Details

Time bar (total: 2.9m)

sample92.0ms

Algorithm
intervals
Results
56.0ms90×body1280valid
11.0ms132×body80valid
9.0ms24×body640valid
3.0ms9×body320valid
0.0ms1×body160valid

simplify32.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
32.0ms
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 x))))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize21.0ms

Local error

Found 3 expressions with local error:

1.7b
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
0.0b
(/ 1/2 (hypot 1 x))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt *-un-lft-identity
12×add-cube-cbrt
9×times-frac
8×sqrt-prod
5×add-cbrt-cube add-exp-log add-log-exp
4×pow1 difference-of-squares
3×associate-/r* insert-posit16 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
3 → 65
Calls
3 calls:
Slowest
42.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
9.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
4.0ms
(/ 1/2 (hypot 1 x))

series135.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
66.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
58.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
11.0ms
(/ 1/2 (hypot 1 x))

simplify3.8s

Counts
94 → 74
Calls
94 calls:
Slowest
405.0ms
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
329.0ms
(/ (* (* 1/2 1/2) 1/2) (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
243.0ms
(sqrt (+ (pow (/ 1/2 (hypot 1 x)) 3) (pow 1/2 3)))
219.0ms
(* (* (- 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))))
195.0ms
(* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x)))

prune1.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.8b

localize39.0ms

Local error

Found 4 expressions with local error:

1.2b
(- 1/2 (/ 1/2 (hypot 1 x)))
0.0b
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
0.0b
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
0.0b
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
77×*-un-lft-identity
76×add-sqr-sqrt
44×times-frac
33×distribute-lft-out
20×sqrt-prod
19×add-cube-cbrt
16×difference-of-squares
8×distribute-lft-out-- add-log-exp
6×associate-/r* add-cbrt-cube add-exp-log associate-/l*
5×pow1
4×insert-posit16
3×flip3-+ flip-+
2×flip3-- sqrt-div associate-/r/ flip-- associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp div-inv
Counts
4 → 114
Calls
4 calls:
Slowest
59.0ms
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
34.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
17.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
11.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
56.0ms
(+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
46.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))
41.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))

simplify11.5s

Counts
173 → 126
Calls
173 calls:
Slowest
497.0ms
(* (* (+ 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))))
453.0ms
(- (pow 1/2 3) (pow (/ 1/2 (hypot 1 x)) 3))
448.0ms
(/ (* (* (- 1/2 (/ 1/2 (hypot 1 x))) (- 1/2 (/ 1/2 (hypot 1 x)))) (- 1/2 (/ 1/2 (hypot 1 x)))) (* (* (+ 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)))))
361.0ms
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3)))
340.0ms
(* (* (/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))) (/ (- 1/2 (/ 1/2 (hypot 1 x))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))

prune1.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 12.8b

localize57.0ms

Local error

Found 4 expressions with local error:

1.2b
(- 1/4 (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))
0.1b
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
0.0b
(/ (- 1/4 (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b
(/ (/ (- 1/4 (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
309×*-un-lft-identity
300×times-frac
220×add-sqr-sqrt
128×add-cube-cbrt
125×distribute-lft-out
46×sqrt-prod
34×difference-of-squares
26×associate-/l*
23×add-cbrt-cube add-exp-log
18×associate-/r/
13×swap-sqr associate-*r* associate-*l* div-inv
11×pow1
10×associate-/r*
9×flip3-+ flip-+
8×cbrt-undiv div-exp
6×add-log-exp
4×prod-exp cbrt-unprod insert-posit16 unswap-sqr
3×div-sub associate-/l/
2×clear-num frac-2neg flip3-- flip--
1×pow2 frac-times sub-neg pow-plus diff-log pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 303
Calls
4 calls:
Slowest
65.0ms
(/ (/ (- 1/4 (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
23.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
21.0ms
(/ (- 1/4 (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))
8.0ms
(- 1/4 (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))

series464.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
244.0ms
(/ (/ (- 1/4 (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
144.0ms
(/ (- 1/4 (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))
53.0ms
(- 1/4 (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))
24.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))

simplify1.5m

Counts
486 → 315
Calls
486 calls:
Slowest
911.0ms
(/ (/ (- (sqrt 1/4) (/ 1/2 (hypot 1 x))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
778.0ms
(/ (/ (- 1/4 (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))) (- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))) (* (cbrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (cbrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))))
746.0ms
(/ (* (cbrt (/ (- 1/4 (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))) (cbrt (/ (- 1/4 (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))) (sqrt 1))
570.0ms
(* (/ (* (cbrt 1/2) (cbrt 1/2)) (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x)))) (/ (* (cbrt 1/2) (cbrt 1/2)) (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x)))))
569.0ms
(log (/ (/ (- 1/4 (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))

prune3.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 12.7b

localize61.0ms

Local error

Found 4 expressions with local error:

12.4b
(cbrt (* (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))) (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x)))))
1.2b
(- 1/4 (cbrt (* (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))) (* (* (/ 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)))

rewrite301.0ms

Algorithm
rewrite-expression-head
Rules
131×frac-times
89×associate-*l/
87×add-sqr-sqrt
80×times-frac
63×cbrt-div
62×*-un-lft-identity
60×add-cube-cbrt
57×associate-*r/
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
18×pow1
8×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
6×add-log-exp
4×insert-posit16
3×pow-prod-down
2×cbrt-prod pow2 pow-plus pow3 pow-sqr *-commutative pow-prod-up difference-of-squares
1×sub-neg flip3-- pow1/3 diff-log rem-cbrt-cube flip-- distribute-lft-out--
Counts
4 → 226
Calls
4 calls:
Slowest
238.0ms
(cbrt (* (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))) (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x)))))
24.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
24.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
7.0ms
(- 1/4 (cbrt (* (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))) (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))))))

series191.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
85.0ms
(- 1/4 (cbrt (* (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))) (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))))))
37.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
35.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
34.0ms
(cbrt (* (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))) (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x)))))

simplify52.1s

Counts
336 → 238
Calls
336 calls:
Slowest
904.0ms
(cbrt (* (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) 1/2) (* (* (/ 1/2 (hypot 1 x)) 1/2) (/ 1/2 (hypot 1 x)))))
854.0ms
(cbrt (* (* (* (/ 1/2 (hypot 1 x)) 1/2) 1/2) (* (* (/ 1/2 (hypot 1 x)) 1/2) (/ 1/2 (hypot 1 x)))))
843.0ms
(cbrt (* (* (* (/ 1/2 (hypot 1 x)) 1/2) (/ 1/2 (hypot 1 x))) (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) 1/2)))
777.0ms
(cbrt (* (* (* 1/2 (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))) (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) 1/2)))
746.0ms
(cbrt (* (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) 1/2) (* (* 1/2 (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x)))))

prune3.1s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 12.7b

regimes49.0ms

Accuracy

0% (0.3b remaining)

Error of 14.9b against oracle of 14.7b and baseline of 14.9b

bsearch2.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
2.0s2891×body1280valid
778.0ms614×body640valid
429.0ms4006×body80valid
103.0ms334×body320valid
33.0ms155×body160valid