Details

sample26.0ms

Algorithm

intervals

Results

5.0ms	293×	body	80	nan
3.0ms	43×	body	1280	valid
3.0ms	141×	body	80	valid
2.0ms	37×	body	640	valid
1.0ms	19×	body	320	valid
1.0ms	16×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.3b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
4.3b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite59.0ms

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:

7.0ms	(sqrt (+ x 1.0))
48.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series99.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(sqrt (+ x 1.0))
69.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify39.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	299	1161
1	921	822
2	5001	744

prune139.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
33×	`distribute-lft-out`
32×	`sqrt-prod`
24×	`times-frac`
21×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
7×	`fma-def`
6×	`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 → 94

Calls

3 calls:

7.0ms	(sqrt (+ x 1.0))
31.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
54.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series235.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(sqrt (+ x 1.0))
67.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
139.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify49.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	409	789
1	1675	716
2	5001	675

prune223.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite395.0ms

Algorithm

rewrite-expression-head

Rules

597×	`*-un-lft-identity`
420×	`sqrt-prod`
256×	`distribute-lft-out`
247×	`times-frac`
130×	`add-sqr-sqrt`
99×	`add-cube-cbrt`
71×	`swap-sqr`
33×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `unswap-sqr`
8×	`associate-/l*`
7×	`div-inv`
5×	`sqrt-div` `pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `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 → 324

Calls

4 calls:

47.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
52.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
53.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
218.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

series795.0ms

Counts

4 → 12

Calls

4 calls:

345.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
137.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
146.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
167.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify134.0ms

Algorithm

egg-herbie

Counts

336 → 336

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	723	3900
1	3733	3364
2	5002	3360

prune625.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
0.2b	(* (* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

rewrite655.0ms

Algorithm

rewrite-expression-head

Rules

301×	`*-un-lft-identity`
294×	`sqrt-prod`
165×	`times-frac`
132×	`add-sqr-sqrt`
116×	`distribute-lft-out`
84×	`add-cube-cbrt`
81×	`associate-r`
34×	`associate-l`
22×	`sqrt-div`
18×	`unswap-sqr`
16×	`pow1`
15×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
10×	`pow-prod-down` `associate-/r/`
8×	`associate-/l*`
7×	`flip3-+` `flip-+`
6×	`frac-times` `associate-*l/`
5×	`sqrt-pow1` `pow1/2` `div-inv`
4×	`expm1-log1p-u` `associate-*r/` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`sqrt-unprod`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `*-commutative`

Counts

4 → 297

Calls

4 calls:

55.0ms	(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
53.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
212.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
315.0ms	(* (* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

318.0ms	(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
142.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
580.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
168.0ms	(* (* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

simplify72.0ms

Algorithm

egg-herbie

Counts

309 → 309

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1189	5386
1	5002	5090

prune949.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes42.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	16	6

end0.0ms

sample706.0ms

Algorithm

intervals

Results

138.0ms	7890×	body	80	nan
137.0ms	1719×	body	1280	valid
81.0ms	1221×	body	640	valid
76.0ms	4122×	body	80	valid
30.0ms	624×	body	320	valid
10.0ms	314×	body	160	valid