 0.5) (log t) (- (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t))
49.0ms
(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))
27.0ms
(+ (log (sqrt (+ x y))) (log z))

series773.0ms

Counts
4 → 12
Calls
4 calls:
217.0ms
(- (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t)
195.0ms
(fma (- a 0.5) (log t) (- (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t))
198.0ms
(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))
162.0ms
(+ (log (sqrt (+ x y))) (log z))

simplify1.6s

Counts
184 → 184
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02373665
16272754
224392244
done50022168

prune783.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (sqrt (+ x y)))
0.5b
(cbrt (sqrt (+ x y)))
0.5b
(cbrt (sqrt (+ x y)))
0.5b
(* (cbrt (sqrt (+ x y))) (cbrt (sqrt (+ x y))))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
69×cbrt-prod
44×add-sqr-sqrt
42×*-un-lft-identity
40×sqrt-prod
22×add-cube-cbrt
18×cbrt-div sqrt-div
14×swap-sqr
11×pow1
10×associate-*r* associate-*l*
9×flip3-+ pow1/3 flip-+ distribute-lft-out unswap-sqr
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 128
Calls
4 calls:
6.0ms
(cbrt (sqrt (+ x y)))
5.0ms
(cbrt (sqrt (+ x y)))
5.0ms
(cbrt (sqrt (+ x y)))
75.0ms
(* (cbrt (sqrt (+ x y))) (cbrt (sqrt (+ x y))))

series776.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(cbrt (sqrt (+ x y)))
183.0ms
(cbrt (sqrt (+ x y)))
175.0ms
(cbrt (sqrt (+ x y)))
244.0ms
(* (cbrt (sqrt (+ x y))) (cbrt (sqrt (+ x y))))

simplify1.2s

Counts
140 → 140
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01412042
13161838
214201730
done50011665

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (log (sqrt (+ x y))) (/ (+ (pow (log (sqrt (+ x y))) 3) (pow (log z) 3)) (fma (log (sqrt (+ x y))) (log (sqrt (+ x y))) (* (log z) (- (log z) (log (sqrt (+ x y))))))))
0.5b
(- (log z) (log (sqrt (+ x y))))
0.7b
(pow (log (sqrt (+ x y))) 3)
0.8b
(pow (log z) 3)

rewrite258.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
35×log-pow
34×pow1
29×add-sqr-sqrt
27×add-cube-cbrt
24×prod-diff
17×log-prod
10×unpow-prod-down cube-prod
8×sqrt-prod
7×associate-+l+ sqrt-pow1 pow1/2 associate--r+
6×add-exp-log pow-unpow fma-def add-cbrt-cube
5×add-log-exp
4×expm1-log1p-u log-div fma-neg sqrt-div log1p-expm1-u distribute-lft-out distribute-lft-out--
3×flip3-+ associate--l+ flip-+
2×cube-mult pow-to-exp associate-+l- pow-pow unpow3 pow-exp associate--r- rem-cube-cbrt sqr-pow
1×+-commutative sub-neg flip3-- diff-log sum-log flip-- difference-of-squares
Counts
4 → 147
Calls
4 calls:
206.0ms
(+ (log (sqrt (+ x y))) (/ (+ (pow (log (sqrt (+ x y))) 3) (pow (log z) 3)) (fma (log (sqrt (+ x y))) (log (sqrt (+ x y))) (* (log z) (- (log z) (log (sqrt (+ x y))))))))
27.0ms
(- (log z) (log (sqrt (+ x y))))
5.0ms
(pow (log (sqrt (+ x y))) 3)
10.0ms
(pow (log z) 3)

series2.3m

Counts
4 → 12
Calls
4 calls:
2.3m
(+ (log (sqrt (+ x y))) (/ (+ (pow (log (sqrt (+ x y))) 3) (pow (log z) 3)) (fma (log (sqrt (+ x y))) (log (sqrt (+ x y))) (* (log z) (- (log z) (log (sqrt (+ x y))))))))
174.0ms
(- (log z) (log (sqrt (+ x y))))
360.0ms
(pow (log (sqrt (+ x y))) 3)
257.0ms
(pow (log z) 3)

simplify3.4s

Counts
159 → 159
Iterations

Useful iterations: done (3.4s)

IterNodesCost
0114221695
1414719934
done500119680

prune2.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

regimes937.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02136
12536
done2536

end0.0ms

sample13.4s

Algorithm
intervals
Results
7.9s56261×body80nan
1.1s8031×body80valid