Details

sample73.0ms

Algorithm

intervals

Results

30.0ms	85×	body	1280	valid
21.0ms	139×	body	80	valid
5.0ms	20×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	5×	body	160	valid

simplify57.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	19	12
2	26	12
3	32	12
4	34	12
5	40	12
6	42	12
done	42	12

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

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-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u`
3×	`fma-def` `fma-neg` `associate-/r` `associate-/l`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sum-log` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 92

Calls

4 calls:

19.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
8.0ms	(/ 1.0 (hypot 1.0 x))
32.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
13.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

140.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
119.0ms	(/ 1.0 (hypot 1.0 x))
301.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
453.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.2s

Counts

104 → 104

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	223	2270
1	537	1836
2	1582	1593
done	5001	1460

prune379.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.2b	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
21×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1` `associate-/r*`
6×	`associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `div-exp` `clear-num` `associate-/r/` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `pow-prod-down` `sqrt-prod`

Counts

4 → 98

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
35.0ms	(/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
12.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
9.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

series2.3s

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ 1.0 (hypot 1.0 x))
1.7s	(/ (- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
355.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
125.0ms	(- (* 1.0 1.0) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))

simplify2.3s

Counts

110 → 110

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	342	3335
1	994	3143
2	3930	2907
done	5000	2906

prune616.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.4b

localize370.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ (- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (* (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4))))
0.0b	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
1.2b	(- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

64×	`prod-diff`
42×	`add-sqr-sqrt`
36×	`sqr-pow`
30×	`*-un-lft-identity`
24×	`add-cube-cbrt` `unpow-prod-down` `cube-prod` `difference-of-squares`
18×	`cube-mult` `unpow3`
13×	`times-frac` `associate-/l*`
12×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
8×	`fma-neg`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u`
3×	`difference-cubes` `pow-unpow` `flip3-+` `flip-+` `distribute-lft-out--`
2×	`cbrt-undiv` `cube-div` `flip3--` `pow-pow` `sqrt-pow1` `sqrt-div` `associate-*r/` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `associate-/l/` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `frac-2neg` `pow1/2` `diff-log` `div-sub` `clear-num` `associate-/r*` `sqrt-prod` `div-inv`

Counts

4 → 185

Calls

4 calls:

19.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
90.0ms	(/ (- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (* (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4))))
15.0ms	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
23.0ms	(- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

series39.6s

Counts

4 → 12

Calls

4 calls:

449.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
38.2s	(/ (- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) (* (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4))))
377.0ms	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
570.0ms	(- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

simplify2.6s

Counts

197 → 197

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	982	17210
1	3090	13657
done	5000	12782

prune1.8s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.4b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
0.0b	(/ (cbrt (pow (- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) 3)) (* (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4))))
0.0b	(cbrt (pow (- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) 3))
1.2b	(- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

96×	`cbrt-prod`
75×	`add-sqr-sqrt`
71×	`unpow-prod-down` `cube-prod`
64×	`prod-diff`
63×	`sqr-pow`
56×	`difference-of-squares`
47×	`*-un-lft-identity`
35×	`times-frac` `associate-/l*`
33×	`add-cube-cbrt`
21×	`cube-mult` `unpow3`
12×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`fma-neg`
7×	`pow1` `difference-cubes` `distribute-lft-out--`
6×	`cube-div` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-div` `associate-*l/` `log1p-expm1-u`
3×	`pow-unpow` `flip3--` `flip--`
2×	`cbrt-undiv` `pow-pow` `flip3-+` `div-exp` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `associate-/l/` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `frac-2neg` `pow1/3` `diff-log` `pow-prod-down` `clear-num` `associate-/r*` `rem-cbrt-cube` `div-inv`

Counts

4 → 258

Calls

4 calls:

30.0ms	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
126.0ms	(/ (cbrt (pow (- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) 3)) (* (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4))))
33.0ms	(cbrt (pow (- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) 3))
22.0ms	(- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

series41.1s

Counts

4 → 12

Calls

4 calls:

426.0ms	(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
39.3s	(/ (cbrt (pow (- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) 3)) (* (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (fma (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (pow 1.0 4))))
699.0ms	(cbrt (pow (- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)) 3))
638.0ms	(- (pow (* 1.0 1.0) 3) (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3))

simplify2.5s

Counts

270 → 270

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	1025	21900
1	3142	17574
done	5000	16738

prune1.9s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 12.0b

regimes397.0ms

Accuracy

99.6% (0.0b remaining)

Error of 13.0b against oracle of 13.0b and baseline of 14.8b

bsearch3.0ms

simplify13.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	66	187
1	72	187
done	72	187

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.3s	2884×	body	1280	valid
256.0ms	4024×	body	80	valid
135.0ms	623×	body	640	valid
101.0ms	318×	body	320	valid
15.0ms	151×	body	160	valid