Details

Time bar (total: 1.6m)

sample83.0ms

Algorithm
intervals
Results
50.0ms101×body1280valid
12.0ms128×body80valid
6.0ms15×body640valid
3.0ms10×body320valid
0.0ms2×body160valid

simplify52.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
52.0ms
(- 1 (sqrt (* 1/2 (+ 1 (/ 1 (hypot 1 x))))))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.9b
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.0b
(/ 1/2 (hypot 1 x))
0.0b
(hypot 1 x)
0.0b
(+ (/ 1/2 (hypot 1 x)) 1/2)

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
41×add-sqr-sqrt
33×add-cube-cbrt
21×prod-diff
18×times-frac
16×sqrt-prod
13×fma-def
8×add-log-exp
6×add-cbrt-cube add-exp-log
5×distribute-lft-out
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u difference-of-squares
3×associate-/r* fma-neg associate-/l* distribute-lft-out--
2×div-inv
1×cbrt-undiv +-commutative hypot-udef clear-num sum-log sub-neg frac-2neg flip3-+ flip3-- diff-log div-exp flip-+ flip--
Counts
4 → 115
Calls
4 calls:
Slowest
49.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
11.0ms
(+ (/ 1/2 (hypot 1 x)) 1/2)
7.0ms
(/ 1/2 (hypot 1 x))
0.0ms
(hypot 1 x)

series340.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(- 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
83.0ms
(+ (/ 1/2 (hypot 1 x)) 1/2)
79.0ms
(/ 1/2 (hypot 1 x))
62.0ms
(hypot 1 x)

simplify7.2s

Counts
108 → 127
Calls
108 calls:
Slowest
509.0ms
(- (+ (* 1/4 (/ 1 (pow x 3))) 1/2) (* 1/2 (/ 1 x)))
384.0ms
(/ (* (* 1/2 1/2) 1/2) (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x)))
334.0ms
(- (* 1/4 (/ 1 (pow x 3))) (+ (* 3/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
328.0ms
(- (+ (* 3/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))) (* 1/4 (/ 1 (pow x 3))))
308.0ms
(- (+ (* 1/8 (pow x 2)) (* 69/1024 (pow x 6))) (* 11/128 (pow x 4)))

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.6b

localize52.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
0.5b
(- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
0.0b
(/ (- (* 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))))
0.0b
(/ 1/2 (hypot 1 x))

rewrite223.0ms

Algorithm
rewrite-expression-head
Rules
71×*-un-lft-identity
54×add-sqr-sqrt
36×sqrt-prod
33×times-frac
32×add-cube-cbrt
26×distribute-lft-out
19×pow1
12×sqrt-div
11×swap-sqr
10×add-cbrt-cube add-exp-log
9×associate-/r*
8×sqrt-pow1 pow1/2 difference-of-squares
7×flip3-+ associate-*r* associate-*l* flip-+ associate-/l*
6×add-log-exp
5×pow-prod-up
4×expm1-log1p-u frac-times insert-posit16 log1p-expm1-u unswap-sqr
3×pow-prod-down pow-sqr
2×cbrt-undiv clear-num frac-2neg flip3-- div-exp associate-*l/ associate-*r/ associate-/r/ div-inv flip-- associate-/l/
1×pow2 sub-neg rem-square-sqrt pow-plus fma-neg sqrt-unprod diff-log div-sub prod-diff prod-exp *-commutative cbrt-unprod
Counts
4 → 167
Calls
4 calls:
Slowest
112.0ms
(/ (- (* 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))))
62.0ms
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
36.0ms
(- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
7.0ms
(/ 1/2 (hypot 1 x))

series632.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
393.0ms
(/ (- (* 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))))
82.0ms
(- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))
80.0ms
(/ 1/2 (hypot 1 x))
77.0ms
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))

simplify15.0s

Counts
186 → 179
Calls
186 calls:
Slowest
704.0ms
(/ (* (* (- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (- (* 1 1) (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))) (- (* 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))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
612.0ms
(+ (* 1/8 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 2) (sqrt 1/2))))) (+ (* 1/32 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 3) (pow (sqrt 1/2) 2))))) (+ (* 1/8 (/ 1 (* x (* (pow (+ (sqrt 1/2) 1) 2) (sqrt 1/2))))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 2) (pow (sqrt 1/2) 3))))) (+ (* 1/2 (/ 1 (* x (+ (sqrt 1/2) 1)))) (* 1/2 (/ 1 (+ (sqrt 1/2) 1))))))))
486.0ms
(- (+ (* 1/4 (/ 1 (pow x 3))) 1/2) (* 1/2 (/ 1 x)))
466.0ms
(- (pow (* 1 1) 3) (pow (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 3))
465.0ms
(- (+ (* 1/8 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 2) (sqrt 1/2))))) (+ (* 1/32 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 3) (pow (sqrt 1/2) 2))))) (+ (* 1/64 (/ 1 (* (pow x 2) (* (pow (+ (sqrt 1/2) 1) 2) (pow (sqrt 1/2) 3))))) (* 1/2 (/ 1 (+ (sqrt 1/2) 1)))))) (+ (* 1/8 (/ 1 (* x (* (pow (+ (sqrt 1/2) 1) 2) (sqrt 1/2))))) (* 1/2 (/ 1 (* x (+ (sqrt 1/2) 1))))))

prune2.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
0.4b
(- 1/2 (/ 1/2 (hypot 1 x)))
0.0b
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
0.0b
(/ 1/2 (hypot 1 x))

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
166×add-sqr-sqrt *-un-lft-identity
128×times-frac
89×add-cube-cbrt
88×sqrt-prod
44×distribute-lft-out
39×prod-diff
22×difference-of-squares
21×associate-/r*
12×add-exp-log associate-/l*
11×distribute-lft-out--
10×add-cbrt-cube
6×pow1 div-inv add-log-exp
4×expm1-log1p-u sqrt-div div-exp associate-/r/ insert-posit16 log1p-expm1-u
3×cbrt-undiv clear-num frac-2neg fma-neg pow-flip
2×flip3-+ flip3-- flip-+ flip-- associate-/l/
1×rec-exp sub-neg sqrt-pow1 pow1/2 diff-log 1-exp div-sub inv-pow
Counts
4 → 241
Calls
4 calls:
Slowest
103.0ms
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
67.0ms
(/ 1 (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
13.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))
7.0ms
(/ 1/2 (hypot 1 x))

series1.7s

Counts
4 → 12
Calls
4 calls:
Slowest
1.2s
(/ (- 1/2 (/ 1/2 (hypot 1 x))) (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
419.0ms
(/ 1 (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
78.0ms
(/ 1/2 (hypot 1 x))
76.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

simplify27.5s

Counts
324 → 253
Calls
324 calls:
Slowest
531.0ms
(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)))))))
507.0ms
(- (+ (* 1/4 (/ 1 (pow x 3))) 1/2) (* 1/2 (/ 1 x)))
458.0ms
(sqrt (+ (* 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))))))
441.0ms
(sqrt (+ (* 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))))))
428.0ms
(- (+ (* 5/32 (* (pow x 6) (sqrt 1/2))) (+ (* 1/256 (/ (pow x 4) (sqrt 1/2))) (* 1/4 (* (pow x 2) (sqrt 1/2))))) (+ (* 1/32768 (/ (pow x 6) (pow (sqrt 1/2) 3))) (+ (* 3/16 (* (pow x 4) (sqrt 1/2))) (* 11/2048 (/ (pow x 6) (sqrt 1/2))))))

prune3.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize101.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
0.5b
(* (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (+ (* 1/2 1/2) (+ (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (* 1/2 (/ 1/2 (hypot 1 x))))))
0.4b
(- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))))
0.2b
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))

rewrite319.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
94×*-un-lft-identity
76×times-frac
67×add-cube-cbrt
41×sqrt-prod
22×associate-*l* add-exp-log
21×prod-diff
20×add-cbrt-cube distribute-lft-out
16×associate-*r*
15×pow1
13×swap-sqr
9×associate-/r*
8×sqrt-div div-inv
7×flip3-+ flip-+
6×div-exp add-log-exp unswap-sqr
5×frac-times cbrt-undiv prod-exp cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-neg associate-*l/ associate-*r/ pow-flip associate-/l*
2×pow-prod-down associate-/r/ *-commutative
1×pow2 distribute-rgt-in rec-exp clear-num sub-neg frac-2neg distribute-lft-in sqrt-pow1 pow-plus flip3-- pow1/2 diff-log 1-exp pow-sqr pow-prod-up flip-- distribute-lft-out-- inv-pow difference-of-squares
Counts
4 → 211
Calls
4 calls:
Slowest
190.0ms
(* (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (+ (* 1/2 1/2) (+ (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (* 1/2 (/ 1/2 (hypot 1 x))))))
79.0ms
(/ 1 (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
25.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
18.0ms
(- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
574.0ms
(* (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (+ (* 1/2 1/2) (+ (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (* 1/2 (/ 1/2 (hypot 1 x))))))
401.0ms
(/ 1 (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))))
101.0ms
(- 1/8 (/ 1/8 (* (* (hypot 1 x) (hypot 1 x)) (hypot 1 x))))
84.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))

simplify26.3s

Counts
241 → 223
Calls
241 calls:
Slowest
536.0ms
(* (* (* (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))) (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))) (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))) (* (* (+ (* 1/2 1/2) (+ (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (* 1/2 (/ 1/2 (hypot 1 x))))) (+ (* 1/2 1/2) (+ (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (* 1/2 (/ 1/2 (hypot 1 x)))))) (+ (* 1/2 1/2) (+ (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (* 1/2 (/ 1/2 (hypot 1 x)))))))
528.0ms
(fma (- (/ 1/8 (hypot 1 x))) (/ 1 (* (hypot 1 x) (hypot 1 x))) (* (/ 1/8 (hypot 1 x)) (/ 1 (* (hypot 1 x) (hypot 1 x)))))
522.0ms
(* (sqrt (sqrt (+ 1 (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))))) (sqrt (+ (* 1/2 1/2) (+ (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (* 1/2 (/ 1/2 (hypot 1 x)))))))
475.0ms
(fma (* (cbrt 1/8) (cbrt 1/8)) (cbrt 1/8) (- (* (/ 1/8 (hypot 1 x)) (/ 1 (* (hypot 1 x) (hypot 1 x))))))
456.0ms
(+ (* 3/128 (* (/ 1 (* (pow x 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (pow (+ (sqrt 1/2) 1) 5))))) (+ (* 1/64 (* (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (pow (+ (sqrt 1/2) 1) 3))))) (+ (sqrt (/ 1 (+ (sqrt 1/2) 1))) (* 1/8 (* (/ 1 (* x (sqrt 1/2))) (sqrt (/ 1 (pow (+ (sqrt 1/2) 1) 3))))))))

prune3.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

regimes218.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.5b

bsearch246.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.1s2785×body1280valid
537.0ms4107×body80valid
298.0ms633×body640valid
118.0ms312×body320valid
35.0ms163×body160valid