Details

Time bar (total: 8.0s)

sample30.0ms

Algorithm
intervals
Results
15.0ms92×body1280valid
4.0ms137×body80valid
2.0ms17×body640valid
1.0ms7×body320valid
0.0ms3×body160valid

simplify23.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0912
11912
22212
32612
42812
53312
63512
done3512

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
1.3b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity
10×add-cube-cbrt
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1
1×cbrt-undiv sub-neg flip3-- frac-2neg diff-log div-exp clear-num flip-- div-inv distribute-lft-out-- difference-of-squares
Counts
2 → 41
Calls
2 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series88.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
82.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.0s

Counts
47 → 47
Iterations

Useful iterations: done (1.9s)

IterNodesCost
085626
1158590
2340542
3791540
41996540
done5000538

prune100.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x))) 1.0) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b
(/ 0.5 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.8b
(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity
27×add-sqr-sqrt
23×times-frac
22×add-cube-cbrt
13×add-exp-log add-cbrt-cube
10×associate-/r*
9×add-log-exp
7×associate-/l*
4×pow1 cbrt-undiv flip3-- div-exp associate-*l/ frac-sub flip-- associate-/l/
3×frac-2neg diff-log clear-num div-inv distribute-lft-out--
2×sub-neg associate--l+ associate-/r/ distribute-lft-out difference-of-squares
1×associate--l- flip3-+ prod-exp cbrt-unprod flip-+
Counts
4 → 105
Calls
4 calls:
47.0ms
(/ (* (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x))) 1.0) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.0ms
(/ 0.5 (hypot 1.0 x))
2.0ms
(/ 1.0 (hypot 1.0 x))
21.0ms
(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

series224.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(/ (* (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x))) 1.0) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
5.0ms
(/ 0.5 (hypot 1.0 x))
6.0ms
(/ 1.0 (hypot 1.0 x))
34.0ms
(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

simplify777.0ms

Counts
117 → 117
Iterations

Useful iterations: done (773.0ms)

IterNodesCost
01961967
14591889
214521685
done50001679

prune288.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 0.5 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.8b
(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))
0.8b
(log (exp (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt *-un-lft-identity
22×add-cube-cbrt
20×times-frac
9×add-log-exp
8×add-exp-log log-pow add-cbrt-cube
7×log-prod exp-prod
6×associate-/r* associate-/l* distribute-lft-out--
5×pow1
4×sub-neg exp-sum associate--l+ difference-of-squares
3×diff-log
2×cbrt-undiv flip3-- frac-2neg div-exp clear-num frac-sub flip-- div-inv
1×associate--l- log-div exp-diff rem-log-exp
Counts
4 → 100
Calls
4 calls:
2.0ms
(/ 0.5 (hypot 1.0 x))
2.0ms
(/ 1.0 (hypot 1.0 x))
21.0ms
(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))
54.0ms
(log (exp (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))))

series76.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 0.5 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
31.0ms
(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))
35.0ms
(log (exp (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))))

simplify1.1s

Counts
112 → 112
Iterations

Useful iterations: 3 (369.0ms)

IterNodesCost
01691317
13121213
27141129
319241125
done50011125

prune323.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (hypot 1.0 x))
0.3b
(* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))
0.8b
(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))
0.8b
(log (exp (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
25×*-un-lft-identity
19×cbrt-prod
15×add-cube-cbrt
12×pow1
9×add-log-exp
8×log-pow
7×log-prod exp-prod pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l* distribute-lft-out--
4×sub-neg exp-sum associate--l+ add-cbrt-cube difference-of-squares unswap-sqr
3×diff-log
2×flip3-- times-frac pow-prod-down pow-sqr pow-prod-up frac-sub flip--
1×associate--l- pow2 log-div pow-plus exp-diff rem-log-exp prod-exp *-commutative cbrt-unprod
Counts
4 → 97
Calls
4 calls:
0.0ms
(cbrt (hypot 1.0 x))
5.0ms
(* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))
23.0ms
(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))
53.0ms
(log (exp (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))))

series288.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(cbrt (hypot 1.0 x))
121.0ms
(* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))
34.0ms
(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))
32.0ms
(log (exp (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))))

simplify1.3s

Counts
109 → 109
Iterations

Useful iterations: 3 (706.0ms)

IterNodesCost
01431361
12721212
27001054
323331028
done50001028

prune351.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.4b

regimes33.0ms

Accuracy

0% (0.3b remaining)

Error of 14.8b against oracle of 14.6b and baseline of 14.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02445
13045
done3045

end0.0ms

sample803.0ms

Algorithm
intervals
Results
455.0ms2825×body1280valid
118.0ms4065×body80valid
80.0ms637×body640valid
31.0ms331×body320valid
8.0ms142×body160valid