Details

Time bar (total: 1.3m)

sample74.0ms

Algorithm
intervals
Results
37.0ms94×body1280valid
9.0ms131×body80valid
5.0ms16×body640valid
3.0ms13×body320valid
0.0ms2×body160valid

simplify39.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b
(hypot 1.0 x)
1.5b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity prod-diff
10×add-cube-cbrt
4×add-log-exp
3×fma-neg sqrt-prod
2×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u
1×hypot-udef sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 41
Calls
2 calls:
0.0ms
(hypot 1.0 x)
12.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series931.0ms

Counts
2 → 6
Calls
2 calls:
464.0ms
(hypot 1.0 x)
467.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify3.3s

Counts
47 → 47
Iterations
IterNodes
done5000
34285
21053
1361
0148

prune264.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 13.2b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite492.0ms

Algorithm
rewrite-expression-head
Rules
24×pow1
14×associate-*r/
13×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
9×times-frac
8×pow-prod-down
6×flip3-+ sqrt-div pow-prod-up flip-+ add-log-exp
4×expm1-log1p-u frac-times sqrt-pow1 associate-*r* log1p-expm1-u
3×associate-/r* prod-exp cbrt-unprod associate-/l*
2×flip3-- pow1/2 associate-*l/ flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-sub div-exp associate-*l* prod-diff *-commutative sqrt-prod fma-udef div-inv
Counts
4 → 93
Calls
4 calls:
0.0ms
(fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
104.0ms
(* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
294.0ms
(/ (- (* 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 1.0 (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
89.0ms
(- (* 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)))))))

series12.7s

Counts
4 → 12
Calls
4 calls:
737.0ms
(fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.6s
(* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
8.3s
(/ (- (* 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 1.0 (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.1s
(- (* 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)))))))

simplify12.8s

Counts
105 → 105
Iterations
IterNodes
done5003
11976
0571

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 13.2b

localize92.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt
66×sqrt-prod
51×times-frac
44×*-un-lft-identity add-cube-cbrt
19×pow1
18×swap-sqr
16×associate-*r* associate-*l*
9×unswap-sqr
8×sqrt-pow1 add-cbrt-cube pow1/2 add-exp-log add-log-exp
5×pow-prod-up div-inv
4×expm1-log1p-u sqrt-div log1p-expm1-u
3×associate-/r* flip3-- pow-prod-down pow-sqr flip-- associate-/l*
2×sub-neg fma-neg diff-log prod-diff associate-/l/
1×pow2 frac-times cbrt-undiv clear-num rem-square-sqrt frac-2neg pow-plus sqrt-unprod div-sub div-exp associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Counts
4 → 153
Calls
4 calls:
307.0ms
(/ (- (* 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 1.0 (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
779.0ms
(* (sqrt (/ (- (* 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 1.0 (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (/ (- (* 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 1.0 (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
96.0ms
(- (* 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)))))))
90.0ms
(- (* 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)))))))

series20.4s

Counts
4 → 12
Calls
4 calls:
8.6s
(/ (- (* 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 1.0 (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
8.2s
(* (sqrt (/ (- (* 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 1.0 (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (/ (- (* 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 1.0 (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
1.8s
(- (* 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)))))))
1.9s
(- (* 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)))))))

simplify15.1s

Counts
165 → 165
Iterations
IterNodes
done5002
11788
0556

prune1.8s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 13.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (+ (- (/ 0.5 x) (/ (/ (/ 0.125 x) x) x)) x))
0.1b
(/ (/ (/ 0.125 x) x) x)
0.1b
(/ (/ 0.125 x) x)
1.0b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (+ (- (/ 0.5 x) (/ (/ (/ 0.125 x) x) x)) x))))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
483×times-frac
270×*-un-lft-identity
250×add-sqr-sqrt
248×add-cube-cbrt
59×associate-/l*
23×div-inv
20×add-cbrt-cube add-exp-log
12×prod-diff
11×associate-/r*
10×cbrt-undiv div-exp
8×distribute-lft-out
6×add-log-exp
5×distribute-lft-out--
4×expm1-log1p-u pow1 log1p-expm1-u
3×clear-num frac-2neg fma-neg sqrt-prod
2×associate-/r/ associate-/l/
1×sub-neg flip3-+ flip3-- diff-log flip-+ flip-- difference-of-squares
Counts
4 → 336
Calls
4 calls:
1.1s
(/ 1.0 (+ (- (/ 0.5 x) (/ (/ (/ 0.125 x) x) x)) x))
20.0ms
(/ (/ (/ 0.125 x) x) x)
9.0ms
(/ (/ 0.125 x) x)
7.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (+ (- (/ 0.5 x) (/ (/ (/ 0.125 x) x) x)) x))))))

series425.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ 1.0 (+ (- (/ 0.5 x) (/ (/ (/ 0.125 x) x) x)) x))
57.0ms
(/ (/ (/ 0.125 x) x) x)
36.0ms
(/ (/ 0.125 x) x)
237.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (+ (- (/ 0.5 x) (/ (/ (/ 0.125 x) x) x)) x))))))

simplify2.2s

Counts
348 → 348
Iterations
IterNodes
done5054
23120
11285
0586

prune1.9s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 13.2b

regimes246.0ms

Accuracy

0% (0.2b remaining)

Error of 15.2b against oracle of 15.0b and baseline of 15.2b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done21
121
017

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.4s2942×body1280valid
243.0ms3991×body80valid
221.0ms623×body640valid
69.0ms142×body160valid
47.0ms302×body320valid