Details

Time bar (total: 10.4s)

sample41.0ms

Algorithm
intervals
Results
20.0ms93×body1280valid
6.0ms131×body80valid
3.0ms17×body640valid
1.0ms9×body320valid
0.0ms6×body160valid

simplify67.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0912
11912
22412
32812
43012
53512
63612
done3612

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1.0 x)
0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b
(/ 1.0 (hypot 1.0 x))
2.0b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-sqr-sqrt
12×add-cube-cbrt
9×times-frac
8×add-log-exp
6×add-exp-log add-cbrt-cube
4×pow1
3×associate-/r* associate-/l*
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg flip3-+ diff-log div-exp clear-num sum-log flip-- flip-+ div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 60
Calls
4 calls:
0.0ms
(hypot 1.0 x)
23.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
10.0ms
(/ 1.0 (hypot 1.0 x))
13.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series169.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(hypot 1.0 x)
37.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
7.0ms
(/ 1.0 (hypot 1.0 x))
121.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.5s

Counts
72 → 72
Iterations

Useful iterations: 3 (874.0ms)

IterNodesCost
0101854
1220801
2766737
34740735
done5001735

prune257.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 16.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.5b
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
20×add-sqr-sqrt add-cube-cbrt
18×times-frac
8×add-exp-log add-cbrt-cube add-log-exp
6×associate-/r* associate-/l*
4×pow1
2×cbrt-undiv frac-2neg div-exp clear-num div-inv associate--r+
1×+-commutative distribute-rgt-in sub-neg flip3-- distribute-lft-in flip3-+ diff-log sum-log flip-- flip-+ distribute-lft-out
Counts
4 → 80
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
10.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
8.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series141.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(/ 1.0 (hypot 1.0 x))
9.0ms
(/ 1.0 (hypot 1.0 x))
85.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
34.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify841.0ms

Counts
92 → 92
Iterations

Useful iterations: done (837.0ms)

IterNodesCost
01091174
12771112
213681008
done50021003

prune318.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.5b
(- (* 1.0 (- 1.0 0.5)) (* (/ 1.0 (hypot 1.0 x)) 0.5))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
20×add-sqr-sqrt add-cube-cbrt
18×times-frac
8×add-exp-log add-cbrt-cube add-log-exp
6×associate-/r* associate-/l*
4×pow1 associate--l+
3×sub-neg
2×cbrt-undiv distribute-rgt-in flip3-- frac-2neg distribute-lft-in associate-*r/ div-exp associate-*l/ clear-num frac-sub flip-- div-inv
1×+-commutative flip3-+ diff-log sum-log flip-+ distribute-lft-out
Counts
4 → 84
Calls
4 calls:
10.0ms
(/ 1.0 (hypot 1.0 x))
10.0ms
(/ 1.0 (hypot 1.0 x))
12.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
40.0ms
(- (* 1.0 (- 1.0 0.5)) (* (/ 1.0 (hypot 1.0 x)) 0.5))

series185.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(/ 1.0 (hypot 1.0 x))
14.0ms
(/ 1.0 (hypot 1.0 x))
96.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
62.0ms
(- (* 1.0 (- 1.0 0.5)) (* (/ 1.0 (hypot 1.0 x)) 0.5))

simplify905.0ms

Counts
96 → 96
Iterations

Useful iterations: 2 (293.0ms)

IterNodesCost
01311276
13261216
213441110
done50021110

prune347.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(+ (* (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt 0.5)) 1.0)
0.5b
(* (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt 0.5))
1.5b
(- (* 1.0 (- 1.0 0.5)) (* (/ 1.0 (hypot 1.0 x)) 0.5))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
18×*-un-lft-identity
16×add-cube-cbrt
11×sqrt-prod
9×times-frac
8×pow1 add-exp-log add-cbrt-cube add-log-exp
7×associate-*l*
6×associate-*r*
4×associate-*l/ associate--l+ unswap-sqr
3×sub-neg pow-prod-down associate-/r* associate-/l*
2×distribute-rgt-in flip3-- distribute-lft-in sqrt-pow1 flip3-+ pow1/2 sqrt-div associate-*r/ frac-sub flip-- flip-+
1×cbrt-undiv +-commutative frac-2neg sqrt-unprod diff-log div-exp prod-exp clear-num sum-log *-commutative cbrt-unprod div-inv distribute-lft-out
Counts
4 → 89
Calls
4 calls:
7.0ms
(/ 1.0 (hypot 1.0 x))
43.0ms
(+ (* (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt 0.5)) 1.0)
80.0ms
(* (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt 0.5))
22.0ms
(- (* 1.0 (- 1.0 0.5)) (* (/ 1.0 (hypot 1.0 x)) 0.5))

series259.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(/ 1.0 (hypot 1.0 x))
92.0ms
(+ (* (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt 0.5)) 1.0)
119.0ms
(* (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt 0.5))
39.0ms
(- (* 1.0 (- 1.0 0.5)) (* (/ 1.0 (hypot 1.0 x)) 0.5))

simplify1.1s

Counts
101 → 101
Iterations

Useful iterations: 2 (368.0ms)

IterNodesCost
01721538
14171448
217021342
done50021342

prune357.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 16.1b

regimes267.0ms

Accuracy

0% (0.0b remaining)

Error of 15.2b against oracle of 15.2b and baseline of 15.2b

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02243
13143
done3143

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.5s2878×body1280valid
318.0ms4062×body80valid
174.0ms593×body640valid
53.0ms315×body320valid
16.0ms152×body160valid