Details

sample41.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
11.0ms	252×	body	80	nan

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 0.2b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite23.0ms

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:

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

series153.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(* 6.0 (- x 1.0))
35.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
77.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify45.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (39.0ms)

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

prune124.0ms

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: 0.0b

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))))

rewrite31.0ms

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:

5.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
13.0ms	(* 6.0 (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))))
9.0ms	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series190.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
79.0ms	(* 6.0 (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))))
71.0ms	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify55.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (45.0ms)

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

prune176.0ms

Filtered

102 candidates to 76 candidates (74.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	101	4	105

Merged error: 0b

Counts

105 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

150×	`add-sqr-sqrt`
144×	`*-un-lft-identity`
123×	`times-frac`
108×	`cbrt-prod`
78×	`add-cube-cbrt`
30×	`swap-sqr` `distribute-lft-out--`
24×	`associate-r` `associate-l` `difference-of-squares`
15×	`associate-/l*`
14×	`associate-/r/`
12×	`add-exp-log`
11×	`pow1`
10×	`add-cbrt-cube`
9×	`associate-/r*` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`pow1/3` `associate-/l/`
4×	`cbrt-div` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `flip--`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 228

Calls

4 calls:

9.0ms	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))
9.0ms	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))
9.0ms	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))
29.0ms	(* (cbrt (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))) (cbrt (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))))

series446.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))
71.0ms	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))
72.0ms	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))
232.0ms	(* (cbrt (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))) (cbrt (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))))

simplify88.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	528	3794
1	1990	3643
2	5002	3486

prune598.0ms

Filtered

240 candidates to 174 candidates (72.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	240	0	240
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	240	4	244

Merged error: 0b

Counts

244 → 4

localize15.0ms

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)))))
0.1b	(* (/ 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)))))

rewrite68.0ms

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)))))
32.0ms	(* (/ 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)))))

series392.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(sqrt (+ (+ x 1.0) (* 4.0 (sqrt x))))
116.0ms	(/ 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))))))
132.0ms	(/ (- x 1.0) (sqrt (+ (+ x 1.0) (* 4.0 (sqrt x)))))

simplify100.0ms

Algorithm

egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 2 (68.0ms)

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

prune391.0ms

Filtered

215 candidates to 140 candidates (65.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	215	4	219

Merged error: 0b

Counts

219 → 4

regimes16.0ms

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

sample643.0ms

Algorithm

intervals

Results

246.0ms	8000×	body	80	valid
218.0ms	7896×	body	80	nan