Details

sample51.0ms

Algorithm

intervals

Results

10.0ms	297×	body	80	nan
8.0ms	52×	body	640	valid
7.0ms	38×	body	1280	valid
6.0ms	132×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	15×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
3.9b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite159.0ms

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:

7.0ms	(sqrt (+ x 1.0))
21.0ms	(/ 1.0 (sqrt (+ x 1.0)))
10.0ms	(/ 1.0 (sqrt x))
113.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt (+ x 1.0))
84.0ms	(/ 1.0 (sqrt (+ x 1.0)))
40.0ms	(/ 1.0 (sqrt x))
131.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify96.0ms

Counts: 145 → 145

prune465.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 16.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
4.0b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`sqrt-prod`
20×	`*-un-lft-identity`
18×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `add-cube-cbrt`
7×	`associate-r`
6×	`sqrt-div` `associate-r/` `associate-l*` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `difference-of-squares` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+` `distribute-lft-out` `distribute-lft-out--`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `times-frac` `sqrt-unprod` `diff-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 93

Calls

4 calls:

17.0ms	(sqrt (+ x 1.0))
93.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
45.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
71.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series507.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (+ x 1.0))
320.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
69.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
85.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify55.0ms

Counts: 105 → 105

prune284.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
2.4b	(+ x (- 1.0 x))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log` `add-cbrt-cube`
22×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`sqrt-prod`
11×	`add-log-exp`
8×	`pow1` `cbrt-undiv` `add-cube-cbrt` `div-exp` `prod-exp` `cbrt-unprod`
7×	`associate-r` `distribute-lft-out`
6×	`associate-l`
5×	`associate-*r/`
4×	`flip3-+` `sqrt-div` `flip-+` `unswap-sqr`
3×	`pow-prod-down` `sum-log`
2×	`+-commutative` `associate-+r+` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`associate-+r-` `sub-neg` `frac-2neg` `times-frac` `sqrt-unprod` `diff-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l/` `associate-/l*` `distribute-lft-out--`

Counts

4 → 92

Calls

4 calls:

33.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
60.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
38.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
33.0ms	(+ x (- 1.0 x))

series770.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
619.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
56.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms	(+ x (- 1.0 x))

simplify74.0ms

Counts: 104 → 104

prune334.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
31×	`sqrt-prod`
29×	`add-exp-log` `add-cbrt-cube`
27×	`add-sqr-sqrt`
21×	`distribute-lft-out`
19×	`add-cube-cbrt` `times-frac`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod`
7×	`associate-r` `associate-/r*`
6×	`associate-l` `add-log-exp`
5×	`associate-*r/`
4×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `associate-/l*` `unswap-sqr`
3×	`pow-prod-down`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `div-inv`
1×	`+-commutative` `sqrt-unprod` `sum-log` `*-commutative` `associate-/l/`

Counts

4 → 116

Calls

4 calls:

57.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
50.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
71.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
31.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

series1.0s

Counts

4 → 12

Calls

4 calls:

79.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
203.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
640.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
87.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

simplify84.0ms

Counts: 128 → 128

prune351.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify62.0ms

end0.0ms

sample1.9s

Algorithm

intervals

Results

580.0ms	1855×	body	640	valid
389.0ms	7805×	body	80	nan
292.0ms	1154×	body	1280	valid
219.0ms	4071×	body	80	valid
87.0ms	337×	body	160	valid
62.0ms	583×	body	320	valid