Details

sample382.0ms

Algorithm

intervals

Results

60.0ms	217×	body	10240	exit
25.0ms	401×	body	80	nan
16.0ms	246×	body	80	valid
2.0ms	15×	body	160	valid

simplify72.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.5b

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))
2.8b	(- (exp (* 2.0 x)) 1.0)
2.9b	(- (exp x) 1.0)

rewrite56.0ms

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:

15.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
17.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
8.0ms	(- (exp x) 1.0)

series196.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
60.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
24.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify55.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (39.0ms)

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

prune378.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

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))
2.8b	(fma (- 1.0) 1.0 (exp (+ x x)))
2.8b	(- (exp (* 2.0 x)) 1.0)

rewrite43.0ms

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:

21.0ms	(/ (- (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)

series243.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
63.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
45.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
24.0ms	(- (exp (* 2.0 x)) 1.0)

simplify107.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (79.0ms)

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

prune633.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (pow (exp x) 3) (pow 1.0 3))))
2.8b	(- (exp (* 2.0 x)) 1.0)
2.8b	(fma (- 1.0) 1.0 (exp (+ x x)))
2.9b	(- (* 1.0 1.0) (* (exp x) 1.0))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

373×	`*-un-lft-identity`
327×	`times-frac`
193×	`add-sqr-sqrt`
123×	`add-cube-cbrt`
90×	`distribute-lft-out`
72×	`unpow-prod-down` `cube-prod`
35×	`distribute-lft-out--` `difference-of-squares`
33×	`associate-/r*`
18×	`sum-cubes`
13×	`associate-/r/`
10×	`prod-diff`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`div-inv`
6×	`flip3-+` `flip-+`
5×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `fma-neg` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`distribute-rgt-out--` `frac-2neg` `div-sub` `clear-num` `fma-udef`

Counts

4 → 278

Calls

4 calls:

46.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (pow (exp x) 3) (pow 1.0 3))))
5.0ms	(- (exp (* 2.0 x)) 1.0)
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
3.0ms	(- (* 1.0 1.0) (* (exp x) 1.0))

series241.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (pow (exp x) 3) (pow 1.0 3))))
28.0ms	(- (exp (* 2.0 x)) 1.0)
40.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
35.0ms	(- (* 1.0 1.0) (* (exp x) 1.0))

simplify75.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1064	5786
1	5001	5495

prune900.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0)))
0.0b	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
2.9b	(- (exp x) 1.0)
2.9b	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
31×	`times-frac`
30×	`add-cube-cbrt`
21×	`sqrt-prod`
9×	`prod-diff`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `flip--` `associate-/l*`
2×	`rem-sqrt-square` `div-inv`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `diff-log` `div-exp` `clear-num` `fma-udef`

Counts

4 → 112

Calls

4 calls:

9.0ms	(sqrt (/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0)))
7.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
5.0ms	(- (exp x) 1.0)
0.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

series370.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(sqrt (/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0)))
113.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
14.0ms	(- (exp x) 1.0)
85.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	356	1725
1	1097	1468
2	5001	1437

prune343.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes29.0ms

Accuracy

77.8% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 2.9b

bsearch47.0ms

Steps

Iters	Range		Point
7	-0.00029412782026305056	-3.444742101060518e-06	-1.434798355623991e-05

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	27
1	37	27

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.6s	6617×	body	10240	exit
730.0ms	12481×	body	80	nan
463.0ms	7395×	body	80	valid
93.0ms	730×	body	160	valid