Details

sample36.0ms

Algorithm

intervals

Results

9.0ms	61×	body	1280	valid
7.0ms	252×	body	80	nan
5.0ms	43×	body	640	valid
4.0ms	132×	body	80	valid
1.0ms	13×	body	320	valid
0.0ms	7×	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: 29.4b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
1.5b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 35

Calls

2 calls:

4.0ms	(sqrt (+ x 1.0))
22.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series104.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(sqrt (+ x 1.0))
71.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify57.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	182	265
1	544	243
2	2020	233
3	5002	230

prune79.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
20×	`sqrt-prod`
18×	`times-frac`
17×	`distribute-lft-out`
15×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
6×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/l*`
2×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

2 → 57

Calls

2 calls:

4.0ms	(sqrt (+ x 1.0))
26.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series167.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(sqrt (+ x 1.0))
135.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify35.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	309	501
1	1128	459
2	5002	448

prune137.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
0.2b	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
13×	`cbrt-prod`
10×	`associate-r`
9×	`times-frac` `sqrt-prod`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `cbrt-div`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`associate-l` `associate-/r` `distribute-lft-out` `associate-/l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 86

Calls

4 calls:

14.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
13.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))

series449.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
95.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
88.0ms	(cbrt (+ x 1.0))
85.0ms	(cbrt (+ x 1.0))

simplify101.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	850	1475
1	3967	1385
2	5002	1364

prune346.0ms

Pruning

9 alts after pruning (8 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	(* (sqrt (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))) (sqrt (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

53×	`pow1`
28×	`sqrt-pow1`
24×	`sqrt-div`
20×	`pow-prod-down`
18×	`cbrt-div`
17×	`*-un-lft-identity`
14×	`associate-*r/`
13×	`add-sqr-sqrt`
12×	`cbrt-prod`
11×	`add-cube-cbrt`
10×	`pow1/2` `pow-prod-up`
9×	`flip3-+` `flip-+`
6×	`add-exp-log` `pow-sqr` `add-cbrt-cube`
4×	`frac-times` `swap-sqr` `associate-r` `associate-l` `sqrt-prod` `add-log-exp`
3×	`pow1/3` `distribute-lft-out`
2×	`associate-*l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))
39.0ms	(* (sqrt (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))) (sqrt (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))

series366.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(cbrt (+ x 1.0))
89.0ms	(cbrt (+ x 1.0))
88.0ms	(cbrt (+ x 1.0))
100.0ms	(* (sqrt (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))) (sqrt (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	400	1126
1	1601	972
2	5001	915

prune353.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes66.0ms

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	9	5
1	9	5

end0.0ms

sample1.0s

Algorithm

intervals

Results

268.0ms	1744×	body	1280	valid
228.0ms	7896×	body	80	nan
147.0ms	1250×	body	640	valid
138.0ms	4077×	body	80	valid
55.0ms	627×	body	320	valid
19.0ms	302×	body	160	valid