Details

Time bar (total: 39.5s)

sample387.0ms

Algorithm
intervals
Results
216.0ms1942×body80nan
23.0ms257×body80valid

simplify9.1s

Counts
1 → 1
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
01516
12716
26115
315515
435615
585815
6159815
7219415
8261815
9263015
done263015

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

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))
0.5b
(+ (log (+ x y)) (log z))

rewrite171.0ms

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:
148.0ms
(- (+ (log (+ x y)) (log z)) t)
0.0ms
(fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))
15.0ms
(+ (log (+ x y)) (log z))

series547.0ms

Counts
3 → 9
Calls
3 calls:
289.0ms
(- (+ (log (+ x y)) (log z)) t)
131.0ms
(fma (- a 0.5) (log t) (- (+ (log (+ x y)) (log z)) t))
127.0ms
(+ (log (+ x y)) (log z))

simplify2.8s

Counts
101 → 101
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
01701568
13881337
210001146
339211059
done50001059

prune453.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (log z) t)
0.2b
(fma (- a 0.5) (log t) (* 1 (+ (log (+ x y)) (- (log z) t))))
0.2b
(+ (log (+ x y)) (- (log z) t))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
24×add-sqr-sqrt prod-diff
22×add-cube-cbrt
17×pow1 associate-+r+
14×log-pow
10×log-prod
7×distribute-lft-out
6×associate--l+ distribute-lft-out-- add-log-exp
4×associate-+l+ fma-def fma-neg
3×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
2×associate-+l- sub-neg log-div flip3-+ diff-log sum-log flip-+
1×+-commutative associate-+r- flip3-- flip-- fma-udef difference-of-squares
Counts
3 → 94
Calls
3 calls:
11.0ms
(- (log z) t)
1.0ms
(fma (- a 0.5) (log t) (* 1 (+ (log (+ x y)) (- (log z) t))))
70.0ms
(+ (log (+ x y)) (- (log z) t))

series514.0ms

Counts
3 → 9
Calls
3 calls:
83.0ms
(- (log z) t)
150.0ms
(fma (- a 0.5) (log t) (* 1 (+ (log (+ x y)) (- (log z) t))))
281.0ms
(+ (log (+ x y)) (- (log z) t))

simplify3.5s

Counts
103 → 103
Iterations

Useful iterations: 3 (1.9s)

IterNodesCost
01851379
14251174
210471008
34355943
done5000943

prune583.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (sqrt (+ x y)))
0.2b
(fma (- a 0.5) (log t) (* 1 (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (- (log z) t)))))
0.2b
(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (- (log z) t)))
0.2b
(+ (log (sqrt (+ x y))) (- (log z) t))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
68×*-un-lft-identity
35×pow1 distribute-lft-out
34×log-pow
24×log-prod
20×add-sqr-sqrt add-cube-cbrt
18×associate-+r+
14×associate-+l+
12×fma-def prod-diff sqrt-prod distribute-lft-out--
9×add-log-exp
8×log-div sqrt-div
7×sum-log
6×associate-+l- flip3-+ flip-+
5×add-exp-log associate-+r-
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×sqrt-pow1 pow1/2 associate--l+
2×+-commutative diff-log
1×sub-neg rem-log-exp fma-udef
Counts
4 → 133
Calls
4 calls:
11.0ms
(log (sqrt (+ x y)))
1.0ms
(fma (- a 0.5) (log t) (* 1 (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (- (log z) t)))))
110.0ms
(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (- (log z) t)))
53.0ms
(+ (log (sqrt (+ x y))) (- (log z) t))

series790.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(log (sqrt (+ x y)))
224.0ms
(fma (- a 0.5) (log t) (* 1 (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (- (log z) t)))))
247.0ms
(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (- (log z) t)))
202.0ms
(+ (log (sqrt (+ x y))) (- (log z) t))

simplify1.2s

Counts
145 → 145
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02362219
15911882
216131651
done50011543

prune815.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (+ (log (fabs (cbrt (+ x y)))) (log (sqrt (cbrt (+ x y))))) (- (log z) t))
0.2b
(+ (log (fabs (cbrt (+ x y)))) (log (sqrt (cbrt (+ x y)))))
0.5b
(cbrt (+ x y))
0.5b
(cbrt (+ x y))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
69×*-un-lft-identity
38×distribute-lft-out
33×pow1
29×log-pow
27×associate-+r+
20×add-sqr-sqrt add-cube-cbrt
16×log-prod
12×cbrt-prod prod-diff
11×fma-def
10×distribute-lft-out-- add-log-exp
8×cbrt-div flip3-+ flip-+
7×sum-log sqrt-prod
5×associate-+r-
4×add-exp-log expm1-log1p-u log-div associate-+l+ sqrt-div frac-add add-cbrt-cube log1p-expm1-u
3×associate--l+
2×+-commutative associate-+l- flip3-- pow1/3 diff-log flip--
1×sub-neg
Counts
4 → 131
Calls
4 calls:
131.0ms
(+ (+ (log (fabs (cbrt (+ x y)))) (log (sqrt (cbrt (+ x y))))) (- (log z) t))
34.0ms
(+ (log (fabs (cbrt (+ x y)))) (log (sqrt (cbrt (+ x y)))))
8.0ms
(cbrt (+ x y))
8.0ms
(cbrt (+ x y))

series1.2s

Counts
4 → 12
Calls
4 calls:
488.0ms
(+ (+ (log (fabs (cbrt (+ x y)))) (log (sqrt (cbrt (+ x y))))) (- (log z) t))
285.0ms
(+ (log (fabs (cbrt (+ x y)))) (log (sqrt (cbrt (+ x y)))))
202.0ms
(cbrt (+ x y))
191.0ms
(cbrt (+ x y))

simplify1.1s

Counts
143 → 143
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02552602
16602421
218082282
done50012249

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes585.0ms

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: 1 (2.0ms)

IterNodesCost
02432
13130
done3130

end0.0ms

sample14.1s

Algorithm
intervals
Results
8.0s56457×body80nan
1.6s8035×body80valid