Details

Time bar (total: 13.4s)

sample38.0ms

Algorithm
intervals
Results
16.0ms510×body80valid

simplify35.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01115
12415
24414
35814
46014
done6014

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b
(fma (/ x y) (/ x y) (/ (* z z) (* t t)))
19.2b
(/ (* z z) (* t t))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
4×cbrt-undiv div-exp prod-exp cbrt-unprod
2×pow1 add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity log1p-expm1-u add-log-exp
1×frac-2neg times-frac clear-num associate-/r* fma-udef div-inv associate-/l*
Counts
2 → 33
Calls
2 calls:
0.0ms
(fma (/ x y) (/ x y) (/ (* z z) (* t t)))
13.0ms
(/ (* z z) (* t t))

series160.0ms

Counts
2 → 6
Calls
2 calls:
126.0ms
(fma (/ x y) (/ x y) (/ (* z z) (* t t)))
33.0ms
(/ (* z z) (* t t))

simplify3.6s

Counts
39 → 39
Iterations

Useful iterations: done (3.6s)

IterNodesCost
066517
1153509
2520379
32009364
done5000354

prune109.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot (/ x y) (/ z t))
0.0b
(hypot (/ x y) (/ z t))
0.4b
(* (hypot (/ x y) (/ z t)) (hypot (/ x y) (/ z t)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×hypot-udef
5×add-exp-log add-cbrt-cube
3×expm1-log1p-u swap-sqr associate-*r* associate-*l* log1p-expm1-u add-log-exp
1×pow2 pow-plus sqrt-unprod pow-prod-down prod-exp rem-square-sqrt pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
Counts
3 → 49
Calls
3 calls:
0.0ms
(hypot (/ x y) (/ z t))
0.0ms
(hypot (/ x y) (/ z t))
8.0ms
(* (hypot (/ x y) (/ z t)) (hypot (/ x y) (/ z t)))

series339.0ms

Counts
3 → 9
Calls
3 calls:
97.0ms
(hypot (/ x y) (/ z t))
98.0ms
(hypot (/ x y) (/ z t))
144.0ms
(* (hypot (/ x y) (/ z t)) (hypot (/ x y) (/ z t)))

simplify1.2s

Counts
58 → 58
Iterations

Useful iterations: done (1.2s)

IterNodesCost
050831
1104748
2253629
3654547
41823538
done5000508

prune164.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (hypot (/ x y) (/ z t)) (* (sqrt (hypot (/ x y) (/ z t))) (sqrt (hypot (/ x y) (/ z t)))))
0.5b
(* (sqrt (hypot (/ x y) (/ z t))) (sqrt (hypot (/ x y) (/ z t))))
2.4b
(sqrt (hypot (/ x y) (/ z t)))
2.4b
(sqrt (hypot (/ x y) (/ z t)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
38×pow1
31×add-sqr-sqrt
24×sqrt-prod
16×sqrt-pow1 pow1/2
15×add-cube-cbrt *-un-lft-identity pow-prod-up
11×add-exp-log add-cbrt-cube
9×swap-sqr associate-*l*
7×associate-*r*
6×pow-prod-down
5×pow-sqr unswap-sqr
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×sqrt-unprod
2×rem-sqrt-square *-commutative
1×pow2 hypot-udef pow-plus rem-square-sqrt
Counts
4 → 110
Calls
4 calls:
28.0ms
(* (hypot (/ x y) (/ z t)) (* (sqrt (hypot (/ x y) (/ z t))) (sqrt (hypot (/ x y) (/ z t)))))
16.0ms
(* (sqrt (hypot (/ x y) (/ z t))) (sqrt (hypot (/ x y) (/ z t))))
1.0ms
(sqrt (hypot (/ x y) (/ z t)))
1.0ms
(sqrt (hypot (/ x y) (/ z t)))

series434.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(* (hypot (/ x y) (/ z t)) (* (sqrt (hypot (/ x y) (/ z t))) (sqrt (hypot (/ x y) (/ z t)))))
92.0ms
(* (sqrt (hypot (/ x y) (/ z t))) (sqrt (hypot (/ x y) (/ z t))))
95.0ms
(sqrt (hypot (/ x y) (/ z t)))
95.0ms
(sqrt (hypot (/ x y) (/ z t)))

simplify2.1s

Counts
122 → 122
Iterations

Useful iterations: done (2.1s)

IterNodesCost
0992276
11831398
24481133
313021100
done50001078

prune500.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* (sqrt (sqrt (hypot (/ x y) (/ z t)))) (sqrt (sqrt (hypot (/ x y) (/ z t))))) (sqrt (hypot (/ x y) (/ z t))))
2.4b
(sqrt (hypot (/ x y) (/ z t)))
2.4b
(sqrt (hypot (/ x y) (/ z t)))
2.4b
(sqrt (hypot (/ x y) (/ z t)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
60×sqrt-pow1
51×pow1
36×pow1/2
34×pow-prod-up
16×add-sqr-sqrt
14×sqrt-prod
9×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
8×pow-sqr
7×pow-prod-down
6×pow-plus associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square prod-exp cbrt-unprod
2×sqrt-unprod swap-sqr unswap-sqr
1×associate-*l* *-commutative
Counts
4 → 99
Calls
4 calls:
58.0ms
(* (* (sqrt (sqrt (hypot (/ x y) (/ z t)))) (sqrt (sqrt (hypot (/ x y) (/ z t))))) (sqrt (hypot (/ x y) (/ z t))))
2.0ms
(sqrt (hypot (/ x y) (/ z t)))
1.0ms
(sqrt (hypot (/ x y) (/ z t)))
1.0ms
(sqrt (hypot (/ x y) (/ z t)))

series374.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(* (* (sqrt (sqrt (hypot (/ x y) (/ z t)))) (sqrt (sqrt (hypot (/ x y) (/ z t))))) (sqrt (hypot (/ x y) (/ z t))))
90.0ms
(sqrt (hypot (/ x y) (/ z t)))
94.0ms
(sqrt (hypot (/ x y) (/ z t)))
95.0ms
(sqrt (hypot (/ x y) (/ z t)))

simplify2.2s

Counts
111 → 111
Iterations

Useful iterations: 3 (175.0ms)

IterNodesCost
0891812
1177895
2325814
3470799
4718799
51960799
done5000799

prune236.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes579.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01236
11436
done1436

end0.0ms

sample1.1s

Algorithm
intervals
Results
514.0ms15511×body80valid