Details

sample76.0ms

Algorithm

intervals

Results

38.0ms	78×	body	1280	valid
15.0ms	51×	body	640	valid
8.0ms	23×	body	2560	valid
4.0ms	23×	body	320	valid
3.0ms	68×	body	80	valid
1.0ms	13×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	5
1	9	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: 51.4b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

1.2b	(+ x (sqrt (+ (* x x) 1.0)))
2.2b	(log (+ x (sqrt (+ (* x x) 1.0))))
12.6b	(sqrt (+ (* x x) 1.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

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))

series289.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(+ x (sqrt (+ (* x x) 1.0)))
177.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
47.0ms	(sqrt (+ (* x x) 1.0))

simplify145.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (139.0ms)

Iter	Nodes	Cost
0	309	393
1	1027	364
2	4764	348
3	5002	347

prune146.0ms

Filtered

51 candidates to 42 candidates (82.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	44	7	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	7	52

Merged error: 0.0b

Counts

52 → 7

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.1b	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
220×	`associate-r`
182×	`add-sqr-sqrt`
140×	`unpow-prod-down` `cube-prod`
118×	`add-cube-cbrt` `*-un-lft-identity`
80×	`sqrt-prod`
40×	`sqr-pow`
30×	`cube-mult` `unpow3`
25×	`add-exp-log` `unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
7×	`add-cbrt-cube`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
4×	`pow1`
3×	`associate-r/` `associate-l*`
2×	`diff-log` `frac-sub` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `flip3--` `flip3-+` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `flip--` `flip-+` `div-inv`

Counts

2 → 286

Calls

2 calls:

13.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
55.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series302.0ms

Counts

2 → 6

Calls

2 calls:

162.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
140.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify120.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	854	2083
1	4642	1650
2	5002	1650

prune389.0ms

Filtered

292 candidates to 111 candidates (38.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	292	0	292
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	292	7	299

Merged error: 0.0b

Counts

299 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
0.0b	(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
0.1b	(/ 0.125 (pow x 3))
12.6b	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
43×	`add-sqr-sqrt`
40×	`times-frac`
30×	`add-cube-cbrt`
18×	`add-log-exp`
13×	`unpow-prod-down` `cube-prod`
12×	`associate-/r*`
10×	`add-exp-log`
9×	`distribute-lft-out`
6×	`log-prod` `add-cbrt-cube` `distribute-lft-out--`
5×	`pow1` `sum-log` `difference-of-squares` `sqr-pow`
4×	`cube-mult` `diff-log` `unpow3`
3×	`associate-+r+` `flip3-+` `div-exp` `flip-+` `associate-/l*`
2×	`sub-neg` `log-div` `associate--l+` `frac-sub`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `associate-+r-` `flip3--` `frac-2neg` `rem-log-exp` `pow-exp` `clear-num` `log-pow` `flip--` `div-inv`

Counts

4 → 125

Calls

4 calls:

21.0ms	(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
22.0ms	(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
5.0ms	(/ 0.125 (pow x 3))
20.0ms	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
41.0ms	(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
36.0ms	(/ 0.125 (pow x 3))
342.0ms	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify72.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	505	977
1	2345	921
2	5001	919

prune225.0ms

Filtered

137 candidates to 80 candidates (58.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	137	7	144

Merged error: 0.0b

Counts

144 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 0.09375 (pow x 4))
0.1b	(- (log 2) (- (- (/ 0.09375 (pow x 4)) (log x)) (/ (/ 0.25 x) x)))
0.1b	(/ (/ 0.25 x) x)
6.8b	(- (- (/ 0.09375 (pow x 4)) (log x)) (/ (/ 0.25 x) x))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 170

Calls

4 calls:

5.0ms	(/ 0.09375 (pow x 4))
37.0ms	(- (log 2) (- (- (/ 0.09375 (pow x 4)) (log x)) (/ (/ 0.25 x) x)))
9.0ms	(/ (/ 0.25 x) x)
33.0ms	(- (- (/ 0.09375 (pow x 4)) (log x)) (/ (/ 0.25 x) x))

series231.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 0.09375 (pow x 4))
102.0ms	(- (log 2) (- (- (/ 0.09375 (pow x 4)) (log x)) (/ (/ 0.25 x) x)))
25.0ms	(/ (/ 0.25 x) x)
68.0ms	(- (- (/ 0.09375 (pow x 4)) (log x)) (/ (/ 0.25 x) x))

simplify68.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	721	1389
1	2664	1284
2	5001	1281

prune376.0ms

Filtered

182 candidates to 118 candidates (64.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	182	7	189

Merged error: 0.0b

Counts

189 → 7

regimes109.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.5b

bsearch83.0ms

Steps

Iters	Range		Point
9	0.004314681149180372	39972.03059165128	0.9010654647035116
9	-2.6022242175013632	-1.4174312616962401e-08	-0.9950215155112431

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	27
1	41	27

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.0s	2296×	body	1280	valid
424.0ms	1577×	body	640	valid
262.0ms	793×	body	2560	valid
128.0ms	756×	body	320	valid
91.0ms	2210×	body	80	valid
35.0ms	368×	body	160	valid

Details

sample76.0ms

simplify4.0ms

prune2.0ms

localize6.0ms

rewrite16.0ms

series289.0ms

simplify145.0ms

prune146.0ms

localize12.0ms

rewrite94.0ms

series302.0ms

simplify120.0ms

prune389.0ms

localize10.0ms

rewrite73.0ms

series463.0ms

simplify72.0ms

prune225.0ms

localize13.0ms

rewrite91.0ms

series231.0ms

simplify68.0ms

prune376.0ms

regimes109.0ms

bsearch83.0ms

simplify2.0ms

end0.0ms

sample2.1s

Profiling