Details

Time bar (total: 11.5s)

sample36.0ms

Algorithm
intervals
Results
19.0ms513×body80valid

simplify24.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01115
12415
24414
35814
46014
done6014

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.6b

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b
(fma (/ x y) (/ x y) (/ (* z z) (* t t)))
23.4b
(/ (* z z) (* t t))

rewrite6.0ms

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)))
5.0ms
(/ (* z z) (* t t))

series121.0ms

Counts
2 → 6
Calls
2 calls:
94.0ms
(fma (/ x y) (/ x y) (/ (* z z) (* t t)))
28.0ms
(/ (* z z) (* t t))

simplify2.4s

Counts
39 → 39
Iterations

Useful iterations: 3 (713.0ms)

IterNodesCost
066517
1169509
2635379
34823364
done5000364

prune103.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot (/ x y) (/ z t))
0.0b
(hypot (/ x y) (/ z t))
0.5b
(* (hypot (/ x y) (/ z t)) (hypot (/ x y) (/ z t)))

rewrite5.0ms

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))
3.0ms
(* (hypot (/ x y) (/ z t)) (hypot (/ x y) (/ z t)))

series274.0ms

Counts
3 → 9
Calls
3 calls:
77.0ms
(hypot (/ x y) (/ z t))
77.0ms
(hypot (/ x y) (/ z t))
119.0ms
(* (hypot (/ x y) (/ z t)) (hypot (/ x y) (/ z t)))

simplify736.0ms

Counts
58 → 58
Iterations

Useful iterations: 3 (153.0ms)

IterNodesCost
050831
1103748
2285629
31361547
done5001547

prune155.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (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))))
1.4b
(sqrt (hypot (/ x y) (/ z t)))
1.4b
(sqrt (hypot (/ x y) (/ z t)))

rewrite25.0ms

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:
14.0ms
(* (hypot (/ x y) (/ z t)) (* (sqrt (hypot (/ x y) (/ z t))) (sqrt (hypot (/ x y) (/ z t)))))
7.0ms
(* (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)))

series351.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(* (hypot (/ x y) (/ z t)) (* (sqrt (hypot (/ x y) (/ z t))) (sqrt (hypot (/ x y) (/ z t)))))
74.0ms
(* (sqrt (hypot (/ x y) (/ z t))) (sqrt (hypot (/ x y) (/ z t))))
76.0ms
(sqrt (hypot (/ x y) (/ z t)))
77.0ms
(sqrt (hypot (/ x y) (/ z t)))

simplify2.7s

Counts
122 → 122
Iterations

Useful iterations: 3 (550.0ms)

IterNodesCost
0992276
12031398
25381133
331811100
done50011100

prune269.0ms

Pruning

15 alts after pruning (14 fresh and 1 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))))
1.4b
(sqrt (hypot (/ x y) (/ z t)))
1.4b
(sqrt (hypot (/ x y) (/ z t)))
1.4b
(sqrt (hypot (/ x y) (/ z t)))

rewrite41.0ms

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:
33.0ms
(* (* (sqrt (sqrt (hypot (/ x y) (/ z t)))) (sqrt (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)))
1.0ms
(sqrt (hypot (/ x y) (/ z t)))

series302.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (* (sqrt (sqrt (hypot (/ x y) (/ z t)))) (sqrt (sqrt (hypot (/ x y) (/ z t))))) (sqrt (hypot (/ x y) (/ z t))))
76.0ms
(sqrt (hypot (/ x y) (/ z t)))
76.0ms
(sqrt (hypot (/ x y) (/ z t)))
71.0ms
(sqrt (hypot (/ x y) (/ z t)))

simplify2.3s

Counts
111 → 111
Iterations

Useful iterations: 3 (682.0ms)

IterNodesCost
0891812
1201895
2469814
32507799
done5001799

prune221.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes361.0ms

Accuracy

0% (0.7b 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
01747
12147
done2147

end0.0ms

sample953.0ms

Algorithm
intervals
Results
569.0ms15465×body80valid