Details

Time bar (total: 18.5s)

sample60.0ms

Algorithm
intervals
Results
39.0ms673×body80valid

simplify2.8s

Counts
1 → 1
Iterations
IterNodes
done5053
73274
6782
5232
4111
365
240
125
012

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.0b
(* 4.0 (* b b))
0.0b
(+ (* a a) (* b b))
0.4b
(pow (+ (* a a) (* b b)) 2.0)

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-exp-log
9×add-cbrt-cube
8×add-sqr-sqrt add-log-exp
7×*-un-lft-identity add-cube-cbrt
3×pow-unpow unpow-prod-down associate-*l* pow-prod-down prod-exp cbrt-unprod
2×+-commutative sum-log flip3-+ flip-+
1×pow-to-exp pow-pow associate-*r* pow-exp *-commutative unswap-sqr sqr-pow
Counts
4 → 58
Calls
4 calls:
43.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
13.0ms
(* 4.0 (* b b))
6.0ms
(+ (* a a) (* b b))
11.0ms
(pow (+ (* a a) (* b b)) 2.0)

series330.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
41.0ms
(* 4.0 (* b b))
43.0ms
(+ (* a a) (* b b))
148.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify1.2s

Counts
70 → 70
Iterations
IterNodes
done5006
21168
1369
0117

prune273.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
14.3b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
14.3b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
14.3b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite406.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 flip-+
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 87
Calls
4 calls:
311.0ms
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
24.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
26.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
40.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series854.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
252.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
236.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
189.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify1.9s

Counts
99 → 99
Iterations
IterNodes
done5004
32246
2759
1288
0121

prune542.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize96.0ms

Local error

Found 4 expressions with local error:

13.6b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
13.6b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
14.3b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
14.3b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-prod pow1 sqrt-prod
4×cbrt-div flip3-+ add-cbrt-cube sqrt-div add-exp-log flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
46.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
47.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
24.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
25.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series698.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
130.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
253.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
202.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify1.5s

Counts
68 → 68
Iterations
IterNodes
done5007
32062
2578
1205
093

prune467.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

localize163.0ms

Local error

Found 4 expressions with local error:

13.6b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
13.6b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
14.3b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
14.3b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-prod pow1 sqrt-prod
4×cbrt-div flip3-+ add-cbrt-cube sqrt-div add-exp-log flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
56.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
67.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
36.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
41.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series740.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
115.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
237.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
263.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify1.6s

Counts
68 → 68
Iterations
IterNodes
done5007
32062
2578
1205
093

prune573.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

regimes789.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify13.0ms

Iterations
IterNodes
done30
130
023

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.4s20710×body80valid