Details

sample394.0ms

Algorithm

intervals

Results

57.0ms	186×	body	10240	exit
13.0ms	444×	body	80	nan
7.0ms	238×	body	80	valid
1.0ms	18×	body	160	valid

simplify73.0ms

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: 3.8b

localize14.0ms

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))
3.9b	(- (exp (* 2.0 x)) 1.0)
3.9b	(- (exp x) 1.0)

rewrite106.0ms

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))
19.0ms	(- (exp (* 2.0 x)) 1.0)
13.0ms	(- (exp x) 1.0)

series202.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
61.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
25.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify53.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (39.0ms)

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

prune391.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize16.0ms

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)
3.9b	(fma (- 1.0) 1.0 (exp (+ x x)))
3.9b	(- (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)

series236.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
8.0ms	(+ (exp x) 1.0)
46.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
24.0ms	(- (exp (* 2.0 x)) 1.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (34.0ms)

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

prune275.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp x))
0.0b	(sqrt (exp x))
3.9b	(fma (- 1.0) 1.0 (exp (+ x x)))
3.9b	(- (exp (* 2.0 x)) 1.0)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
9×	`prod-diff`
8×	`sqrt-pow1`
6×	`pow1` `exp-prod` `sqrt-prod` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg`
2×	`rem-sqrt-square` `pow1/2`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `fma-udef` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 74

Calls

4 calls:

3.0ms	(sqrt (exp x))
3.0ms	(sqrt (exp x))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
13.0ms	(- (exp (* 2.0 x)) 1.0)

series95.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (exp x))
13.0ms	(sqrt (exp x))
41.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
29.0ms	(- (exp (* 2.0 x)) 1.0)

simplify89.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	219	440
1	605	348
2	2891	335
3	5002	308

prune303.0ms

Pruning

3 alts after pruning (1 fresh and 2 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))
27.5b	(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))
1.0ms	(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

series101.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
79.0ms	(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

simplify64.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (61.0ms)

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

prune73.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes30.0ms

Accuracy

99.5% (0.0b remaining)

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

bsearch89.0ms

Steps

Iters	Range		Point
8	1.0287578034236322e-17	2.6801423773796306e-14	5.549336637458991e-17
9	-5.8848704152608634e-05	-2.0012008038825942e-10	-1.029879697390661e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	31
1	35	31

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	6416×	body	10240	exit
385.0ms	12703×	body	80	nan
235.0ms	7391×	body	80	valid
58.0ms	741×	body	160	valid