Details

sample58.0ms

Algorithm

intervals

Results

11.0ms	286×	body	80	nan
8.0ms	45×	body	1280	valid
8.0ms	57×	body	640	valid
5.0ms	122×	body	80	valid
2.0ms	20×	body	320	valid
1.0ms	12×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune49.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite115.0ms

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:

13.0ms	(sqrt (+ x 1.0))
94.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series162.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(sqrt (+ x 1.0))
116.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify987.0ms

Counts

95 → 95

Iterations

Useful iterations: done (982.0ms)

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

prune356.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

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))))

rewrite148.0ms

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))
39.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
89.0ms	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

series389.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(sqrt (+ x 1.0))
100.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
237.0ms	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

simplify1.7s

Counts

102 → 102

Iterations

Useful iterations: done (1.7s)

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

prune569.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

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:

26.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
2.0ms	(cbrt x)
2.0ms	(cbrt x)

series1.4s

Counts

4 → 12

Calls

4 calls:

363.0ms	(* (cbrt x) (cbrt x))
338.0ms	(cbrt x)
341.0ms	(cbrt x)
345.0ms	(cbrt x)

simplify1.5s

Counts

93 → 93

Iterations

Useful iterations: done (1.4s)

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

prune707.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite626.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity`
274×	`sqrt-prod`
157×	`times-frac`
119×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 258

Calls

4 calls:

79.0ms	(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
78.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
77.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
358.0ms	(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

659.0ms	(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
262.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
258.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
305.0ms	(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

simplify2.8s

Counts

270 → 270

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	317	6276
1	734	4476
2	3335	4198
done	5002	4140

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes108.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	12	18
1	14	16
2	15	16
done	15	16

end0.0ms

sample2.6s

Algorithm

intervals

Results

791.0ms	1235×	body	640	valid
497.0ms	7916×	body	80	nan
493.0ms	1773×	body	1280	valid
177.0ms	4046×	body	80	valid
125.0ms	617×	body	320	valid
27.0ms	329×	body	160	valid