Details

Time bar (total: 1.3m)

sample73.0ms

Algorithm
intervals
Results
40.0ms101×body1280valid
9.0ms125×body80valid
6.0ms19×body640valid
1.0ms6×body320valid
1.0ms5×body160valid

simplify24.0ms

Counts
1 → 1
Iterations
IterNodes
done34
434
332
226
119
09

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b
(/ 1.0 (hypot 1.0 x))
2.2b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
23×add-sqr-sqrt
21×add-cube-cbrt
12×prod-diff
9×times-frac
8×add-log-exp
7×pow1
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u sqrt-prod log1p-expm1-u
3×associate-/r* fma-def fma-neg associate-/l*
2×sqrt-pow1 flip3-+ sqrt-div associate-*r/ flip-+
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg flip3-- pow1/2 diff-log div-exp pow-prod-down div-inv flip-- distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 92
Calls
4 calls:
19.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
10.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
4.0ms
(/ 1.0 (hypot 1.0 x))
25.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
405.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
145.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
139.0ms
(/ 1.0 (hypot 1.0 x))
528.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.1s

Counts
104 → 104
Iterations
IterNodes
done5004
21749
1565
0222

prune688.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.1b

localize94.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* 0.5 1.0) (hypot 1.0 x))
0.0b
(* (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))) (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))
0.0b
(/ (- (* 1.0 (* 1.0 1.0)) (* (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))) (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))))
1.8b
(- (* 1.0 (* 1.0 1.0)) (* (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))) (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))))

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
18×*-un-lft-identity add-cube-cbrt
15×times-frac
13×add-cbrt-cube add-exp-log
9×pow1
6×associate-/r* flip3-+ sqrt-div associate-*r* pow3 flip-+ add-log-exp
5×difference-cubes cube-unmult associate-/l*
4×expm1-log1p-u frac-times sqrt-prod log1p-expm1-u
3×cbrt-undiv div-exp associate-*l*
2×clear-num frac-2neg flip3-- associate-*l/ prod-exp associate-*r/ pow-prod-up cbrt-unprod div-inv flip-- unswap-sqr associate-/l/
1×sub-neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff pow-prod-down *-commutative
Counts
4 → 111
Calls
4 calls:
8.0ms
(/ (* 0.5 1.0) (hypot 1.0 x))
90.0ms
(* (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))) (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))
84.0ms
(/ (- (* 1.0 (* 1.0 1.0)) (* (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))) (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))))
28.0ms
(- (* 1.0 (* 1.0 1.0)) (* (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))) (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))))

series8.3s

Counts
4 → 12
Calls
4 calls:
123.0ms
(/ (* 0.5 1.0) (hypot 1.0 x))
720.0ms
(* (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))) (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))
6.2s
(/ (- (* 1.0 (* 1.0 1.0)) (* (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))) (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))))
1.3s
(- (* 1.0 (* 1.0 1.0)) (* (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))) (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))))

simplify7.0s

Counts
123 → 123
Iterations
IterNodes
done5002
11789
0577

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.1b

localize136.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))) (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))
0.5b
(/ (* (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))) (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))))
0.5b
(/ (* 1.0 (* 1.0 1.0)) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))))
2.2b
(- (/ (* 1.0 (* 1.0 1.0)) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))) (/ (* (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))) (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))))

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
51×times-frac
49×prod-diff
48×add-sqr-sqrt
43×*-un-lft-identity
41×add-cube-cbrt
20×add-cbrt-cube add-exp-log
19×div-inv
12×flip3-+ sqrt-div flip-+
9×pow1
8×frac-times associate-/l/
7×fma-neg
6×associate-/r* associate-*r* add-log-exp
5×cbrt-undiv div-exp prod-exp cbrt-unprod
4×expm1-log1p-u associate-*l/ associate-*r/ sqrt-prod log1p-expm1-u
3×associate-*l*
2×clear-num frac-2neg pow-prod-up associate-/l* unswap-sqr
1×sub-neg sqrt-pow1 flip3-- distribute-rgt-out-- pow1/2 diff-log pow3 pow-prod-down *-commutative frac-sub flip-- distribute-lft-out-- sub-div difference-of-squares
Counts
4 → 166
Calls
4 calls:
91.0ms
(* (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))) (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))
32.0ms
(/ (* (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))) (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))))
32.0ms
(/ (* 1.0 (* 1.0 1.0)) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))))
50.0ms
(- (/ (* 1.0 (* 1.0 1.0)) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))) (/ (* (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))) (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))))

series18.2s

Counts
4 → 12
Calls
4 calls:
816.0ms
(* (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))) (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))
4.9s
(/ (* (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))) (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))))
2.0s
(/ (* 1.0 (* 1.0 1.0)) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))))
10.5s
(- (/ (* 1.0 (* 1.0 1.0)) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))) (/ (* (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))) (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))))

simplify10.3s

Counts
178 → 178
Iterations
IterNodes
done5001
12163
0674

prune2.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.1b

localize186.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (* 1.0 (* 1.0 1.0)) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))))
1.8b
(log (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))
2.2b
(- (/ (* 1.0 (* 1.0 1.0)) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))) (/ (exp (+ (log (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) (log (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))))) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))))
2.2b
(log (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
139×times-frac
112×prod-diff
104×add-sqr-sqrt
101×*-un-lft-identity
99×add-cube-cbrt
27×div-inv
21×exp-sum
15×add-exp-log
13×add-cbrt-cube
9×log-prod
7×pow1 fma-neg
6×add-log-exp
4×expm1-log1p-u log-div log-pow log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp prod-exp sqrt-prod cbrt-unprod
2×flip3-+ sqrt-div rem-log-exp flip-+ difference-of-squares
1×clear-num sub-neg frac-2neg sqrt-pow1 flip3-- distribute-rgt-out-- pow1/2 diff-log frac-sub flip-- associate-/l* distribute-lft-out-- sub-div
Counts
4 → 201
Calls
4 calls:
29.0ms
(/ (* 1.0 (* 1.0 1.0)) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))))
15.0ms
(log (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))
102.0ms
(- (/ (* 1.0 (* 1.0 1.0)) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))) (/ (exp (+ (log (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) (log (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))))) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))))
18.0ms
(log (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))

series12.0s

Counts
4 → 12
Calls
4 calls:
1.5s
(/ (* 1.0 (* 1.0 1.0)) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))))
368.0ms
(log (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))
9.5s
(- (/ (* 1.0 (* 1.0 1.0)) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))) (/ (exp (+ (log (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) (log (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))))) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))))
533.0ms
(log (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))

simplify7.5s

Counts
213 → 213
Iterations
IterNodes
done5002
11914
0651

prune2.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.1b

regimes242.0ms

Accuracy

0% (0.3b remaining)

Error of 14.9b against oracle of 14.6b and baseline of 14.9b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done24
124
018

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.5s2822×body1280valid
229.0ms4068×body80valid
219.0ms654×body640valid
68.0ms162×body160valid
50.0ms294×body320valid