Details

Time bar (total: 2.1m)

sample109.0ms

Algorithm
intervals
Results
60.0ms101×body1280valid
23.0ms124×body80valid
8.0ms17×body640valid
3.0ms9×body320valid
1.0ms5×body160valid

simplify41.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
41.0ms
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 x))))))

prune7.0ms

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))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
41×add-sqr-sqrt
27×add-cube-cbrt
21×prod-diff
20×sqrt-prod
10×times-frac
6×add-cbrt-cube add-exp-log add-log-exp
5×pow1 distribute-lft-out
4×expm1-log1p-u insert-posit16 log1p-expm1-u difference-of-squares
3×associate-/r* fma-neg associate-/l* distribute-lft-out--
2×sqrt-div hypot-def
1×cbrt-undiv rem-sqrt-square hypot-udef clear-num sub-neg frac-2neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log div-exp flip-+ div-inv flip--
Counts
4 → 108
Calls
4 calls:
Slowest
55.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
10.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
3.0ms
(/ 1/2 (hypot 1 x))
0.0ms
(hypot 1 x)

series393.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
184.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
80.0ms
(sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))
76.0ms
(/ 1/2 (hypot 1 x))
54.0ms
(hypot 1 x)

simplify11.4s

Counts
159 → 120
Calls
159 calls:
Slowest
485.0ms
(- (pow 1 3) (pow (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) 3))
431.0ms
(- (* 1/4 (/ 1 (pow x 3))) (+ (* 3/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
429.0ms
(- (+ (* 1/8 (pow x 2)) (* 69/1024 (pow x 6))) (* 11/128 (pow x 4)))
349.0ms
(/ (* (* 1/2 1/2) 1/2) (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
337.0ms
(- (+ (* 3/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))) (* 1/4 (/ 1 (pow x 3))))

prune947.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

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)

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
57×*-un-lft-identity
55×add-cube-cbrt
46×times-frac
39×prod-diff
8×add-cbrt-cube add-exp-log
6×associate-/r* associate-/l* add-log-exp
5×div-inv
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×fma-neg
2×cbrt-undiv clear-num frac-2neg div-exp difference-of-squares
1×hypot-udef sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 131
Calls
4 calls:
Slowest
11.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))
7.0ms
(/ 1/2 (hypot 1 x))
6.0ms
(/ 1/2 (hypot 1 x))
0.0ms
(hypot 1 x)

series335.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
91.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))
90.0ms
(/ 1/2 (hypot 1 x))
88.0ms
(/ 1/2 (hypot 1 x))
65.0ms
(hypot 1 x)

simplify22.5s

Counts
206 → 143
Calls
206 calls:
Slowest
845.0ms
(fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1/2 (cbrt (hypot 1 x))) (/ 1 (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x)))))))
491.0ms
(fma (- (/ 1/2 (cbrt (hypot 1 x)))) (/ 1 (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x)))) (* (/ 1/2 (cbrt (hypot 1 x))) (/ 1 (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))))))
490.0ms
(fma (- (/ 1/2 (cbrt (hypot 1 x)))) (/ 1 (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x)))) (* (/ 1/2 (cbrt (hypot 1 x))) (/ 1 (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))))))
488.0ms
(fma (sqrt 1/2) (sqrt 1/2) (- (* (/ 1/2 (cbrt (hypot 1 x))) (/ 1 (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x)))))))
476.0ms
(fma (- (/ 1/2 (cbrt (hypot 1 x)))) (/ 1 (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x)))) (* (/ 1/2 (cbrt (hypot 1 x))) (/ 1 (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x))))))

prune1.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

1.3b
(- 1/8 (* (* (/ 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)))
0.0b
(/ 1/2 (hypot 1 x))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
59×times-frac add-cbrt-cube add-exp-log
49×*-un-lft-identity add-cube-cbrt
30×pow1
26×associate-*r*
22×prod-exp cbrt-unprod
18×cbrt-undiv div-exp
14×associate-*l*
13×swap-sqr
7×pow-plus pow-prod-up
6×frac-times associate-*l/ div-inv add-log-exp unswap-sqr
4×expm1-log1p-u pow-prod-down associate-*r/ insert-posit16 log1p-expm1-u
3×pow2 associate-/r* fma-neg prod-diff pow-sqr associate-/l*
2×*-commutative
1×clear-num sub-neg frac-2neg flip3-- diff-log pow3 flip--
Counts
4 → 186
Calls
4 calls:
Slowest
57.0ms
(* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x)))
16.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
4.0ms
(- 1/8 (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))))
4.0ms
(/ 1/2 (hypot 1 x))

series383.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
111.0ms
(* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x)))
103.0ms
(- 1/8 (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))))
89.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
80.0ms
(/ 1/2 (hypot 1 x))

simplify35.0s

Counts
232 → 198
Calls
232 calls:
Slowest
676.0ms
(* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ (* (cbrt 1/2) (cbrt 1/2)) 1))
652.0ms
(* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1 (* (cbrt (hypot 1 x)) (cbrt (hypot 1 x)))))
637.0ms
(* (* (* (* (/ 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)))) (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))))
619.0ms
(* (* (* (* (/ 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)))) (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))))
614.0ms
(- (pow 1/8 3) (pow (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))) 3))

prune2.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

1.3b
(- 1/8 (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))))
0.6b
(exp (log (- 1/8 (* (* (/ 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)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
57×add-cbrt-cube add-exp-log
50×times-frac
43×*-un-lft-identity add-cube-cbrt
31×pow1
26×associate-*r*
22×prod-exp cbrt-unprod
17×cbrt-undiv div-exp
14×associate-*l*
13×swap-sqr
7×pow-plus pow-prod-up
6×frac-times associate-*l/ add-log-exp unswap-sqr
5×div-inv
4×expm1-log1p-u exp-prod pow-prod-down associate-*r/ insert-posit16 log1p-expm1-u
3×pow2 log-prod fma-neg exp-sum prod-diff pow-sqr
2×log-div flip3-- exp-diff *-commutative flip--
1×sub-neg diff-log pow3 log-pow rem-exp-log
Counts
4 → 176
Calls
4 calls:
Slowest
56.0ms
(* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x)))
33.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
4.0ms
(- 1/8 (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))))
4.0ms
(exp (log (- 1/8 (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))))))

series446.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
146.0ms
(exp (log (- 1/8 (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))))))
107.0ms
(- 1/8 (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))))
101.0ms
(* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x)))
92.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))

simplify42.0s

Counts
216 → 188
Calls
216 calls:
Slowest
820.0ms
(- (+ (* 3/16 (pow x 2)) (* 35/128 (pow x 6))) (* 15/64 (pow x 4)))
709.0ms
(* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ (* (cbrt 1/2) (cbrt 1/2)) 1))
706.0ms
(- (pow 1/8 3) (pow (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))) 3))
701.0ms
(exp (log (- (pow 1/8 3) (pow (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))) 3))))
693.0ms
(* (* (* (* (/ 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)))) (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (/ 1/2 (hypot 1 x))))

prune2.5s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes178.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.0b

bsearch210.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.9s2933×body1280valid
731.0ms591×body640valid
447.0ms4014×body80valid
86.0ms303×body320valid
31.0ms159×body160valid