Details

sample77.0ms

Algorithm

intervals

Results

51.0ms	181×	body	1280	valid
7.0ms	42×	body	640	valid
6.0ms	289×	body	80	valid
2.0ms	18×	body	320	valid
0.0ms	8×	body	160	valid

simplify219.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	5
1	26	5
2	41	5
3	55	5
4	67	5
5	104	5
6	161	5
7	344	5
8	1454	5
9	5001	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: 27.5b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
3.0b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`prod-diff`
16×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`add-log-exp`
5×	`fma-def`
4×	`frac-add`
3×	`flip3--` `fma-neg` `flip--` `distribute-lft-out--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `expm1-log1p-u` `sub-neg` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+`

Counts

2 → 65

Calls

2 calls:

5.0ms	(- (exp x) 2.0)
9.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series69.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(- (exp x) 2.0)
57.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify34.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	282	506
1	1008	381
2	5001	367

prune136.0ms

Filtered

71 candidates to 51 candidates (71.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	3	72

Merged error: 0.0b

Counts

72 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
0.0b	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
0.1b	(* 1/12 (pow x 4))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`add-exp-log`
7×	`associate-r`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube`
4×	`unpow-prod-down`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`fma-udef` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 47

Calls

3 calls:

1.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
1.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
5.0ms	(* 1/12 (pow x 4))

series217.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
123.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
35.0ms	(* 1/12 (pow x 4))

simplify100.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	143	265
1	544	240
2	2626	237
3	5001	237

prune110.0ms

Filtered

56 candidates to 39 candidates (69.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	56	3	59

Merged error: 0.0b

Counts

59 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp (- x)) 3)
0.1b	(pow (- (exp x) 2.0) 3)
0.2b	(/ (+ (pow (- (exp x) 2.0) 3) (pow (exp (- x)) 3)) (fma (exp (* -1 x)) (- (exp (- x)) (- (exp x) 2.0)) (* (- (exp x) 2.0) (- (exp x) 2.0))))
3.0b	(+ (pow (- (exp x) 2.0) 3) (pow (exp (- x)) 3))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

152×	`*-un-lft-identity`
53×	`unpow-prod-down` `cube-prod`
45×	`distribute-lft-out`
42×	`add-sqr-sqrt`
39×	`times-frac`
34×	`add-cube-cbrt`
24×	`distribute-lft-out--`
20×	`cube-div`
16×	`fma-def`
13×	`associate-/l*`
12×	`pow-pow`
10×	`exp-prod`
8×	`frac-add` `add-cbrt-cube`
7×	`add-exp-log`
6×	`pow1` `pow-unpow` `associate-/l/` `add-log-exp`
5×	`neg-sub0` `exp-neg` `flip3--` `exp-diff` `sum-cubes` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`distribute-lft-neg-in` `cube-mult` `distribute-rgt-neg-in` `unpow3` `associate-/r*` `sqr-pow`
2×	`pow-to-exp` `flip3-+` `pow-exp` `flip-+` `rem-cube-cbrt`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 186

Calls

4 calls:

5.0ms	(pow (exp (- x)) 3)
5.0ms	(pow (- (exp x) 2.0) 3)
22.0ms	(/ (+ (pow (- (exp x) 2.0) 3) (pow (exp (- x)) 3)) (fma (exp (* -1 x)) (- (exp (- x)) (- (exp x) 2.0)) (* (- (exp x) 2.0) (- (exp x) 2.0))))
21.0ms	(+ (pow (- (exp x) 2.0) 3) (pow (exp (- x)) 3))

series561.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(pow (exp (- x)) 3)
43.0ms	(pow (- (exp x) 2.0) 3)
340.0ms	(/ (+ (pow (- (exp x) 2.0) 3) (pow (exp (- x)) 3)) (fma (exp (* -1 x)) (- (exp (- x)) (- (exp x) 2.0)) (* (- (exp x) 2.0) (- (exp x) 2.0))))
151.0ms	(+ (pow (- (exp x) 2.0) 3) (pow (exp (- x)) 3))

simplify118.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	650	3170
1	3052	3012
2	5002	3000

prune447.0ms

Filtered

198 candidates to 110 candidates (55.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	198	3	201

Merged error: 0.0b

Counts

201 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log (+ (pow (- (exp x) 2.0) 3) (pow (exp (- x)) 3))))
0.2b	(/ (exp (log (+ (pow (- (exp x) 2.0) 3) (pow (exp (- x)) 3)))) (fma (exp (* -1 x)) (- (exp (- x)) (- (exp x) 2.0)) (* (- (exp x) 2.0) (- (exp x) 2.0))))
0.3b	(log (+ (pow (- (exp x) 2.0) 3) (pow (exp (- x)) 3)))
3.0b	(+ (pow (- (exp x) 2.0) 3) (pow (exp (- x)) 3))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

193×	`*-un-lft-identity`
78×	`log-prod`
65×	`exp-sum`
63×	`distribute-lft-out`
61×	`unpow-prod-down` `cube-prod`
48×	`times-frac`
39×	`add-sqr-sqrt`
35×	`add-cube-cbrt`
32×	`cube-div`
30×	`distribute-lft-out--`
20×	`exp-diff`
18×	`log-div`
16×	`fma-def` `frac-add` `associate-/l*`
8×	`neg-sub0` `exp-neg` `flip3--` `flip--`
7×	`sum-cubes`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `associate-/l/` `add-log-exp`
4×	`expm1-log1p-u` `exp-prod` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`associate-/r*`
2×	`log-pow` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `frac-2neg` `unpow3` `div-exp` `rem-log-exp` `clear-num` `sum-log` `div-inv` `rem-exp-log` `sqr-pow`

Counts

4 → 193

Calls

4 calls:

23.0ms	(exp (log (+ (pow (- (exp x) 2.0) 3) (pow (exp (- x)) 3))))
25.0ms	(/ (exp (log (+ (pow (- (exp x) 2.0) 3) (pow (exp (- x)) 3)))) (fma (exp (* -1 x)) (- (exp (- x)) (- (exp x) 2.0)) (* (- (exp x) 2.0) (- (exp x) 2.0))))
19.0ms	(log (+ (pow (- (exp x) 2.0) 3) (pow (exp (- x)) 3)))
21.0ms	(+ (pow (- (exp x) 2.0) 3) (pow (exp (- x)) 3))

series947.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(exp (log (+ (pow (- (exp x) 2.0) 3) (pow (exp (- x)) 3))))
362.0ms	(/ (exp (log (+ (pow (- (exp x) 2.0) 3) (pow (exp (- x)) 3)))) (fma (exp (* -1 x)) (- (exp (- x)) (- (exp x) 2.0)) (* (- (exp x) 2.0) (- (exp x) 2.0))))
268.0ms	(log (+ (pow (- (exp x) 2.0) 3) (pow (exp (- x)) 3)))
157.0ms	(+ (pow (- (exp x) 2.0) 3) (pow (exp (- x)) 3))

simplify92.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	607	4433
1	2481	4112
2	5001	4050

prune523.0ms

Filtered

205 candidates to 107 candidates (52.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	205	3	208

Merged error: 0.0b

Counts

208 → 3

regimes16.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	5
1	11	5

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.6s	5573×	body	1280	valid
199.0ms	1280×	body	640	valid
176.0ms	7925×	body	80	valid
62.0ms	648×	body	320	valid
21.0ms	322×	body	160	valid