Details

sample299.0ms

Algorithm

intervals

Results

13.0ms	416×	body	80	nan
9.0ms	224×	body	80	overflowed
8.0ms	234×	body	80	valid
2.0ms	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

prune3.0ms

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)))
0.1b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.5b	(- (exp (* 2.0 x)) 1.0)
4.7b	(- (exp x) 1.0)

rewrite110.0ms

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:

28.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
38.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
23.0ms	(- (exp (* 2.0 x)) 1.0)
14.0ms	(- (exp x) 1.0)

series184.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
55.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
22.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

simplify56.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (39.0ms)

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

prune381.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
0.0b	(+ (exp x) 1.0)
4.5b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.5b	(- (exp (* 2.0 x)) 1.0)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
9×	`prod-diff`
8×	`add-log-exp`
7×	`pow1`
5×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `fma-neg` `flip-+`
2×	`frac-times` `sqrt-pow1` `associate-*r/`
1×	`+-commutative` `sub-neg` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `associate-*l/` `sum-log` `sqrt-prod` `flip--` `fma-udef` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 73

Calls

4 calls:

18.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
9.0ms	(+ (exp x) 1.0)
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
16.0ms	(- (exp (* 2.0 x)) 1.0)

series212.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
7.0ms	(+ (exp x) 1.0)
41.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
22.0ms	(- (exp (* 2.0 x)) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	361	673
1	1258	564
2	5002	559

prune269.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
0.1b	(pow (- (exp (* 2.0 x)) 1.0) 3)
4.5b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.5b	(- (exp (* 2.0 x)) 1.0)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`cbrt-prod`
10×	`unpow-prod-down` `cube-prod`
9×	`prod-diff`
6×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `flip3--` `fma-neg` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow-pow` `pow1/3` `diff-log` `pow-exp` `rem-cbrt-cube` `fma-udef` `rem-cube-cbrt`

Counts

4 → 98

Calls

4 calls:

16.0ms	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
15.0ms	(pow (- (exp (* 2.0 x)) 1.0) 3)
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
14.0ms	(- (exp (* 2.0 x)) 1.0)

series134.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
52.0ms	(pow (- (exp (* 2.0 x)) 1.0) 3)
38.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
22.0ms	(- (exp (* 2.0 x)) 1.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	331	742
1	1260	635
2	5001	625

prune313.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
27.4b	(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

rewrite2.0ms

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:

0.0ms	(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)))

series94.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
74.0ms	(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	139	185
1	458	173
2	2447	165
3	5001	162

prune73.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes22.0ms

Accuracy

77.8% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 2.9b

bsearch36.0ms

Steps

Iters	Range		Point
7	-0.0014397831090811255	-6.027254205251813e-06	-1.1247925004240297e-05

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	18
1	30	18

end0.0ms

sample1.3s

Algorithm

intervals

Results

412.0ms	12633×	body	80	nan
256.0ms	7396×	body	80	valid
208.0ms	6694×	body	80	overflowed
58.0ms	722×	body	160	valid