Details

Time bar (total: 20.8s)

sample108.0ms

Algorithm
intervals
Results
69.0ms90×body1280valid
13.0ms134×body80valid
7.0ms16×body640valid
3.0ms9×body320valid
1.0ms7×body160valid

simplify24.0ms

Counts
1 → 1
Iterations
IterNodes
425
325
223
119
09

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b
(+ 1/2 (/ 1/2 (hypot 1 x)))
0.0b
(/ 1/2 (hypot 1 x))
2.4b
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
45×*-un-lft-identity
42×add-sqr-sqrt
28×add-cube-cbrt
21×prod-diff
20×sqrt-prod
10×times-frac
8×add-log-exp
6×add-cbrt-cube add-exp-log distribute-lft-out
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u difference-of-squares
3×associate-/r* fma-def fma-neg associate-/l* distribute-lft-out--
2×flip3-+ sqrt-div flip-+ hypot-def
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log div-exp div-inv flip--
Counts
4 → 115
Calls
4 calls:
9.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
6.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
8.0ms
(/ 1/2 (hypot 1 x))
42.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series408.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
81.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
82.0ms
(/ 1/2 (hypot 1 x))
148.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify2.3s

Counts
127 → 127
Iterations
IterNodes
32808
21146
1488
0213

prune442.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt *-un-lft-identity
56×add-cube-cbrt
46×times-frac
39×prod-diff
8×add-cbrt-cube add-exp-log add-log-exp
6×associate-/r* associate-/l*
5×div-inv
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u distribute-lft-out
3×fma-def fma-neg
2×cbrt-undiv clear-num frac-2neg div-exp sqrt-prod difference-of-squares
1×+-commutative sum-log sub-neg flip3-+ flip3-- diff-log flip-+ flip-- distribute-lft-out--
Counts
4 → 140
Calls
4 calls:
22.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
7.0ms
(/ 1/2 (hypot 1 x))
6.0ms
(/ 1/2 (hypot 1 x))
8.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

series371.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
76.0ms
(/ 1/2 (hypot 1 x))
77.0ms
(/ 1/2 (hypot 1 x))
91.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

simplify5.0s

Counts
152 → 152
Iterations
IterNodes
34414
21665
1618
0247

prune543.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ 1/2 (hypot 1 x)))
0.1b
(sqrt (/ 1/2 (hypot 1 x)))
0.7b
(* (sqrt (/ 1/2 (hypot 1 x))) (sqrt (/ 1/2 (hypot 1 x))))
1.9b
(- 1/2 (* (sqrt (/ 1/2 (hypot 1 x))) (sqrt (/ 1/2 (hypot 1 x)))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
92×sqrt-prod
87×add-sqr-sqrt
62×times-frac
52×*-un-lft-identity add-cube-cbrt
21×pow1
18×swap-sqr
16×associate-*r* associate-*l*
10×sqrt-pow1 pow1/2
9×unswap-sqr
6×add-cbrt-cube sqrt-div add-exp-log div-inv add-log-exp
5×pow-prod-up
4×expm1-log1p-u rem-sqrt-square insert-posit16 log1p-expm1-u
3×fma-neg prod-diff pow-prod-down pow-sqr
1×pow2 frac-times sub-neg rem-square-sqrt pow-plus flip3-- sqrt-unprod diff-log associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod flip-- difference-of-squares
Counts
4 → 168
Calls
4 calls:
2.0ms
(sqrt (/ 1/2 (hypot 1 x)))
2.0ms
(sqrt (/ 1/2 (hypot 1 x)))
22.0ms
(* (sqrt (/ 1/2 (hypot 1 x))) (sqrt (/ 1/2 (hypot 1 x))))
5.0ms
(- 1/2 (* (sqrt (/ 1/2 (hypot 1 x))) (sqrt (/ 1/2 (hypot 1 x)))))

series610.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(sqrt (/ 1/2 (hypot 1 x)))
151.0ms
(sqrt (/ 1/2 (hypot 1 x)))
185.0ms
(* (sqrt (/ 1/2 (hypot 1 x))) (sqrt (/ 1/2 (hypot 1 x))))
154.0ms
(- 1/2 (* (sqrt (/ 1/2 (hypot 1 x))) (sqrt (/ 1/2 (hypot 1 x)))))

simplify1.7s

Counts
180 → 180
Iterations
IterNodes
33444
21217
1446
0218

prune783.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) x)
0.1b
(* (* x x) x)
0.3b
(* (* x x) 11/128)
21.2b
(fma 69/1024 (* (* (* x x) x) (* (* x x) x)) (* (* x x) (- 1/8 (* (* x x) 11/128))))

rewrite61.0ms

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×associate-*r* pow-prod-down prod-exp cbrt-unprod
7×*-un-lft-identity add-cube-cbrt
4×pow2 expm1-log1p-u pow-sqr insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* *-commutative unswap-sqr
2×pow3
1×fma-udef
Counts
4 → 95
Calls
4 calls:
24.0ms
(* (* x x) x)
15.0ms
(* (* x x) x)
16.0ms
(* (* x x) 11/128)
1.0ms
(fma 69/1024 (* (* (* x x) x) (* (* x x) x)) (* (* x x) (- 1/8 (* (* x x) 11/128))))

series185.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (* x x) x)
38.0ms
(* (* x x) x)
31.0ms
(* (* x x) 11/128)
80.0ms
(fma 69/1024 (* (* (* x x) x) (* (* x x) x)) (* (* x x) (- 1/8 (* (* x x) 11/128))))

simplify4.4s

Counts
107 → 107
Iterations
IterNodes
46178
31908
2584
1200
090

prune280.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes101.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 30.2b

bsearch1.0ms

simplify9.0ms

Iterations
IterNodes
230
130
025

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.1s2799×body1280valid
481.0ms4097×body80valid
382.0ms624×body640valid
98.0ms321×body320valid
32.0ms159×body160valid