Details

sample48.0ms

Algorithm

intervals

Results

12.0ms	264×	body	160	nan
12.0ms	548×	body	80	nan
8.0ms	256×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	5
1	11	5
2	11	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 31.6b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (+ x (sqrt (- (* x x) 1.0))))
0.0b	(+ x (sqrt (- (* x x) 1.0)))
29.5b	(sqrt (- (* x x) 1.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`add-exp-log` `log-prod` `sqrt-prod`
3×	`add-cbrt-cube`
2×	`log-div` `flip3-+` `sqrt-div` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow` `flip--` `difference-of-squares`

Counts

3 → 43

Calls

3 calls:

6.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
9.0ms	(+ x (sqrt (- (* x x) 1.0)))
4.0ms	(sqrt (- (* x x) 1.0))

series311.0ms

Counts

3 → 9

Calls

3 calls:

186.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
75.0ms	(+ x (sqrt (- (* x x) 1.0)))
50.0ms	(sqrt (- (* x x) 1.0))

simplify131.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (125.0ms)

Iter	Nodes	Cost
0	316	408
1	1042	379
2	4663	366
3	5002	365

prune108.0ms

Filtered

52 candidates to 43 candidates (82.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	49	3	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	3	53

Merged error: 0b

Counts

53 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x (sqrt 1.0)))
0.0b	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`sqrt-prod`
16×	`*-un-lft-identity`
14×	`sqrt-div`
10×	`pow1` `add-cube-cbrt`
9×	`associate-r`
7×	`add-exp-log` `associate-l`
6×	`flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
4×	`frac-times` `unswap-sqr`
3×	`log-prod` `flip3--` `sqrt-pow1` `pow1/2` `pow-prod-down` `flip--`
2×	`log-div` `associate-r/` `associate-l/` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sqrt-unprod` `rem-log-exp` `prod-exp` `sum-log` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 83

Calls

4 calls:

4.0ms	(sqrt (+ x (sqrt 1.0)))
2.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
2.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
15.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series658.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt (+ x (sqrt 1.0)))
265.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
142.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
191.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify48.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	491	1081
1	1717	994
2	5002	974

prune212.0ms

Filtered

95 candidates to 72 candidates (75.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	95	3	98

Merged error: 0b

Counts

98 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log x) (/ (/ 0.25 x) x))
0.1b	(/ (/ 0.25 x) x)
0.2b	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
0.2b	(/ 0.09375 (pow x 4))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

99×	`times-frac`
88×	`*-un-lft-identity`
74×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
16×	`associate-/l*`
14×	`add-exp-log`
12×	`unpow-prod-down` `distribute-lft-out--`
11×	`pow1` `associate--l+` `add-cbrt-cube`
10×	`associate-/r*` `add-log-exp`
9×	`log-prod`
8×	`distribute-lft-out`
7×	`associate-+r+` `log-pow`
6×	`div-exp` `div-inv`
4×	`cbrt-undiv` `diff-log` `sqr-pow`
3×	`sub-neg` `associate-+l+` `sum-log` `difference-of-squares`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `flip3--` `flip3-+` `pow-exp` `flip--` `flip-+` `associate-/l/`

Counts

4 → 167

Calls

4 calls:

17.0ms	(- (log x) (/ (/ 0.25 x) x))
6.0ms	(/ (/ 0.25 x) x)
30.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
5.0ms	(/ 0.09375 (pow x 4))

series505.0ms

Counts

4 → 12

Calls

4 calls:

342.0ms	(- (log x) (/ (/ 0.25 x) x))
37.0ms	(/ (/ 0.25 x) x)
92.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
35.0ms	(/ 0.09375 (pow x 4))

simplify72.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	683	1218
1	2492	1094
2	5001	1089

prune347.0ms

Filtered

179 candidates to 117 candidates (65.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	179	3	182

Merged error: 0b

Counts

182 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (- (* x x) 1.0)))
29.5b	(sqrt (- (* x x) 1.0))
29.5b	(sqrt (- (* x x) 1.0))
29.5b	(sqrt (- (* x x) 1.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `sqrt-prod`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-div`
7×	`pow1` `cbrt-prod`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--` `add-log-exp` `difference-of-squares`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 65

Calls

4 calls:

5.0ms	(cbrt (sqrt (- (* x x) 1.0)))
4.0ms	(sqrt (- (* x x) 1.0))
4.0ms	(sqrt (- (* x x) 1.0))
4.0ms	(sqrt (- (* x x) 1.0))

series342.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt (sqrt (- (* x x) 1.0)))
54.0ms	(sqrt (- (* x x) 1.0))
50.0ms	(sqrt (- (* x x) 1.0))
55.0ms	(sqrt (- (* x x) 1.0))

simplify109.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	274	527
1	844	512
2	3517	502
3	5001	498

prune213.0ms

Filtered

77 candidates to 65 candidates (84.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	77	3	80

Merged error: 0b

Counts

80 → 3

regimes14.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

end0.0ms

sample1.3s

Algorithm

intervals

Results

375.0ms	16081×	body	80	nan
354.0ms	7371×	body	160	nan
244.0ms	8000×	body	80	valid