Details

sample73.0ms

Algorithm

intervals

Results

50.0ms	180×	body	1280	valid
5.0ms	245×	body	80	valid
5.0ms	33×	body	640	valid
2.0ms	24×	body	320	valid
1.0ms	13×	body	160	valid

simplify218.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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	1452	5
9	5002	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: 31.4b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
6.0b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite17.0ms

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)))

series72.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(- (exp x) 2.0)
59.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify35.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	279	506
1	980	381
2	5002	367

prune137.0ms

Filtered

71 candidates to 51 candidates (71.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	4	72

Merged error: 0.0b

Counts

72 → 4

localize9.0ms

Local error

Found 1 expressions with local error:

0.1b	(* 1/12 (pow x 4))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 28

Calls

1 calls:

6.0ms

(* 1/12 (pow x 4))

series39.0ms

Counts

1 → 3

Calls

1 calls:

39.0ms

(* 1/12 (pow x 4))

simplify72.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	102	105
1	406	100
2	1824	97
3	5002	97

prune62.0ms

Filtered

31 candidates to 19 candidates (61.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	31	4	35

Merged error: 0.0b

Counts

35 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 2.0)
0.0b	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
0.0b	(* (+ (exp x) 2.0) (exp x))
5.5b	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity`
43×	`add-sqr-sqrt`
39×	`times-frac`
33×	`add-cube-cbrt`
20×	`associate-l`
15×	`associate-r`
14×	`add-exp-log`
13×	`associate-/r*`
11×	`add-cbrt-cube`
6×	`pow1` `distribute-lft-out` `add-log-exp`
5×	`*-commutative` `unswap-sqr`
4×	`expm1-log1p-u` `associate-*l/` `prod-exp` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `div-exp` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `associate-/r/` `cbrt-unprod`
1×	`+-commutative` `frac-2neg` `pow-prod-down` `clear-num` `sum-log` `fma-udef` `div-inv`

Counts

4 → 125

Calls

4 calls:

4.0ms	(+ (exp x) 2.0)
12.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
8.0ms	(* (+ (exp x) 2.0) (exp x))
1.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

series345.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (exp x) 2.0)
220.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
23.0ms	(* (+ (exp x) 2.0) (exp x))
94.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

simplify62.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	444	1994
1	1697	1870
2	5003	1870

prune298.0ms

Filtered

137 candidates to 104 candidates (75.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	138	3	141

Merged error: 0.0b

Counts

141 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (cbrt (exp x)))
0.0b	(* (/ 1 (* (+ (exp x) 2.0) (* (cbrt (exp x)) (cbrt (exp x))))) (/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (cbrt (exp x))))
0.0b	(* (cbrt (exp x)) (cbrt (exp x)))
5.5b	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

1195×	`add-sqr-sqrt`
903×	`associate-/r*`
612×	`frac-times`
602×	`cbrt-prod`
556×	`associate-r`
494×	`*-un-lft-identity`
431×	`add-cube-cbrt`
417×	`unswap-sqr`
307×	`associate-l`
273×	`times-frac`
199×	`associate-/l*`
146×	`swap-sqr`
93×	`add-cbrt-cube`
82×	`add-exp-log`
67×	`clear-num`
66×	`frac-2neg`
56×	`*-commutative`
53×	`associate-*l/`
52×	`cbrt-unprod`
39×	`prod-exp`
34×	`cbrt-undiv`
23×	`div-exp`
16×	`distribute-lft-out`
13×	`pow1`
12×	`associate-*r/`
6×	`rec-exp` `pow1/3` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`associate-/r/` `pow-sqr` `un-div-inv` `pow-prod-up`
1×	`pow2` `flip3-+` `pow-plus` `flip-+` `fma-udef`

Counts

4 → 1052

Calls

4 calls:

4.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (cbrt (exp x)))
108.0ms	(* (/ 1 (* (+ (exp x) 2.0) (* (cbrt (exp x)) (cbrt (exp x))))) (/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (cbrt (exp x))))
7.0ms	(* (cbrt (exp x)) (cbrt (exp x)))
1.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

series638.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (cbrt (exp x)))
220.0ms	(* (/ 1 (* (+ (exp x) 2.0) (* (cbrt (exp x)) (cbrt (exp x))))) (/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (cbrt (exp x))))
95.0ms	(* (cbrt (exp x)) (cbrt (exp x)))
101.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

simplify294.0ms

Algorithm

egg-herbie

Counts

1064 → 1064

Iterations

Useful iterations: 1 (78.0ms)

Iter	Nodes	Cost
0	4071	29103
1	5001	28079

prune2.4s

Filtered

1064 candidates to 616 candidates (57.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	1064	0	1064
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	1064	3	1067

Merged error: 0.0b

Counts

1067 → 3

regimes20.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

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

1.7s	5650×	body	1280	valid
191.0ms	1206×	body	640	valid
167.0ms	7902×	body	80	valid
61.0ms	654×	body	320	valid
19.0ms	321×	body	160	valid