Details

sample340.0ms

Algorithm

intervals

Results

46.0ms	196×	body	10240	exit
15.0ms	427×	body	80	nan
9.0ms	230×	body	80	valid
3.0ms	30×	body	160	valid

simplify82.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	41	7
3	75	7
4	182	7
5	576	7
6	2666	7
7	5001	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.6b	(- (exp (* 2.0 x)) 1.0)
5.7b	(- (exp x) 1.0)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
51×	`times-frac`
41×	`add-cube-cbrt`
31×	`sqrt-prod`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`add-log-exp`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 155

Calls

4 calls:

14.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
16.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series205.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
55.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
35.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify59.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	480	1694
1	1523	1484
2	5001	1470

prune398.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
0.1b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
5.6b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.6b	(- (exp (* 2.0 x)) 1.0)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac`
171×	`*-un-lft-identity`
127×	`add-sqr-sqrt`
87×	`add-cube-cbrt`
22×	`associate-/r*` `distribute-lft-out`
20×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/r/`
11×	`add-exp-log` `add-cbrt-cube`
9×	`prod-diff`
8×	`div-inv` `associate-/l*`
7×	`flip3-+` `flip-+`
6×	`add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-neg`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `div-sub` `fma-udef`

Counts

4 → 206

Calls

4 calls:

23.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
7.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series248.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
62.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
47.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
25.0ms	(- (exp (* 2.0 x)) 1.0)

simplify110.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	805	3596
1	3551	3384
2	5003	3382

prune656.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
0.1b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
5.6b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.6b	(- (exp (* 2.0 x)) 1.0)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
105×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
71×	`add-cube-cbrt`
22×	`associate-/r*`
17×	`add-exp-log`
16×	`distribute-lft-out`
11×	`associate-/r/` `add-cbrt-cube`
9×	`prod-diff`
8×	`div-exp`
6×	`div-inv` `associate-/l*` `add-log-exp`
5×	`pow1` `flip3-+` `flip-+`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `flip--` `fma-udef` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 171

Calls

4 calls:

11.0ms	(/ 1 (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
7.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series201.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ 1 (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
66.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
41.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
29.0ms	(- (exp (* 2.0 x)) 1.0)

simplify76.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	580	2235
1	2536	1984
2	5001	1881

prune433.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))))
0.1b	(expm1 (log1p (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))))
5.6b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.6b	(- (exp (* 2.0 x)) 1.0)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
6×	`add-log-exp`
5×	`expm1-log1p-u`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg`
1×	`sub-neg` `log1p-udef` `expm1-log1p` `flip3--` `diff-log` `log1p-expm1` `flip--` `fma-udef` `distribute-lft-out--` `expm1-udef` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

0.0ms	(log1p (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))))
0.0ms	(expm1 (log1p (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series560.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(log1p (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))))
271.0ms	(expm1 (log1p (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))))
43.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
25.0ms	(- (exp (* 2.0 x)) 1.0)

simplify39.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	315	802
1	1051	652
2	5001	648

prune245.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes33.0ms

Accuracy

73.5% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.0b

bsearch31.0ms

Steps

Iters	Range		Point
4	-9.18026288086769e-16	-6.177090465987301e-16	-7.158129959812892e-16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	25
1	38	25

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.5s	6622×	body	10240	exit
432.0ms	12573×	body	80	nan
277.0ms	7347×	body	80	valid
68.0ms	760×	body	160	valid