Details

sample75.0ms

Algorithm

intervals

Results

16.0ms	72×	body	640	valid
13.0ms	286×	body	80	nan
9.0ms	30×	body	1280	valid
7.0ms	122×	body	80	valid
3.0ms	20×	body	320	valid
1.0ms	12×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	11	11
2	14	11
done	14	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
2.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
69×	`times-frac`
50×	`sqrt-prod`
42×	`add-cube-cbrt`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `associate-/r/` `flip-+`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `frac-sub` `flip--`

Counts

4 → 133

Calls

4 calls:

12.0ms	(sqrt (+ x 1.0))
26.0ms	(/ 1.0 (sqrt (+ x 1.0)))
12.0ms	(/ 1.0 (sqrt x))
130.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series454.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(sqrt (+ x 1.0))
124.0ms	(/ 1.0 (sqrt (+ x 1.0)))
64.0ms	(/ 1.0 (sqrt x))
217.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify1.3s

Counts

145 → 145

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	215	1942
1	463	1778
2	1680	1704
done	5001	1700

prune806.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 22.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
2.4b	(exp (log (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))
2.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
99×	`times-frac`
64×	`sqrt-prod`
49×	`add-cube-cbrt`
23×	`log-prod` `exp-sum`
22×	`distribute-lft-out--`
18×	`difference-of-squares`
13×	`associate-/r*`
10×	`distribute-lft-out`
8×	`add-exp-log` `add-cbrt-cube`
6×	`div-inv` `associate-/l*` `add-log-exp`
5×	`pow1`
4×	`exp-prod`
3×	`log-div` `exp-diff`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `sqrt-div` `div-exp` `clear-num` `associate-/r/` `frac-sub` `flip--`
1×	`sub-neg` `flip3-+` `diff-log` `log-pow` `flip-+` `rem-exp-log`

Counts

4 → 155

Calls

4 calls:

20.0ms	(/ 1.0 (sqrt (+ x 1.0)))
11.0ms	(/ 1.0 (sqrt x))
91.0ms	(exp (log (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))
113.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series617.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ 1.0 (sqrt (+ x 1.0)))
61.0ms	(/ 1.0 (sqrt x))
217.0ms	(exp (log (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))))
217.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify1.3s

Counts

167 → 167

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	270	2756
1	528	2451
2	1691	2326
done	5000	2320

prune964.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 22.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
0.3b	(/ 1.0 (sqrt x))
0.3b	(/ 1.0 (sqrt x))
2.6b	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

190×	`sqrt-prod`
152×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
122×	`times-frac`
54×	`add-cube-cbrt`
32×	`difference-of-squares`
31×	`associate-r`
24×	`distribute-lft-out--`
21×	`distribute-lft-out`
18×	`sqrt-div`
15×	`associate-l`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`frac-times`
8×	`div-inv`
6×	`pow1` `associate-/l*` `add-log-exp`
5×	`flip3--` `frac-sub` `flip--`
4×	`flip3-+` `frac-add` `flip-+`
3×	`sub-neg` `associate-r/` `associate-l/`
2×	`cbrt-undiv` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `div-exp` `clear-num`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 196

Calls

4 calls:

961.0ms	(* (+ (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
11.0ms	(/ 1.0 (sqrt x))
11.0ms	(/ 1.0 (sqrt x))
132.0ms	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

1.0s	(* (+ (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
44.0ms	(/ 1.0 (sqrt x))
60.0ms	(/ 1.0 (sqrt x))
422.0ms	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

simplify642.0ms

Counts

208 → 208

Iterations

Useful iterations: done (631.0ms)

Iter	Nodes	Cost
0	383	5119
1	1020	4435
done	5000	4183

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.0b

localize71.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sqrt (/ 1.0 (sqrt (+ x 1.0)))) 3)
0.5b	(* (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt x))))
0.7b	(pow (sqrt (/ 1.0 (sqrt x))) 3)
2.6b	(- (pow (sqrt (/ 1.0 (sqrt x))) 3) (pow (sqrt (/ 1.0 (sqrt (+ x 1.0)))) 3))

rewrite550.0ms

Algorithm

rewrite-expression-head

Rules

612×	`sqrt-prod`
472×	`add-sqr-sqrt`
330×	`times-frac`
262×	`*-un-lft-identity`
183×	`unpow-prod-down` `cube-prod`
148×	`add-cube-cbrt`
100×	`difference-of-squares`
49×	`distribute-lft-out--`
33×	`swap-sqr`
25×	`associate-r` `associate-l`
23×	`pow1`
22×	`sqr-pow`
18×	`distribute-lft-out`
16×	`div-inv` `unswap-sqr`
12×	`sqrt-div`
10×	`sqrt-pow1` `pow1/2`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow-unpow` `pow-pow` `add-log-exp`
5×	`pow-prod-up`
4×	`cube-div` `associate-/r/`
3×	`pow-prod-down` `pow-sqr`
2×	`cube-mult` `pow-to-exp` `flip3-+` `unpow3` `pow-exp` `sqrt-pow2` `flip-+` `rem-cube-cbrt`
1×	`difference-cubes` `pow2` `frac-times` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `frac-sub` `flip--` `cbrt-unprod`

Counts

4 → 442

Calls

4 calls:

19.0ms	(pow (sqrt (/ 1.0 (sqrt (+ x 1.0)))) 3)
59.0ms	(* (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt x))))
15.0ms	(pow (sqrt (/ 1.0 (sqrt x))) 3)
405.0ms	(- (pow (sqrt (/ 1.0 (sqrt x))) 3) (pow (sqrt (/ 1.0 (sqrt (+ x 1.0)))) 3))

series1.6s

Counts

4 → 12

Calls

4 calls:

390.0ms	(pow (sqrt (/ 1.0 (sqrt (+ x 1.0)))) 3)
125.0ms	(* (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt x))))
504.0ms	(pow (sqrt (/ 1.0 (sqrt x))) 3)
550.0ms	(- (pow (sqrt (/ 1.0 (sqrt x))) 3) (pow (sqrt (/ 1.0 (sqrt (+ x 1.0)))) 3))

simplify881.0ms

Counts

454 → 454

Iterations

Useful iterations: done (856.0ms)

Iter	Nodes	Cost
0	567	10824
1	1668	9331
done	5000	9120

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.0b

regimes106.0ms

Accuracy

97.1% (0.3b remaining)

Error of 10.7b against oracle of 10.5b and baseline of 20.1b

bsearch78.0ms

Steps

Iters	Range		Point
9	0.5323112742081106	59347805.45921656	8754.115093484925

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	110
1	61	110
done	61	110

end0.0ms

sample1.9s

Algorithm

intervals

Results

726.0ms	1859×	body	640	valid
291.0ms	7916×	body	80	nan
280.0ms	4044×	body	80	valid
227.0ms	1156×	body	1280	valid
62.0ms	615×	body	320	valid
22.0ms	326×	body	160	valid