Details

sample344.0ms

Algorithm

intervals

Results

38.0ms	198×	body	10240	exit
13.0ms	434×	body	80	nan
8.0ms	236×	body	80	valid
3.0ms	24×	body	160	valid

simplify71.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.3b

localize11.0ms

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))
5.1b	(- (exp (* 2.0 x)) 1.0)
5.1b	(- (exp x) 1.0)

rewrite39.0ms

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:

9.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
10.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
6.0ms	(- (exp (* 2.0 x)) 1.0)
8.0ms	(- (exp x) 1.0)

series206.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
58.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
33.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

simplify60.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (40.0ms)

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

prune394.0ms

Filtered

167 candidates to 110 candidates (65.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

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)))
0.0b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
5.1b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.1b	(- (exp (* 2.0 x)) 1.0)

rewrite35.0ms

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:

14.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
6.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series251.0ms

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)))
66.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
42.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
29.0ms	(- (exp (* 2.0 x)) 1.0)

simplify112.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (79.0ms)

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

prune651.0ms

Filtered

218 candidates to 147 candidates (67.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (expm1 (log1p (- (exp (* 2.0 x)) 1.0))) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
0.0b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
5.1b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.1b	(- (exp (* 2.0 x)) 1.0)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 166

Calls

4 calls:

9.0ms	(/ (expm1 (log1p (- (exp (* 2.0 x)) 1.0))) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
6.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series364.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(/ (expm1 (log1p (- (exp (* 2.0 x)) 1.0))) (/ (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))
45.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
25.0ms	(- (exp (* 2.0 x)) 1.0)

simplify92.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	620	2918
1	2658	2549
2	5001	2523

prune614.0ms

Filtered

178 candidates to 131 candidates (73.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
24.3b	(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
2×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

2 → 25

Calls

2 calls:

3.0ms	(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
2.0ms	(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

series102.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
77.0ms	(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

simplify66.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	139	186
1	458	173
2	2447	165
3	5001	162

prune76.0ms

Filtered

31 candidates to 25 candidates (80.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes28.0ms

Accuracy

72.1% (0.7b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 2.7b

bsearch43.0ms

Steps

Iters	Range		Point
7	-5.6669034693225635e-12	-5.8829093822384e-14	-5.3888208797845926e-12

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	18
1	28	18

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	6661×	body	10240	exit
378.0ms	12605×	body	80	nan
244.0ms	7407×	body	80	valid
53.0ms	699×	body	160	valid