Details

sample123.0ms

Algorithm

intervals

Results

35.0ms	188×	body	2560	nan
27.0ms	174×	body	1280	nan
10.0ms	290×	body	80	nan
10.0ms	256×	body	80	valid
10.0ms	79×	body	640	nan
7.0ms	43×	body	320	nan
1.0ms	19×	body	160	nan

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 (100.0%)

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: 32.4b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
0.2b	(log (+ x (sqrt (- (* x x) 1.0))))
30.2b	(sqrt (- (* x x) 1.0))

rewrite16.0ms

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

series22.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ x (sqrt (- (* x x) 1.0)))
13.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
4.0ms	(sqrt (- (* x x) 1.0))

simplify134.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (129.0ms)

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

prune96.0ms

Filtered

52 candidates to 43 candidates (17.3%)

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: 0.0b

Counts

53 → 3

localize16.0ms

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))))
0.4b	(/ 0.09375 (pow x 4))

rewrite67.0ms

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:

15.0ms	(- (log x) (/ (/ 0.25 x) x))
6.0ms	(/ (/ 0.25 x) x)
32.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
5.0ms	(/ 0.09375 (pow x 4))

series40.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(- (log x) (/ (/ 0.25 x) x))
3.0ms	(/ (/ 0.25 x) x)
10.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
4.0ms	(/ 0.09375 (pow x 4))

simplify64.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	694	1225
1	2546	1106
2	5001	1095

prune258.0ms

Filtered

179 candidates to 119 candidates (33.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	179	3	182

Merged error: 0b

Counts

182 → 3

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ (neg 0.5) x) (/ 0.125 (pow x 3)))
0.2b	(log (+ (* 2 x) (- (/ (neg 0.5) x) (/ 0.125 (pow x 3)))))
0.7b	(/ 0.125 (pow x 3))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
53×	`times-frac`
39×	`*-un-lft-identity`
29×	`add-cube-cbrt`
14×	`unpow-prod-down` `cube-prod`
12×	`associate-/r*`
10×	`difference-of-squares`
9×	`add-exp-log`
6×	`sqr-pow`
5×	`add-cbrt-cube` `add-log-exp`
4×	`pow1` `cube-mult` `unpow3`
3×	`log-prod` `div-exp` `associate-/l*` `distribute-lft-out--`
2×	`log-div`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-neg-in` `frac-2neg` `flip3-+` `diff-log` `div-sub` `rem-log-exp` `pow-exp` `clear-num` `log-pow` `frac-sub` `flip--` `flip-+` `div-inv`

Counts

3 → 106

Calls

3 calls:

55.0ms	(- (/ (neg 0.5) x) (/ 0.125 (pow x 3)))
58.0ms	(log (+ (* 2 x) (- (/ (neg 0.5) x) (/ 0.125 (pow x 3)))))
5.0ms	(/ 0.125 (pow x 3))

series22.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(- (/ (neg 0.5) x) (/ 0.125 (pow x 3)))
9.0ms	(log (+ (* 2 x) (- (/ (neg 0.5) x) (/ 0.125 (pow x 3)))))
4.0ms	(/ 0.125 (pow x 3))

simplify61.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	457	837
1	2004	799
2	5002	799

prune159.0ms

Filtered

115 candidates to 71 candidates (38.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	115	3	118

Merged error: 0b

Counts

118 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
0.4b	(/ 0.09375 (pow x 4))
0.5b	(cbrt (pow (+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))) 3))
0.7b	(pow (+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))) 3)

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

128×	`*-un-lft-identity`
50×	`distribute-lft-out--`
40×	`distribute-lft-out`
35×	`pow1`
34×	`unpow-prod-down`
30×	`log-pow`
28×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt`
22×	`cube-prod`
21×	`times-frac`
10×	`add-exp-log`
9×	`add-log-exp`
8×	`associate--l+`
7×	`associate-+r+` `associate-/r*` `add-cbrt-cube`
6×	`log-prod` `sqr-pow`
4×	`cube-div`
3×	`pow-unpow` `associate-+l+` `flip3-+` `diff-log` `div-exp` `sum-log` `flip-+` `associate-/l*`
2×	`cube-mult` `pow-to-exp` `sub-neg` `cbrt-div` `unpow3` `pow-exp`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 157

Calls

4 calls:

31.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
4.0ms	(/ 0.09375 (pow x 4))
34.0ms	(cbrt (pow (+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))) 3))
32.0ms	(pow (+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))) 3)

series45.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
4.0ms	(/ 0.09375 (pow x 4))
10.0ms	(cbrt (pow (+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))) 3))
22.0ms	(pow (+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))) 3)

simplify111.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	980	2067
1	4445	1969
2	5001	1940

prune265.0ms

Filtered

169 candidates to 81 candidates (52.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	169	3	172

Merged error: 0b

Counts

172 → 3

regimes31.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	8
1	17	8

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.2s	6112×	body	2560	nan
828.0ms	5152×	body	1280	nan
328.0ms	8000×	body	80	valid
324.0ms	2556×	body	640	nan
318.0ms	8782×	body	80	nan
130.0ms	1333×	body	320	nan
39.0ms	596×	body	160	nan

Details

sample123.0ms

simplify5.0ms

prune2.0ms

localize7.0ms

rewrite16.0ms

series22.0ms

simplify134.0ms

prune96.0ms

localize16.0ms

rewrite67.0ms

series40.0ms

simplify64.0ms

prune258.0ms

localize11.0ms

rewrite123.0ms

series22.0ms

simplify61.0ms

prune159.0ms

localize17.0ms

rewrite111.0ms

series45.0ms

simplify111.0ms

prune265.0ms

regimes31.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.7s

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