Details

Time bar (total: 19.1s)

sample82.0ms

Algorithm
intervals
Results
45.0ms516×body80valid

simplify43.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01115
12415
24414
35814
46014
done6014

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.7b

localize30.0ms

Local error

Found 2 expressions with local error:

0.2b
(fma (/ x y) (/ x y) (/ (* z z) (* t t)))
23.3b
(/ (* z z) (* t t))

rewrite16.0ms

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)))
15.0ms
(/ (* z z) (* t t))

series167.0ms

Counts
2 → 6
Calls
2 calls:
133.0ms
(fma (/ x y) (/ x y) (/ (* z z) (* t t)))
34.0ms
(/ (* z z) (* t t))

simplify6.0s

Counts
39 → 39
Iterations

Useful iterations: done (6.0s)

IterNodesCost
066517
1153509
2520379
32009364
done5000354

prune131.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

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)))

rewrite10.0ms

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))
9.0ms
(* (hypot (/ x y) (/ z t)) (hypot (/ x y) (/ z t)))

series435.0ms

Counts
3 → 9
Calls
3 calls:
148.0ms
(hypot (/ x y) (/ z t))
108.0ms
(hypot (/ x y) (/ z t))
178.0ms
(* (hypot (/ x y) (/ z t)) (hypot (/ x y) (/ z t)))

simplify1.9s

Counts
58 → 58
Iterations

Useful iterations: done (1.9s)

IterNodesCost
050831
1104748
2253629
3654547
41823538
done5000508

prune234.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* (/ x y) (/ x y)) (* (/ z t) (/ z t)))
0.3b
(* (/ x y) (/ x y))
0.3b
(* (/ z t) (/ z t))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
83×add-sqr-sqrt
80×times-frac
59×add-cube-cbrt *-un-lft-identity
27×add-exp-log add-cbrt-cube
26×swap-sqr associate-*r* associate-*l*
17×pow1
9×frac-add
8×cbrt-undiv frac-times associate-*r/ div-exp associate-*l/ prod-exp cbrt-unprod div-inv unswap-sqr
5×add-log-exp
3×expm1-log1p-u log1p-expm1-u
2×pow2 pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up
1×+-commutative fma-def flip3-+ sum-log flip-+
Counts
3 → 161
Calls
3 calls:
15.0ms
(+ (* (/ x y) (/ x y)) (* (/ z t) (/ z t)))
23.0ms
(* (/ x y) (/ x y))
33.0ms
(* (/ z t) (/ z t))

series206.0ms

Counts
3 → 9
Calls
3 calls:
134.0ms
(+ (* (/ x y) (/ x y)) (* (/ z t) (/ z t)))
33.0ms
(* (/ x y) (/ x y))
39.0ms
(* (/ z t) (/ z t))

simplify2.3s

Counts
170 → 170
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02612272
17841991
227511709
done50011661

prune578.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* (sqrt (hypot (/ x y) (/ z t))) (sqrt (hypot (/ x y) (/ z t)))) (hypot (/ x y) (/ z t)))
0.5b
(* (sqrt (hypot (/ x y) (/ z t))) (sqrt (hypot (/ x y) (/ z t))))
2.3b
(sqrt (hypot (/ x y) (/ z t)))
2.3b
(sqrt (hypot (/ x y) (/ z t)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
44×pow1
31×add-sqr-sqrt
24×sqrt-prod
22×sqrt-pow1 pow1/2
19×pow-prod-up
15×add-cube-cbrt *-un-lft-identity
11×add-exp-log add-cbrt-cube
9×swap-sqr associate-*r*
7×pow-plus associate-*l* pow-sqr
6×pow-prod-down
5×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 rem-square-sqrt
Counts
4 → 116
Calls
4 calls:
46.0ms
(* (* (sqrt (hypot (/ x y) (/ z t))) (sqrt (hypot (/ x y) (/ z t)))) (hypot (/ x y) (/ z t)))
19.0ms
(* (sqrt (hypot (/ x y) (/ z t))) (sqrt (hypot (/ x y) (/ z t))))
2.0ms
(sqrt (hypot (/ x y) (/ z t)))
2.0ms
(sqrt (hypot (/ x y) (/ z t)))

series591.0ms

Counts
4 → 12
Calls
4 calls:
223.0ms
(* (* (sqrt (hypot (/ x y) (/ z t))) (sqrt (hypot (/ x y) (/ z t)))) (hypot (/ x y) (/ z t)))
130.0ms
(* (sqrt (hypot (/ x y) (/ z t))) (sqrt (hypot (/ x y) (/ z t))))
121.0ms
(sqrt (hypot (/ x y) (/ z t)))
117.0ms
(sqrt (hypot (/ x y) (/ z t)))

simplify3.0s

Counts
128 → 128
Iterations

Useful iterations: done (3.0s)

IterNodesCost
0992319
11931445
25301220
318981112
done50001086

prune366.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

regimes358.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01025
11125
done1125

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.7s15582×body80valid