Details

Time bar (total: 18.2s)

sample118.0ms

Algorithm
intervals
Results
71.0ms103×body1280valid
17.0ms123×body80valid
10.0ms18×body640valid
4.0ms10×body320valid
0.0ms2×body160valid

simplify29.0ms

Counts
1 → 1
Iterations
IterNodes
425
325
223
119
09

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b
(/ 1/2 (hypot 1 x))
2.1b
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity
40×add-sqr-sqrt
26×add-cube-cbrt
21×prod-diff
20×sqrt-prod
10×times-frac
5×add-cbrt-cube add-exp-log distribute-lft-out add-log-exp
4×pow1 difference-of-squares
3×expm1-log1p-u associate-/r* fma-neg insert-posit16 log1p-expm1-u associate-/l* distribute-lft-out--
2×sqrt-div hypot-def
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 → 97
Calls
3 calls:
12.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
4.0ms
(/ 1/2 (hypot 1 x))
33.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series265.0ms

Counts
3 → 9
Calls
3 calls:
89.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
63.0ms
(/ 1/2 (hypot 1 x))
113.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.9s

Counts
106 → 106
Iterations
IterNodes
32448
2978
1440
0198

prune698.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
27×add-sqr-sqrt
18×add-cube-cbrt
11×flip3-+ flip-+ add-log-exp
10×sqrt-div
9×pow1 times-frac
8×add-cbrt-cube add-exp-log
7×associate-*r* sqrt-prod distribute-lft-out
4×expm1-log1p-u frac-times fma-def associate-*l* frac-add insert-posit16 log1p-expm1-u
3×associate-/r* sum-log distribute-rgt-out fma-neg prod-diff associate-/l*
2×associate-*l/ associate-*r/ pow-prod-up unswap-sqr
1×cbrt-undiv +-commutative associate-+l+ clear-num sub-neg frac-2neg distribute-lft1-in sqrt-pow1 flip3-- pow1/2 diff-log div-exp pow3 pow-prod-down prod-exp *-commutative cbrt-unprod div-inv flip--
Counts
4 → 119
Calls
4 calls:
4.0ms
(/ 1/2 (hypot 1 x))
55.0ms
(* (+ 1/2 (/ 1/2 (hypot 1 x))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
49.0ms
(+ (+ 1/2 (/ 1/2 (hypot 1 x))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
5.0ms
(- 1 (* (+ 1/2 (/ 1/2 (hypot 1 x))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))))

series636.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(/ 1/2 (hypot 1 x))
157.0ms
(* (+ 1/2 (/ 1/2 (hypot 1 x))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
193.0ms
(+ (+ 1/2 (/ 1/2 (hypot 1 x))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
202.0ms
(- 1 (* (+ 1/2 (/ 1/2 (hypot 1 x))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))))

simplify1.1s

Counts
131 → 131
Iterations
IterNodes
22173
1652
0264

prune1.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b
(/ 1/2 (hypot 1 x))
0.1b
(exp (log (- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))))
2.1b
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt *-un-lft-identity
29×add-cube-cbrt
24×sqrt-prod
21×prod-diff
10×log-prod times-frac exp-sum
8×difference-of-squares
6×pow1 add-cbrt-cube add-exp-log distribute-lft-out distribute-lft-out-- add-log-exp
4×expm1-log1p-u exp-prod insert-posit16 log1p-expm1-u
3×associate-/r* fma-neg associate-/l*
2×log-div flip3-- exp-diff sqrt-div hypot-def flip--
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log div-exp log-pow flip-+ div-inv rem-exp-log
Counts
4 → 124
Calls
4 calls:
9.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
4.0ms
(/ 1/2 (hypot 1 x))
26.0ms
(exp (log (- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))))
37.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series429.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
69.0ms
(/ 1/2 (hypot 1 x))
142.0ms
(exp (log (- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))))
147.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.6s

Counts
136 → 136
Iterations
IterNodes
32461
21046
1494
0242

prune1.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) x)
0.1b
(* (* x x) x)
0.1b
(* 11/128 (* x x))
18.4b
(fma (* (* (* x x) x) (* (* x x) x)) 69/1024 (* (* x x) (- 1/8 (* 11/128 (* x x)))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
47×pow1
19×add-cbrt-cube add-exp-log
12×pow-plus pow-prod-up
10×add-sqr-sqrt
9×pow-prod-down prod-exp cbrt-unprod
7×*-un-lft-identity associate-*r* add-cube-cbrt
5×associate-*l*
4×pow2 expm1-log1p-u pow-sqr insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative unswap-sqr
2×pow3
1×fma-udef
Counts
4 → 95
Calls
4 calls:
22.0ms
(* (* x x) x)
16.0ms
(* (* x x) x)
33.0ms
(* 11/128 (* x x))
1.0ms
(fma (* (* (* x x) x) (* (* x x) x)) 69/1024 (* (* x x) (- 1/8 (* 11/128 (* x x)))))

series236.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (* x x) x)
66.0ms
(* (* x x) x)
45.0ms
(* 11/128 (* x x))
83.0ms
(fma (* (* (* x x) x) (* (* x x) x)) 69/1024 (* (* x x) (- 1/8 (* 11/128 (* x x)))))

simplify4.4s

Counts
107 → 107
Iterations
IterNodes
45879
31760
2583
1201
089

prune556.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes123.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch1.0ms

simplify8.0ms

Iterations
IterNodes
232
132
025

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.2s2875×body1280valid
450.0ms4029×body80valid
316.0ms621×body640valid
99.0ms329×body320valid
26.0ms146×body160valid