Details

Time bar (total: 16.6s)

sample82.0ms

Algorithm
intervals
Results
46.0ms96×body1280valid
11.0ms26×body640valid
10.0ms122×body80valid
2.0ms9×body320valid
1.0ms3×body160valid

simplify55.0ms

Counts
1 → 1

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize22.0ms

Local error

Found 3 expressions with local error:

1.3b
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b
(/ 1/2 (hypot 1 x))
0.0b
(hypot 1 x)

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×*-un-lft-identity
11×add-cube-cbrt
9×times-frac
5×add-cbrt-cube add-exp-log add-log-exp
4×sqrt-prod difference-of-squares
3×pow1 associate-/r* insert-posit16 associate-/l* distribute-lft-out--
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-- diff-log div-exp div-inv flip-- distribute-lft-out
Counts
3 → 56
Calls
3 calls:
Slowest
26.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
7.0ms
(/ 1/2 (hypot 1 x))
0.0ms
(hypot 1 x)

series104.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
91.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
11.0ms
(/ 1/2 (hypot 1 x))
2.0ms
(hypot 1 x)

simplify2.4s

Counts
65 → 65

prune652.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b
(- 1/2 (/ 1/2 (hypot 1 x)))
0.0b
(/ 1/2 (hypot 1 x))
0.0b
(/ 1/2 (hypot 1 x))
0.0b
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt *-un-lft-identity
20×add-cube-cbrt
19×times-frac
8×add-cbrt-cube add-exp-log add-log-exp
6×associate-/r* associate-/l*
4×pow1 insert-posit16 distribute-lft-out
2×cbrt-undiv clear-num frac-2neg div-exp sqrt-prod div-inv difference-of-squares
1×+-commutative sum-log sub-neg flip3-+ flip3-- diff-log flip-+ flip-- distribute-lft-out--
Counts
4 → 87
Calls
4 calls:
Slowest
16.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
7.0ms
(/ 1/2 (hypot 1 x))
5.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))
4.0ms
(/ 1/2 (hypot 1 x))

series111.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
53.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
46.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))
6.0ms
(/ 1/2 (hypot 1 x))
6.0ms
(/ 1/2 (hypot 1 x))

simplify2.3s

Counts
99 → 99

prune1.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.3b

localize53.0ms

Local error

Found 4 expressions with local error:

0.8b
(- 1/2 (/ 1/2 (hypot 1 x)))
0.5b
(cbrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
0.5b
(cbrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
0.5b
(cbrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
18×cbrt-prod add-sqr-sqrt
12×distribute-lft-out
7×add-cube-cbrt
6×cbrt-div sqrt-prod add-log-exp
4×pow1 add-cbrt-cube add-exp-log insert-posit16
3×flip3-+ pow1/3 flip-+
2×difference-of-squares
1×sub-neg times-frac flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 67
Calls
4 calls:
Slowest
25.0ms
(cbrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
24.0ms
(cbrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
18.0ms
(cbrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
11.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

series760.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
264.0ms
(cbrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
232.0ms
(cbrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
207.0ms
(cbrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
55.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

simplify1.6s

Counts
79 → 79

prune896.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 14.3b

localize32.0ms

Local error

Found 4 expressions with local error:

19.8b
(cbrt (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))))
0.8b
(- 1/2 (cbrt (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x)))))
0.1b
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
0.1b
(* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
57×add-cbrt-cube add-exp-log
56×add-sqr-sqrt
50×times-frac
41×*-un-lft-identity
39×add-cube-cbrt
30×pow1
26×associate-*r*
22×prod-exp cbrt-unprod
17×cbrt-undiv div-exp
14×associate-*l*
13×swap-sqr
11×frac-times associate-*l/
7×cbrt-div pow-plus associate-*r/ pow-prod-up
6×add-log-exp unswap-sqr
5×div-inv
4×pow-prod-down insert-posit16
3×pow2 pow-sqr
2×pow3 *-commutative
1×cbrt-prod sub-neg flip3-- pow1/3 diff-log rem-cbrt-cube flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 164
Calls
4 calls:
Slowest
30.0ms
(* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x)))
23.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
20.0ms
(cbrt (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))))
6.0ms
(- 1/2 (cbrt (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x)))))

series130.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
54.0ms
(* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x)))
41.0ms
(- 1/2 (cbrt (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x)))))
26.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
9.0ms
(cbrt (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))))

simplify865.0ms

Counts
176 → 176

prune2.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 14.3b

regimes39.0ms

Accuracy

0% (0.3b remaining)

Error of 14.2b against oracle of 13.9b and baseline of 14.2b

bsearch3.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.2s2832×body1280valid
403.0ms4083×body80valid
345.0ms605×body640valid
123.0ms295×body320valid
68.0ms185×body160valid