Details

sample32.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
10.0ms	276×	body	80	nan

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	39	7
2	61	7
3	80	7
4	105	7
5	114	7
6	114	7

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: 0.4b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.0b	(* 6.0 (- x 1.0))
0.3b	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`add-exp-log` `add-cbrt-cube`
9×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1` `associate-r`
4×	`associate-*r/`
3×	`times-frac` `associate-l` `associate-/r*` `sum-log`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `flip3-+` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+l+` `frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 64

Calls

3 calls:

5.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
6.0ms	(* 6.0 (- x 1.0))
11.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series157.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
43.0ms	(* 6.0 (- x 1.0))
79.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify47.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	377	495
1	1642	421
2	5001	420

prune126.0ms

Filtered

73 candidates to 53 candidates (72.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	3	74

Merged error: 0b

Counts

74 → 3

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.0b	(* 6.0 (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))))
0.0b	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
31×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1` `associate-/l*`
4×	`associate-/r/`
3×	`flip3-+` `associate-l` `associate-/r*` `sum-log` `flip-+`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `associate-+l+` `flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--`

Counts

3 → 93

Calls

3 calls:

6.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
14.0ms	(* 6.0 (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))))
13.0ms	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series187.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
80.0ms	(* 6.0 (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))))
73.0ms	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify54.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	439	987
1	1809	895
2	5003	893

prune171.0ms

Filtered

102 candidates to 76 candidates (74.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	102	3	105

Merged error: 0b

Counts

105 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))
0.1b	(/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
0.2b	(* (/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))))
0.3b	(/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
108×	`times-frac`
95×	`*-un-lft-identity`
69×	`add-cube-cbrt`
63×	`sqrt-prod`
36×	`associate-r`
24×	`associate-l`
20×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out--` `difference-of-squares`
12×	`associate-/r*`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`associate-/r/` `associate-/l*`
7×	`pow1`
6×	`cbrt-undiv` `div-exp`
5×	`flip3-+` `flip-+`
4×	`prod-exp` `cbrt-unprod` `div-inv` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--`

Counts

4 → 203

Calls

4 calls:

5.0ms	(sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))
8.0ms	(/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
38.0ms	(* (/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))))
11.0ms	(/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))

series589.0ms

Counts

4 → 12

Calls

4 calls:

257.0ms	(sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))
118.0ms	(/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))
79.0ms	(* (/ 6.0 (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))) (/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))))
135.0ms	(/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))

simplify103.0ms

Algorithm

egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	772	3129
1	3369	2865
2	5001	2758

prune375.0ms

Filtered

215 candidates to 140 candidates (65.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	215	3	218

Merged error: 0b

Counts

218 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.2b	(* 6.0 (+ (sqrt x) (sqrt 1.0)))
0.2b	(* (* 6.0 (+ (sqrt x) (sqrt 1.0))) (- (sqrt x) (sqrt 1.0)))
0.3b	(/ (* (* 6.0 (+ (sqrt x) (sqrt 1.0))) (- (sqrt x) (sqrt 1.0))) (+ (+ x 1.0) (* 4.0 (sqrt x))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt`
18×	`associate-*r/`
17×	`*-un-lft-identity`
14×	`associate-r`
11×	`pow1`
9×	`add-cube-cbrt` `flip3-+` `flip-+` `add-log-exp`
8×	`frac-times` `sqrt-prod` `associate-/l/`
7×	`prod-exp` `cbrt-unprod`
6×	`flip3--` `flip--`
4×	`associate-l` `pow-prod-down` `associate-*l/` `difference-of-squares`
3×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `times-frac` `div-exp` `associate-/r*` `sum-log`
2×	`sub-neg` `associate-/r/` `*-commutative` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+l+` `frac-2neg` `clear-num` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

5.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
8.0ms	(* 6.0 (+ (sqrt x) (sqrt 1.0)))
17.0ms	(* (* 6.0 (+ (sqrt x) (sqrt 1.0))) (- (sqrt x) (sqrt 1.0)))
19.0ms	(/ (* (* 6.0 (+ (sqrt x) (sqrt 1.0))) (- (sqrt x) (sqrt 1.0))) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series714.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
52.0ms	(* 6.0 (+ (sqrt x) (sqrt 1.0)))
214.0ms	(* (* 6.0 (+ (sqrt x) (sqrt 1.0))) (- (sqrt x) (sqrt 1.0)))
408.0ms	(/ (* (* 6.0 (+ (sqrt x) (sqrt 1.0))) (- (sqrt x) (sqrt 1.0))) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify109.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	785	1427
1	4403	1100
2	5002	1075

prune226.0ms

Filtered

118 candidates to 84 candidates (71.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	118	3	121

Merged error: 0b

Counts

121 → 3

regimes13.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

end0.0ms

sample810.0ms

Algorithm

intervals

Results

324.0ms	8000×	body	80	valid
290.0ms	8187×	body	80	nan