Details

sample61.0ms

Algorithm

intervals

Results

13.0ms	58×	body	1280	valid
11.0ms	252×	body	80	nan
7.0ms	40×	body	640	valid
6.0ms	123×	body	80	valid
3.0ms	21×	body	320	valid
1.0ms	14×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

61×	`sqrt-prod`
54×	`*-un-lft-identity`
42×	`add-sqr-sqrt` `prod-diff`
31×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `distribute-lft-out--`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+` `hypot-def`

Counts

2 → 89

Calls

2 calls:

8.0ms	(sqrt (+ x 1.0))
123.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series126.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(sqrt (+ x 1.0))
91.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify823.0ms

Counts

95 → 95

Iterations

Useful iterations: done (818.0ms)

Iter	Nodes	Cost
0	137	1993
1	316	1446
2	1040	1125
done	5000	951

prune223.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt x) (sqrt (+ x 1.0)))
0.2b	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
32×	`distribute-lft-out`
31×	`sqrt-prod`
24×	`times-frac`
21×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
6×	`fma-def` `associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `associate-/l*`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `hypot-def` `div-inv`

Counts

3 → 93

Calls

3 calls:

14.0ms	(sqrt (+ x 1.0))
41.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
104.0ms	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

series317.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(sqrt (+ x 1.0))
95.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
187.0ms	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

simplify1.3s

Counts

102 → 102

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	169	1453
1	428	1178
2	1995	1093
done	5001	1085

prune322.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x 1.0)))
0.1b	(sqrt (sqrt (+ x 1.0)))
0.2b	(/ (+ 1.0 0) (+ (sqrt x) (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
0.3b	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
63×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
29×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
12×	`times-frac` `distribute-lft-out`
10×	`flip3-+` `associate-r` `associate-l` `flip-+`
9×	`pow-prod-up` `unswap-sqr`
8×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `frac-times` `rem-sqrt-square` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-/r*`
2×	`associate-r/` `associate-l/` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 175

Calls

4 calls:

11.0ms	(sqrt (sqrt (+ x 1.0)))
9.0ms	(sqrt (sqrt (+ x 1.0)))
29.0ms	(/ (+ 1.0 0) (+ (sqrt x) (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
68.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series425.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(sqrt (sqrt (+ x 1.0)))
121.0ms	(sqrt (sqrt (+ x 1.0)))
157.0ms	(/ (+ 1.0 0) (+ (sqrt x) (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
43.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify2.2s

Counts

187 → 187

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	266	3296
1	647	1967
2	2930	1850
done	5002	1834

prune638.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

15.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.1s

Counts

4 → 12

Calls

4 calls:

286.0ms	(* (cbrt x) (cbrt x))
259.0ms	(cbrt x)
298.0ms	(cbrt x)
271.0ms	(cbrt x)

simplify1.3s

Counts

93 → 93

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	65	554
1	143	443
2	719	423
done	5000	409

prune482.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes36.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	11	18
1	14	16
2	15	16
done	15	16

end0.0ms

sample2.1s

Algorithm

intervals

Results

897.0ms	8028×	body	80	nan
345.0ms	1755×	body	1280	valid
207.0ms	1232×	body	640	valid
191.0ms	4070×	body	80	valid
64.0ms	605×	body	320	valid
22.0ms	338×	body	160	valid