Details

Time bar (total: 8.0s)

sample31.0ms

Algorithm
intervals
Results
15.0ms92×body1280valid
4.0ms126×body80valid
2.0ms19×body640valid
1.0ms14×body320valid
0.0ms5×body160valid

simplify30.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0912
11912
22412
32812
43012
53512
63612
done3612

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.6b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
5×pow1
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×add-exp-log add-cube-cbrt sqrt-pow1 sqrt-div associate-*r/ add-cbrt-cube
1×sub-neg flip3-- flip3-+ pow1/2 diff-log pow-prod-down sqrt-prod flip-- flip-+ distribute-lft-out-- difference-of-squares
Counts
2 → 27
Calls
2 calls:
14.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series156.0ms

Counts
2 → 6
Calls
2 calls:
73.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
83.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.8s

Counts
33 → 33
Iterations

Useful iterations: done (1.8s)

IterNodesCost
064571
1139516
2350480
3964478
43190476
done5000470

prune71.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 17.6b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (* 1.0 (- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.1b
(- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
8×add-exp-log add-cbrt-cube add-log-exp
7×add-sqr-sqrt
6×pow1
5×add-cube-cbrt
4×times-frac associate-*r/ associate-/r*
3×distribute-lft-out
2×cbrt-undiv flip3-- sqrt-pow1 flip3-+ sqrt-div diff-log div-exp associate-/r/ flip-- flip-+ associate-/l/ distribute-lft-out--
1×sub-neg frac-2neg pow1/2 pow-prod-down prod-exp clear-num sum-log sqrt-prod cbrt-unprod div-inv associate-/l* associate--r+ difference-of-squares
Counts
3 → 57
Calls
3 calls:
52.0ms
(/ (* 1.0 (- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
11.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
35.0ms
(- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))

series285.0ms

Counts
3 → 9
Calls
3 calls:
180.0ms
(/ (* 1.0 (- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
73.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
31.0ms
(- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))

simplify901.0ms

Counts
66 → 66
Iterations

Useful iterations: done (899.0ms)

IterNodesCost
01261488
13361414
211241230
done50001228

prune157.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 17.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5)))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.1b
(- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))
2.1b
(log (exp (- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))))

rewrite301.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
15×add-log-exp
13×add-sqr-sqrt
12×exp-prod
8×pow1
7×add-cube-cbrt log-pow
6×distribute-lft-out--
5×log-prod
4×add-exp-log diff-log exp-sum add-cbrt-cube
3×sub-neg rem-exp-log distribute-lft-out difference-of-squares
2×sqrt-pow1 exp-diff sqrt-div associate-*r/ sum-log
1×log-div flip3-- flip3-+ pow1/2 rem-log-exp pow-prod-down sqrt-prod flip-- flip-+ associate--r+
Counts
4 → 70
Calls
4 calls:
126.0ms
(exp (- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5)))
11.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
33.0ms
(- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))
129.0ms
(log (exp (- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))))

series202.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(exp (- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5)))
74.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
31.0ms
(- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))
32.0ms
(log (exp (- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))))

simplify936.0ms

Counts
82 → 82
Iterations

Useful iterations: done (933.0ms)

IterNodesCost
01061061
1220973
2561876
31874876
done5000874

prune215.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 17.6b

localize25.0ms

Local error

Found 4 expressions with local error:

2.1b
(- 1.0 (/ (/ 1.0 (hypot 1.0 x)) (hypot 1.0 x)))
2.1b
(- 1.0 (/ 1.0 (hypot 1.0 x)))
2.1b
(- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))
2.1b
(log (exp (- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))))

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
20×*-un-lft-identity
13×add-log-exp
7×log-pow difference-of-squares
6×add-cube-cbrt exp-prod distribute-lft-out--
5×pow1 log-prod
4×add-exp-log sub-neg times-frac diff-log add-cbrt-cube
3×flip3-- flip--
2×exp-sum distribute-lft-out
1×log-div exp-diff rem-log-exp sum-log associate--r+
Counts
4 → 69
Calls
4 calls:
21.0ms
(- 1.0 (/ (/ 1.0 (hypot 1.0 x)) (hypot 1.0 x)))
10.0ms
(- 1.0 (/ 1.0 (hypot 1.0 x)))
34.0ms
(- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))
128.0ms
(log (exp (- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))))

series150.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- 1.0 (/ (/ 1.0 (hypot 1.0 x)) (hypot 1.0 x)))
31.0ms
(- 1.0 (/ 1.0 (hypot 1.0 x)))
36.0ms
(- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))
33.0ms
(log (exp (- 1.0 (+ (/ 0.5 (hypot 1.0 x)) 0.5))))

simplify1.1s

Counts
81 → 81
Iterations

Useful iterations: 3 (389.0ms)

IterNodesCost
01321203
12771079
2667963
32367961
done5000961

prune276.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 17.6b

regimes153.0ms

Accuracy

0% (0.0b remaining)

Error of 15.1b against oracle of 15.1b and baseline of 15.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01424
11924
done1924

end0.0ms

sample844.0ms

Algorithm
intervals
Results
463.0ms2875×body1280valid
118.0ms4016×body80valid
82.0ms619×body640valid
27.0ms316×body320valid
10.0ms174×body160valid