Details

sample23.0ms

Algorithm

intervals

Results

4.0ms	56×	body	1280	valid
4.0ms	254×	body	80	nan
3.0ms	44×	body	640	valid
2.0ms	123×	body	80	valid
1.0ms	19×	body	320	valid
0.0ms	14×	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: 32.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
4.2b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite17.0ms

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:

3.0ms	(sqrt (+ x 1.0))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series99.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(sqrt (+ x 1.0))
70.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify45.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (31.0ms)

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

prune131.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite27.0ms

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:

3.0ms	(sqrt (+ x 1.0))
8.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series233.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(sqrt (+ x 1.0))
64.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
139.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify50.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (42.0ms)

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

prune215.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
12×	`times-frac`
8×	`pow1` `sqrt-pow1` `sqrt-div`
6×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
4×	`expm1-log1p-u` `rem-sqrt-square` `pow1/2` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`flip3-+` `associate-/r*` `flip-+`
2×	`associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 93

Calls

4 calls:

4.0ms	(sqrt (sqrt (+ x 1.0)))
4.0ms	(sqrt (sqrt (+ x 1.0)))
1.0ms	(fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x))
5.0ms	(/ (+ 1.0 0) (fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x)))

series668.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(sqrt (sqrt (+ x 1.0)))
83.0ms	(sqrt (sqrt (+ x 1.0)))
211.0ms	(fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x))
291.0ms	(/ (+ 1.0 0) (fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x)))

simplify75.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	743	1316
1	3236	1218
2	5003	1183

prune326.0ms

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

204×	`sqrt-prod`
91×	`add-sqr-sqrt`
81×	`sqrt-pow1`
56×	`*-un-lft-identity`
42×	`sqrt-div`
38×	`pow1`
32×	`add-cube-cbrt`
27×	`pow1/2` `swap-sqr`
16×	`unswap-sqr`
13×	`associate-r` `associate-l` `pow-prod-up`
12×	`times-frac`
11×	`distribute-lft-out`
8×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
7×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`rem-sqrt-square` `associate-/r*`
2×	`associate-r/` `associate-l/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 195

Calls

4 calls:

5.0ms	(sqrt (sqrt (sqrt (+ x 1.0))))
1.0ms	(fma (sqrt (sqrt (+ x 1.0))) (* (sqrt (sqrt (sqrt (+ x 1.0)))) (sqrt (sqrt (sqrt (+ x 1.0))))) (sqrt x))
5.0ms	(/ (+ 1.0 0) (fma (sqrt (sqrt (+ x 1.0))) (* (sqrt (sqrt (sqrt (+ x 1.0)))) (sqrt (sqrt (sqrt (+ x 1.0))))) (sqrt x)))
23.0ms	(* (sqrt (sqrt (sqrt (+ x 1.0)))) (sqrt (sqrt (sqrt (+ x 1.0)))))

series662.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(sqrt (sqrt (sqrt (+ x 1.0))))
206.0ms	(fma (sqrt (sqrt (+ x 1.0))) (* (sqrt (sqrt (sqrt (+ x 1.0)))) (sqrt (sqrt (sqrt (+ x 1.0))))) (sqrt x))
286.0ms	(/ (+ 1.0 0) (fma (sqrt (sqrt (+ x 1.0))) (* (sqrt (sqrt (sqrt (+ x 1.0)))) (sqrt (sqrt (sqrt (+ x 1.0))))) (sqrt x)))
86.0ms	(* (sqrt (sqrt (sqrt (+ x 1.0)))) (sqrt (sqrt (sqrt (+ x 1.0)))))

simplify128.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	985	2445
1	4762	2112
2	5001	2111

prune426.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes31.0ms

Accuracy

0% (0.2b 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	10
1	16	10
2	16	10

end0.0ms

sample618.0ms

Algorithm

intervals

Results

136.0ms	1698×	body	1280	valid
122.0ms	7827×	body	80	nan
81.0ms	1249×	body	640	valid
72.0ms	4106×	body	80	valid
31.0ms	619×	body	320	valid
10.0ms	328×	body	160	valid