Details

sample85.0ms

Algorithm

intervals

Results

20.0ms	105×	body	2560	nan
18.0ms	516×	body	80	nan
13.0ms	80×	body	1280	nan
10.0ms	256×	body	80	valid
5.0ms	41×	body	640	nan
1.0ms	15×	body	320	nan
1.0ms	9×	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 (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: 34.4b

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))))
32.0b	(sqrt (- (* x x) 1.0))

rewrite21.0ms

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))))
8.0ms	(sqrt (- (* x x) 1.0))

series329.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(+ x (sqrt (- (* x x) 1.0)))
204.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
53.0ms	(sqrt (- (* x x) 1.0))

simplify131.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (126.0ms)

Iter	Nodes	Cost
0	316	409
1	1036	379
2	4629	366
3	5001	365

prune112.0ms

Filtered

52 candidates to 43 candidates (82.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	2	53

Merged error: 0.0b

Counts

53 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.2b	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

2.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
2.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
16.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series645.0ms

Counts

3 → 9

Calls

3 calls:

145.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
297.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
203.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify44.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	440	941
1	1553	864
2	5001	848

prune199.0ms

Filtered

76 candidates to 58 candidates (76.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	76	2	78

Merged error: 0.0b

Counts

78 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))
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))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 175

Calls

4 calls:

28.0ms	(- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))
6.0ms	(/ (/ 0.25 x) x)
35.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
4.0ms	(/ 0.09375 (pow x 4))

series236.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))
25.0ms	(/ (/ 0.25 x) x)
105.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
40.0ms	(/ 0.09375 (pow x 4))

simplify65.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	747	1406
1	2728	1293
2	5002	1288

prune420.0ms

Filtered

187 candidates to 121 candidates (64.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	187	2	189

Merged error: 0b

Counts

189 → 2

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))
0.6b	(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)

rewrite114.0ms

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:

34.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
4.0ms	(/ 0.09375 (pow x 4))
33.0ms	(cbrt (pow (+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))) 3))
36.0ms	(pow (+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))) 3)

series630.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
40.0ms	(/ 0.09375 (pow x 4))
284.0ms	(cbrt (pow (+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))) 3))
208.0ms	(pow (+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))) 3)

simplify100.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	832	1969
1	3708	1879
2	5002	1855

prune328.0ms

Filtered

169 candidates to 81 candidates (47.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	169	2	171

Merged error: 0b

Counts

171 → 2

regimes14.0ms

Accuracy

0% (0.2b 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	13	9
1	13	9

end0.0ms

sample2.6s

Algorithm

intervals

Results

580.0ms	2971×	body	2560	nan
574.0ms	16447×	body	80	nan
412.0ms	2541×	body	1280	nan
326.0ms	8000×	body	80	valid
176.0ms	1329×	body	640	nan
64.0ms	644×	body	320	nan
20.0ms	296×	body	160	nan