Details

sample23.0ms

Algorithm

intervals

Results

5.0ms	275×	body	80	nan
4.0ms	44×	body	1280	valid
3.0ms	45×	body	640	valid
3.0ms	140×	body	80	valid
1.0ms	14×	body	320	valid
0.0ms	13×	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: 27.5b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite38.0ms

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:

4.0ms	(sqrt (+ x 1.0))
27.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series103.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(sqrt (+ x 1.0))
66.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify42.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (31.0ms)

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

prune132.0ms

Pruning

3 alts after pruning (3 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))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite58.0ms

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:

4.0ms	(sqrt (+ x 1.0))
18.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
32.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series234.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(sqrt (+ x 1.0))
66.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
140.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify48.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	409	790
1	1672	716
2	5001	675

prune210.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 103

Calls

4 calls:

2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))
23.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (+ x 1.0))
89.0ms	(cbrt (+ x 1.0))
89.0ms	(cbrt (+ x 1.0))
104.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

simplify156.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 3 (147.0ms)

Iter	Nodes	Cost
0	321	818
1	1071	769
2	4756	694
3	5001	692

prune374.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

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:

5.0ms	(sqrt (sqrt (+ x 1.0)))
4.0ms	(sqrt (sqrt (+ x 1.0)))
31.0ms	(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
31.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series361.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(sqrt (sqrt (+ x 1.0)))
91.0ms	(sqrt (sqrt (+ x 1.0)))
142.0ms	(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
38.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify91.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	594	1528
1	2800	1345
2	5001	1318

prune574.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes28.0ms

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

sample657.0ms

Algorithm

intervals

Results

146.0ms	1723×	body	1280	valid
138.0ms	7968×	body	80	nan
82.0ms	4137×	body	80	valid
80.0ms	1228×	body	640	valid
30.0ms	606×	body	320	valid
10.0ms	306×	body	160	valid