Details

Time bar (total: 1.9m)

sample50.0ms

Algorithm
intervals
Results
22.0ms101×body1280valid
5.0ms108×body80valid
4.0ms26×body640valid
2.0ms13×body320valid
1.0ms8×body160valid

simplify63.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize47.0ms

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))
2.8b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite82.0ms

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 insert-posit16 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 → 96
Calls
4 calls:
26.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
19.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
13.0ms
(/ 1.0 (hypot 1.0 x))
13.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
405.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
201.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
190.0ms
(/ 1.0 (hypot 1.0 x))
543.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify3.8s

Counts
108 → 108
Iterations
IterNodes
done5001
21763
1568
0226

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 17.3b

localize192.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.3b
(- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

rewrite729.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
27×times-frac
10×add-cbrt-cube add-exp-log
9×associate-/r* associate-/l*
6×add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×cbrt-undiv clear-num frac-2neg div-exp div-inv
2×flip3-- flip-- associate-/l/
1×sub-neg fma-neg diff-log div-sub prod-diff
Counts
4 → 110
Calls
4 calls:
7.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(/ 1.0 (hypot 1.0 x))
533.0ms
(/ (- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
172.0ms
(- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

series12.4s

Counts
4 → 12
Calls
4 calls:
194.0ms
(/ 1.0 (hypot 1.0 x))
207.0ms
(/ 1.0 (hypot 1.0 x))
9.3s
(/ (- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.7s
(- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

simplify18.4s

Counts
122 → 122
Iterations
IterNodes
done5002
11748
0518

prune2.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 17.3b

localize242.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (log (exp (- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.3b
(- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.3b
(log (exp (- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

rewrite2.5s

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
20×log-pow
15×exp-prod
10×associate-/l*
9×pow1
8×add-cbrt-cube add-exp-log
6×log-prod associate-/r* add-log-exp
4×distribute-rgt-in expm1-log1p-u distribute-lft-in insert-posit16 log1p-expm1-u associate--r+
3×exp-sum
2×cbrt-undiv log-div clear-num sub-neg frac-2neg exp-diff div-exp prod-diff div-inv
1×flip3-- fma-neg diff-log div-sub rem-log-exp flip--
Counts
4 → 120
Calls
4 calls:
13.0ms
(/ 1.0 (hypot 1.0 x))
1.7s
(/ (log (exp (- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
180.0ms
(- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
659.0ms
(log (exp (- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

series14.4s

Counts
4 → 12
Calls
4 calls:
182.0ms
(/ 1.0 (hypot 1.0 x))
9.8s
(/ (log (exp (- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.3s
(- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.2s
(log (exp (- (* (* 1.0 1.0) 1.0) (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

simplify15.7s

Counts
132 → 132
Iterations
IterNodes
done5000
11837
0579

prune2.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 17.3b

localize302.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.4b
(pow (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3)
2.3b
(- (pow (* (* 1.0 1.0) 1.0) 3) (pow (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3))

rewrite242.0ms

Algorithm
rewrite-expression-head
Rules
64×prod-diff
42×add-sqr-sqrt
40×*-un-lft-identity
38×add-cube-cbrt
25×pow1
22×sqr-pow
18×cube-mult unpow-prod-down times-frac unpow3 cube-prod
14×add-cbrt-cube associate-*r/ add-exp-log
9×pow-pow
8×cube-div fma-neg pow-prod-down
6×associate-/r* flip3-+ sqrt-div pow-prod-up flip-+ associate-/l* add-log-exp
4×expm1-log1p-u frac-times sqrt-pow1 insert-posit16 log1p-expm1-u difference-of-squares
3×pow-unpow pow-exp prod-exp cbrt-unprod rem-cube-cbrt
2×cbrt-undiv clear-num frac-2neg pow1/2 div-exp associate-*l/ div-inv
1×pow-to-exp difference-cubes sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 195
Calls
4 calls:
13.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(/ 1.0 (hypot 1.0 x))
166.0ms
(pow (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3)
31.0ms
(- (pow (* (* 1.0 1.0) 1.0) 3) (pow (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3))

series17.1s

Counts
4 → 12
Calls
4 calls:
170.0ms
(/ 1.0 (hypot 1.0 x))
195.0ms
(/ 1.0 (hypot 1.0 x))
4.5s
(pow (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3)
12.2s
(- (pow (* (* 1.0 1.0) 1.0) 3) (pow (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3))

simplify11.5s

Counts
207 → 207
Iterations
IterNodes
done5001
11999
0634

prune3.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.3b

regimes750.0ms

Accuracy

0% (0.2b remaining)

Error of 14.6b against oracle of 14.4b and baseline of 14.6b

bsearch0.0ms

simplify27.0ms

Iterations
IterNodes
done39
139
031

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.2s2850×body1280valid
586.0ms638×body640valid
288.0ms4068×body80valid
53.0ms304×body320valid
16.0ms140×body160valid