Details

sample9.0ms

Algorithm

intervals

Results

4.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	3
1	6	3

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: 15.0b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

15.0b

(/ x (+ (* x x) 1.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
2×	`associate-/r/`
1×	`pow1` `cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

5.0ms

(/ x (+ (* x x) 1.0))

series60.0ms

Counts

1 → 3

Calls

1 calls:

60.0ms

(/ x (+ (* x x) 1.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	165	210
1	555	195
2	1839	192
3	5001	192

prune59.0ms

Filtered

32 candidates to 26 candidates (81.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	28	4	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	4	33

Merged error: 0b

Counts

33 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (sqrt (+ (* x x) 1.0)))
0.0b	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
15.0b	(sqrt (+ (* x x) 1.0))
15.0b	(sqrt (+ (* x x) 1.0))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
30×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`pow1` `sqrt-div` `div-exp`
8×	`prod-exp`
6×	`associate-/r*` `associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`cbrt-unprod` `add-log-exp`
3×	`rec-exp` `pow-flip` `sqrt-pow1` `pow1/2` `1-exp` `div-inv` `associate-/l*`
2×	`rem-sqrt-square`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `inv-pow`

Counts

4 → 164

Calls

4 calls:

7.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
23.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))
4.0ms	(sqrt (+ (* x x) 1.0))

series227.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ 1 (sqrt (+ (* x x) 1.0)))
56.0ms	(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
49.0ms	(sqrt (+ (* x x) 1.0))
44.0ms	(sqrt (+ (* x x) 1.0))

simplify76.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	625	1749
1	3124	1546
2	5002	1414

prune235.0ms

Filtered

176 candidates to 105 candidates (59.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	176	4	180

Merged error: 0b

Counts

180 → 4

localize5.0ms

Local error

Found 2 expressions with local error:

0.4b	(/ 1 (+ (* x x) 1.0))
14.7b	(* x (/ 1 (+ (* x x) 1.0)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`times-frac`
19×	`*-un-lft-identity`
18×	`add-cube-cbrt`
15×	`add-exp-log` `associate-r`
9×	`add-cbrt-cube`
5×	`pow1`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

2 → 71

Calls

2 calls:

6.0ms	(/ 1 (+ (* x x) 1.0))
9.0ms	(* x (/ 1 (+ (* x x) 1.0)))

series99.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ 1 (+ (* x x) 1.0))
60.0ms	(* x (/ 1 (+ (* x x) 1.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	316	470
1	1443	410
2	5001	374

prune84.0ms

Filtered

77 candidates to 47 candidates (61.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	77	4	81

Merged error: 0b

Counts

81 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))) (/ 1 x))
0.1b	(/ 1 (pow x 3))
0.2b	(/ 1 (pow x 5))
18.9b	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

196×	`add-sqr-sqrt`
173×	`times-frac`
112×	`*-un-lft-identity`
63×	`difference-of-squares`
56×	`unpow-prod-down`
47×	`add-cube-cbrt`
40×	`sqr-pow`
26×	`cube-prod`
22×	`add-exp-log`
19×	`associate-/r*`
12×	`div-exp`
8×	`add-cbrt-cube` `add-log-exp`
7×	`distribute-lft-out--`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `div-inv` `associate-/l*`
4×	`pow1` `cube-mult` `associate-+l+` `unpow3`
3×	`sub-neg` `associate-*r/` `frac-add`
2×	`cbrt-undiv` `distribute-rgt-in` `flip3--` `pow-flip` `frac-2neg` `distribute-lft-in` `clear-num` `frac-sub` `flip--` `inv-pow`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+`

Counts

4 → 227

Calls

4 calls:

50.0ms	(+ (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))) (/ 1 x))
5.0ms	(/ 1 (pow x 3))
5.0ms	(/ 1 (pow x 5))
44.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))) (/ 1 x))
30.0ms	(/ 1 (pow x 3))
73.0ms	(/ 1 (pow x 5))
94.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

simplify87.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	687	1931
1	2879	1646
2	5001	1645

prune236.0ms

Filtered

239 candidates to 92 candidates (38.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	239	4	243

Merged error: 0b

Counts

243 → 4

regimes51.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 14.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	23
1	35	23

end0.0ms

sample217.0ms

Algorithm

intervals

Results

136.0ms

8000×

body

valid