Details

sample153.0ms

Algorithm

intervals

Results

61.0ms	577×	body	80	nan
47.0ms	276×	body	160	nan
23.0ms	256×	body	80	valid

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	1825
6	472
5	156
4	60
3	35
2	19
1	16
0	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (+ x (sqrt (- (* x x) 1))))
0.0b	(+ x (sqrt (- (* x x) 1)))
26.4b	(sqrt (- (* x x) 1))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
6×	`sqrt-prod`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`log-prod` `add-exp-log`
3×	`add-cbrt-cube` `insert-posit16`
2×	`log-div` `flip3-+` `sqrt-div` `flip-+` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3--` `pow1/2` `difference-of-sqr-1` `rem-log-exp` `log-pow` `flip--`

Counts

3 → 48

Calls

3 calls:

23.0ms	(log (+ x (sqrt (- (* x x) 1))))
15.0ms	(+ x (sqrt (- (* x x) 1)))
8.0ms	(sqrt (- (* x x) 1))

series313.0ms

Counts

3 → 9

Calls

3 calls:

195.0ms	(log (+ x (sqrt (- (* x x) 1))))
70.0ms	(+ x (sqrt (- (* x x) 1)))
48.0ms	(sqrt (- (* x x) 1))

simplify1.8s

Counts

57 → 57

Iterations

Iter	Nodes
done	5000
3	2252
2	744
1	300
0	135

prune224.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
0.0b	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
0.0b	(sqrt (+ x 1))
0.5b	(* (sqrt (+ x 1)) (sqrt (- x 1)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`sqrt-prod`
17×	`*-un-lft-identity`
14×	`sqrt-div`
10×	`pow1` `associate-r` `add-cube-cbrt`
7×	`associate-l` `add-exp-log`
6×	`flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
4×	`frac-times` `insert-posit16` `unswap-sqr`
3×	`log-prod` `sqrt-pow1` `flip3--` `pow1/2` `pow-prod-down` `flip--`
2×	`log-div` `associate-l/` `associate-r/` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-unprod` `difference-of-sqr-1` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 88

Calls

4 calls:

5.0ms	(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
9.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
5.0ms	(sqrt (+ x 1))
26.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

series419.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
113.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
37.0ms	(sqrt (+ x 1))
96.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

simplify2.2s

Counts

100 → 100

Iterations

Iter	Nodes
done	5002
3	3321
2	996
1	412
0	185

prune431.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (sqrt (+ x 1)) (sqrt (- x 1)))) (cbrt (* (sqrt (+ x 1)) (sqrt (- x 1)))))
0.6b	(cbrt (* (sqrt (+ x 1)) (sqrt (- x 1))))
0.6b	(cbrt (* (sqrt (+ x 1)) (sqrt (- x 1))))
0.6b	(cbrt (* (sqrt (+ x 1)) (sqrt (- x 1))))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

252×	`sqrt-div`
168×	`cbrt-div`
148×	`frac-times`
63×	`flip3-+` `flip3--` `flip-+` `flip--`
50×	`associate-l/` `associate-r/`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 166

Calls

4 calls:

61.0ms	(* (cbrt (* (sqrt (+ x 1)) (sqrt (- x 1)))) (cbrt (* (sqrt (+ x 1)) (sqrt (- x 1)))))
20.0ms	(cbrt (* (sqrt (+ x 1)) (sqrt (- x 1))))
20.0ms	(cbrt (* (sqrt (+ x 1)) (sqrt (- x 1))))
27.0ms	(cbrt (* (sqrt (+ x 1)) (sqrt (- x 1))))

series840.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(* (cbrt (* (sqrt (+ x 1)) (sqrt (- x 1)))) (cbrt (* (sqrt (+ x 1)) (sqrt (- x 1)))))
221.0ms	(cbrt (* (sqrt (+ x 1)) (sqrt (- x 1))))
207.0ms	(cbrt (* (sqrt (+ x 1)) (sqrt (- x 1))))
194.0ms	(cbrt (* (sqrt (+ x 1)) (sqrt (- x 1))))

simplify2.3s

Counts

178 → 178

Iterations

Iter	Nodes
done	5000
3	3137
2	1103
1	558
0	308

prune1.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes20.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	14
1	14
0	9

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.8s	16699×	body	80	nan
1.5s	7978×	body	160	nan
839.0ms	8000×	body	80	valid