Details

Time bar (total: 58.6s)

sample103.0ms

Algorithm
intervals
Results
62.0ms101×body1280valid
14.0ms124×body80valid
8.0ms17×body640valid
3.0ms9×body320valid
1.0ms5×body160valid

simplify39.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
39.0ms
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 x))))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize14.0ms

Local error

Found 4 expressions with local error:

1.9b
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b
(/ 1/2 (hypot 1 x))
0.0b
(hypot 1 x)
0.0b
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
13×add-cube-cbrt
9×times-frac
8×sqrt-prod
6×add-cbrt-cube add-exp-log add-log-exp
5×pow1
4×insert-posit16 difference-of-squares
3×associate-/r* associate-/l* distribute-lft-out--
2×sqrt-div distribute-lft-out
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log div-exp flip-+ div-inv flip--
Counts
4 → 73
Calls
4 calls:
Slowest
33.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
13.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
3.0ms
(/ 1/2 (hypot 1 x))
0.0ms
(hypot 1 x)

series146.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
70.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
63.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
10.0ms
(/ 1/2 (hypot 1 x))
2.0ms
(hypot 1 x)

simplify3.8s

Counts
105 → 85
Calls
105 calls:
Slowest
360.0ms
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
312.0ms
(/ (* (* 1/2 1/2) 1/2) (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
274.0ms
(sqrt (+ (pow (/ 1/2 (hypot 1 x)) 3) (pow 1/2 3)))
267.0ms
(* (* (- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
209.0ms
(+ (* 1 1) (+ (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) (* 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))

prune778.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 15.4b

localize26.0ms

Local error

Found 4 expressions with local error:

1.4b
(- 1/2 (/ 1/2 (hypot 1 x)))
0.0b
(/ 1/2 (hypot 1 x))
0.0b
(/ 1/2 (hypot 1 x))
0.0b
(hypot 1 x)

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
19×times-frac
8×add-cbrt-cube add-exp-log
6×associate-/r* associate-/l* add-log-exp
4×pow1 insert-posit16
2×cbrt-undiv clear-num frac-2neg div-exp div-inv difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 80
Calls
4 calls:
Slowest
7.0ms
(/ 1/2 (hypot 1 x))
6.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))
4.0ms
(/ 1/2 (hypot 1 x))
0.0ms
(hypot 1 x)

series54.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
39.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))
8.0ms
(/ 1/2 (hypot 1 x))
6.0ms
(/ 1/2 (hypot 1 x))
2.0ms
(hypot 1 x)

simplify3.9s

Counts
116 → 92
Calls
116 calls:
Slowest
358.0ms
(/ (* (* 1/2 1/2) 1/2) (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
348.0ms
(- (pow 1/2 3) (pow (/ 1/2 (hypot 1 x)) 3))
340.0ms
(* (* (- 1/2 (/ 1/2 (hypot 1 x))) (- 1/2 (/ 1/2 (hypot 1 x)))) (- 1/2 (/ 1/2 (hypot 1 x))))
308.0ms
(/ (* (* 1/2 1/2) 1/2) (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
228.0ms
(* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x)))

prune910.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.2b

localize94.0ms

Local error

Found 4 expressions with local error:

1.3b
(+ 1/8 (/ (/ (/ -1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x)))
0.1b
(/ (/ -1/8 (hypot 1 x)) (hypot 1 x))
0.1b
(/ (/ (/ -1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x))
0.0b
(/ (+ 1/4 (/ 1/4 (hypot 1 x))) (hypot 1 x))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
249×*-un-lft-identity
239×add-sqr-sqrt add-cube-cbrt
60×associate-/l*
23×div-inv
20×add-cbrt-cube add-exp-log
10×cbrt-undiv div-exp
9×associate-/r*
6×add-log-exp
5×distribute-lft-out
4×pow1 insert-posit16 associate-/l/
3×clear-num frac-2neg
2×flip3-+ flip-+
1×+-commutative sum-log
Counts
4 → 311
Calls
4 calls:
Slowest
39.0ms
(/ (+ 1/4 (/ 1/4 (hypot 1 x))) (hypot 1 x))
30.0ms
(+ 1/8 (/ (/ (/ -1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x)))
22.0ms
(/ (/ (/ -1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x))
15.0ms
(/ (/ -1/8 (hypot 1 x)) (hypot 1 x))

series231.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
103.0ms
(+ 1/8 (/ (/ (/ -1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x)))
54.0ms
(/ (+ 1/4 (/ 1/4 (hypot 1 x))) (hypot 1 x))
52.0ms
(/ (/ (/ -1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x))
22.0ms
(/ (/ -1/8 (hypot 1 x)) (hypot 1 x))

simplify34.4s

Counts
507 → 323
Calls
507 calls:
Slowest
726.0ms
(+ (pow 1/8 3) (pow (/ (/ (/ -1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x)) 3))
522.0ms
(/ (* (* (/ (/ -1/8 (hypot 1 x)) (hypot 1 x)) (/ (/ -1/8 (hypot 1 x)) (hypot 1 x))) (/ (/ -1/8 (hypot 1 x)) (hypot 1 x))) (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
487.0ms
(/ (/ (/ (* (cbrt -1/8) (cbrt -1/8)) (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x)))) (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x)))) (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))))
485.0ms
(* (* (+ 1/8 (/ (/ (/ -1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x))) (+ 1/8 (/ (/ (/ -1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x)))) (+ 1/8 (/ (/ (/ -1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x))))
423.0ms
(/ (/ (/ (* (cbrt -1/8) (cbrt -1/8)) (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x)))) (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x)))) (sqrt (hypot 1 x)))

prune4.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.1b

localize78.0ms

Local error

Found 4 expressions with local error:

1.3b
(+ 1/8 (* (/ (/ -1/8 (cbrt (hypot 1 x))) (hypot 1 x)) (/ (/ (/ 1 (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))
0.2b
(cbrt (hypot 1 x))
0.2b
(cbrt (hypot 1 x))
0.2b
(cbrt (hypot 1 x))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×add-log-exp
4×pow1 add-cbrt-cube add-exp-log insert-posit16
3×pow1/3
1×+-commutative sum-log flip3-+ flip-+
Counts
4 → 48
Calls
4 calls:
Slowest
9.0ms
(+ 1/8 (* (/ (/ -1/8 (cbrt (hypot 1 x))) (hypot 1 x)) (/ (/ (/ 1 (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))
1.0ms
(cbrt (hypot 1 x))
1.0ms
(cbrt (hypot 1 x))
1.0ms
(cbrt (hypot 1 x))

series505.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
157.0ms
(cbrt (hypot 1 x))
138.0ms
(cbrt (hypot 1 x))
122.0ms
(cbrt (hypot 1 x))
87.0ms
(+ 1/8 (* (/ (/ -1/8 (cbrt (hypot 1 x))) (hypot 1 x)) (/ (/ (/ 1 (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))

simplify5.1s

Counts
67 → 60
Calls
67 calls:
Slowest
583.0ms
(- 1/8 (* 1/8 (/ 1 (pow (hypot 1 x) 3))))
360.0ms
(+ (* 1/8 1/8) (- (* (* (/ (/ -1/8 (cbrt (hypot 1 x))) (hypot 1 x)) (/ (/ (/ 1 (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))) (* (/ (/ -1/8 (cbrt (hypot 1 x))) (hypot 1 x)) (/ (/ (/ 1 (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))))) (* 1/8 (* (/ (/ -1/8 (cbrt (hypot 1 x))) (hypot 1 x)) (/ (/ (/ 1 (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))))
329.0ms
(- (* 1/8 1/8) (* (* (/ (/ -1/8 (cbrt (hypot 1 x))) (hypot 1 x)) (/ (/ (/ 1 (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))) (* (/ (/ -1/8 (cbrt (hypot 1 x))) (hypot 1 x)) (/ (/ (/ 1 (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))))))
322.0ms
(* (* (+ 1/8 (* (/ (/ -1/8 (cbrt (hypot 1 x))) (hypot 1 x)) (/ (/ (/ 1 (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))))) (+ 1/8 (* (/ (/ -1/8 (cbrt (hypot 1 x))) (hypot 1 x)) (/ (/ (/ 1 (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))))) (+ 1/8 (* (/ (/ -1/8 (cbrt (hypot 1 x))) (hypot 1 x)) (/ (/ (/ 1 (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x))))))
300.0ms
(+ (pow 1/8 3) (pow (* (/ (/ -1/8 (cbrt (hypot 1 x))) (hypot 1 x)) (/ (/ (/ 1 (hypot 1 x)) (cbrt (hypot 1 x))) (cbrt (hypot 1 x)))) 3))

prune938.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.1b

regimes105.0ms

Accuracy

0% (0.3b remaining)

Error of 15.0b against oracle of 14.7b and baseline of 15.0b

bsearch7.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.3s2933×body1280valid
379.0ms4014×body80valid
307.0ms591×body640valid
85.0ms303×body320valid
29.0ms159×body160valid