Details

sample25.0ms

Algorithm

intervals

Results

5.0ms	288×	body	80	nan
5.0ms	57×	body	1280	valid
2.0ms	133×	body	80	valid
2.0ms	31×	body	640	valid
1.0ms	22×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.1b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite28.0ms

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))
24.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series105.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(sqrt (+ x 1.0))
69.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify58.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (54.0ms)

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

prune82.0ms

Filtered

41 candidates to 28 candidates (68.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

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 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 71

Calls

3 calls:

4.0ms	(sqrt (+ x 1.0))
16.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
23.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series239.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(sqrt (+ x 1.0))
66.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
143.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify38.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	341	624
1	1239	566
2	5001	533

prune161.0ms

Filtered

80 candidates to 53 candidates (66.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 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))

rewrite36.0ms

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:

13.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
16.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))

series469.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
101.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
90.0ms	(cbrt (+ x 1.0))
91.0ms	(cbrt (+ x 1.0))

simplify99.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (85.0ms)

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

prune349.0ms

Filtered

98 candidates to 79 candidates (80.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

22×	`sqrt-prod`
20×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`cbrt-prod`
13×	`associate-r`
12×	`add-cube-cbrt`
8×	`cbrt-div`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `sqrt-div` `flip-+` `distribute-lft-out` `add-log-exp` `unswap-sqr`
3×	`pow1/3` `associate-l`
2×	`associate-*r/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 75

Calls

4 calls:

16.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (sqrt (cbrt (+ x 1.0)))))
2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))

series373.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (sqrt (cbrt (+ x 1.0)))))
91.0ms	(cbrt (+ x 1.0))
91.0ms	(cbrt (+ x 1.0))
92.0ms	(cbrt (+ x 1.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	397	816
1	1356	767
2	5001	748

prune337.0ms

Filtered

87 candidates to 69 candidates (79.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	16
1	16	16

end0.0ms

sample665.0ms

Algorithm

intervals

Results

153.0ms	1766×	body	1280	valid
144.0ms	8031×	body	80	nan
80.0ms	1219×	body	640	valid
74.0ms	4090×	body	80	valid
33.0ms	623×	body	320	valid
10.0ms	302×	body	160	valid