Details

sample48.0ms

Algorithm

intervals

Results

11.0ms	242×	body	160	nan
10.0ms	523×	body	80	nan
7.0ms	256×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	11	9
2	12	9
done	12	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (+ x (sqrt (- (* x x) 1.0))))
0.0b	(- (* x x) 1.0)
0.0b	(+ x (sqrt (- (* x x) 1.0)))
30.6b	(sqrt (- (* x x) 1.0))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1`
5×	`add-exp-log`
4×	`expm1-log1p-u` `log-prod` `sqrt-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `prod-diff`
2×	`log-div` `flip3--` `flip3-+` `sqrt-div` `flip--` `flip-+` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `rem-log-exp` `sum-log` `log-pow`

Counts

4 → 71

Calls

4 calls:

16.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
9.0ms	(- (* x x) 1.0)
20.0ms	(+ x (sqrt (- (* x x) 1.0)))
13.0ms	(sqrt (- (* x x) 1.0))

series343.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
39.0ms	(- (* x x) 1.0)
66.0ms	(+ x (sqrt (- (* x x) 1.0)))
54.0ms	(sqrt (- (* x x) 1.0))

simplify1.7s

Counts

83 → 83

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	172	1045
1	380	921
2	1040	833
3	4247	754
done	5000	753

prune212.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x (sqrt 1.0)))
0.0b	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.6b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
20×	`sqrt-prod`
17×	`*-un-lft-identity`
14×	`sqrt-div`
11×	`add-cube-cbrt`
10×	`pow1`
9×	`associate-r`
7×	`add-exp-log` `associate-l`
6×	`flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
3×	`log-prod` `flip3--` `fma-def` `sqrt-pow1` `pow1/2` `pow-prod-down` `flip--`
2×	`log-div` `associate-r/` `associate-l/` `hypot-def` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sqrt-unprod` `rem-log-exp` `prod-exp` `sum-log` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 96

Calls

4 calls:

10.0ms	(sqrt (+ x (sqrt 1.0)))
4.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
5.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
49.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series676.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(sqrt (+ x (sqrt 1.0)))
277.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
144.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
190.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify884.0ms

Counts

108 → 108

Iterations

Useful iterations: done (881.0ms)

Iter	Nodes	Cost
0	222	1940
1	522	1651
2	1493	1520
done	5000	1477

prune311.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

6.8b	(fma x x (- (* x (- x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))) 1.0))
31.8b	(log (fma x x (- (* x (- x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))) 1.0)))
33.2b	(- x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
43.3b	(log (+ (pow x 3) (pow (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))) 3)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`log-div` `rem-log-exp` `log-pow`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `sum-cubes` `flip--` `flip-+` `fma-udef` `distribute-lft-out`

Counts

4 → 62

Calls

4 calls:

0.0ms	(fma x x (- (* x (- x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))) 1.0))
1.0ms	(log (fma x x (- (* x (- x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))) 1.0)))
6.0ms	(- x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
13.0ms	(log (+ (pow x 3) (pow (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))) 3)))

series1.2s

Counts

4 → 12

Calls

4 calls:

201.0ms	(fma x x (- (* x (- x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))) 1.0))
313.0ms	(log (fma x x (- (* x (- x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))) 1.0)))
183.0ms	(- x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
472.0ms	(log (+ (pow x 3) (pow (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))) 3)))

simplify905.0ms

Counts

74 → 74

Iterations

Useful iterations: done (902.0ms)

Iter	Nodes	Cost
0	229	2056
1	561	1957
2	1671	1675
done	5000	1632

prune401.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes13.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	13	14
done	13	14

end0.0ms

sample1.4s

Algorithm

intervals

Results

354.0ms	7804×	body	160	nan
341.0ms	16496×	body	80	nan
228.0ms	8000×	body	80	valid