Details

Time bar (total: 28.0s)

sample76.0ms

Algorithm
intervals
Results
39.0ms91×body1280valid
9.0ms124×body80valid
7.0ms19×body640valid
4.0ms15×body320valid
1.0ms7×body160valid

simplify124.0ms

Counts
1 → 1
Iterations
IterNodes
done114
6114
5111
489
369
243
121
09

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize24.0ms

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)))))

rewrite62.0ms

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:
8.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
10.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
7.0ms
(/ 1/2 (hypot 1 x))
35.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series361.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
65.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
69.0ms
(/ 1/2 (hypot 1 x))
137.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify3.1s

Counts
127 → 127
Iterations
IterNodes
done5000
34713
21398
1507
0213

prune437.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite523.0ms

Algorithm
rewrite-expression-head
Rules
91×*-un-lft-identity
46×distribute-lft-out
29×add-sqr-sqrt
22×add-cube-cbrt
21×times-frac
18×add-log-exp
16×flip3-+ flip-+
10×pow1
8×sum-log add-cbrt-cube frac-add add-exp-log
7×associate-/r* associate-*l* sqrt-prod
6×fma-def sqrt-div associate-/r/
4×expm1-log1p-u frac-times associate-*r* insert-posit16 log1p-expm1-u
3×fma-neg prod-diff associate-/l*
2×distribute-rgt-in distribute-lft-in sqrt-pow1 pow-plus flip3-- pow1/2 associate-*l/ associate-*r/ pow-prod-up flip-- associate--r+ unswap-sqr associate-/l/
1×cbrt-undiv +-commutative associate-+l+ associate-+r+ clear-num sub-neg frac-2neg diff-log div-sub cube-unmult div-exp pow-prod-down prod-exp *-commutative cbrt-unprod div-inv
Counts
4 → 153
Calls
4 calls:
261.0ms
(+ (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1) (+ 1/2 (/ 1/2 (hypot 1 x))))
55.0ms
(* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))
198.0ms
(/ (- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))) (+ (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1) (+ 1/2 (/ 1/2 (hypot 1 x)))))
5.0ms
(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

series1.9s

Counts
4 → 12
Calls
4 calls:
177.0ms
(+ (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1) (+ 1/2 (/ 1/2 (hypot 1 x))))
110.0ms
(* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))
1.3s
(/ (- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))) (+ (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1) (+ 1/2 (/ 1/2 (hypot 1 x)))))
222.0ms
(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify3.1s

Counts
165 → 165
Iterations
IterNodes
done5000
11249
0387

prune766.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b
(/ (- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))) (fma (sqrt (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1)) (sqrt (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1)) (+ 1/2 (/ 1/2 (hypot 1 x)))))
0.5b
(fma (sqrt (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1)) (sqrt (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1)) (+ 1/2 (/ 1/2 (hypot 1 x))))
1.9b
(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
21×*-un-lft-identity
17×add-cube-cbrt
10×pow1
9×times-frac
8×add-cbrt-cube add-exp-log
7×associate-*l*
6×flip3-+ sqrt-div flip-+ add-log-exp
5×sqrt-prod
4×expm1-log1p-u frac-times associate-*r* insert-posit16 log1p-expm1-u
3×associate-/r* fma-neg prod-diff associate-/l*
2×distribute-rgt-in distribute-lft-in sqrt-pow1 pow-plus flip3-- pow1/2 associate-*l/ associate-*r/ pow-prod-up flip-- distribute-lft-out associate--r+ unswap-sqr associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-sub cube-unmult div-exp pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef div-inv
Counts
4 → 109
Calls
4 calls:
51.0ms
(* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))
12.0ms
(/ (- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))) (fma (sqrt (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1)) (sqrt (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1)) (+ 1/2 (/ 1/2 (hypot 1 x)))))
0.0ms
(fma (sqrt (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1)) (sqrt (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1)) (+ 1/2 (/ 1/2 (hypot 1 x))))
5.0ms
(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

series2.8s

Counts
4 → 12
Calls
4 calls:
147.0ms
(* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))
1.8s
(/ (- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))) (fma (sqrt (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1)) (sqrt (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1)) (+ 1/2 (/ 1/2 (hypot 1 x)))))
628.0ms
(fma (sqrt (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1)) (sqrt (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1)) (+ 1/2 (/ 1/2 (hypot 1 x))))
193.0ms
(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify4.2s

Counts
121 → 121
Iterations
IterNodes
done5000
24221
11086
0358

prune781.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize74.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (* (/ (- 1 (* (sqrt (+ 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 (/ 1/2 (hypot 1 x))))))) (* (/ (- 1 (* (sqrt (+ 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 (/ 1/2 (hypot 1 x))))))) (/ (- 1 (* (sqrt (+ 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 (/ 1/2 (hypot 1 x))))))))))
1.9b
(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))
1.9b
(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))
1.9b
(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite609.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt add-log-exp
9×fma-neg prod-diff
7×cbrt-div
6×associate--r+
5×frac-times associate-*r/
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×distribute-rgt-in sub-neg distribute-lft-in flip3-- diff-log associate-*l/ flip--
1×cbrt-prod pow1/3 cube-unmult rem-cbrt-cube
Counts
4 → 89
Calls
4 calls:
588.0ms
(cbrt (* (/ (- 1 (* (sqrt (+ 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 (/ 1/2 (hypot 1 x))))))) (* (/ (- 1 (* (sqrt (+ 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 (/ 1/2 (hypot 1 x))))))) (/ (- 1 (* (sqrt (+ 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 (/ 1/2 (hypot 1 x))))))))))
9.0ms
(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))
5.0ms
(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))
5.0ms
(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

series1.8s

Counts
4 → 12
Calls
4 calls:
1.2s
(cbrt (* (/ (- 1 (* (sqrt (+ 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 (/ 1/2 (hypot 1 x))))))) (* (/ (- 1 (* (sqrt (+ 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 (/ 1/2 (hypot 1 x))))))) (/ (- 1 (* (sqrt (+ 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 (/ 1/2 (hypot 1 x))))))))))
187.0ms
(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))
203.0ms
(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))
212.0ms
(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify4.2s

Counts
101 → 101
Iterations
IterNodes
done5009
22906
1691
0243

prune716.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes114.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.7b

bsearch1.0ms

simplify10.0ms

Iterations
IterNodes
done33
133
026

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.3s2839×body1280valid
303.0ms4058×body80valid
217.0ms623×body640valid
66.0ms326×body320valid
21.0ms154×body160valid