Details

sample361.0ms

Algorithm

intervals

Results

51.0ms	258×	body	10240	exit
24.0ms	453×	body	80	nan
8.0ms	241×	body	80	valid
1.0ms	19×	body	160	valid

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 3.6b

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))
3.8b	(- (exp (* 2.0 x)) 1.0)
3.9b	(- (exp x) 1.0)

rewrite40.0ms

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:

10.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
11.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series210.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
57.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
35.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify56.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (40.0ms)

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

prune406.0ms

Filtered

167 candidates to 110 candidates (65.9%)

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)
3.8b	(fma (- 1.0) 1.0 (exp (+ x x)))
3.8b	(- (exp (* 2.0 x)) 1.0)

rewrite21.0ms

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:

9.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
4.0ms	(+ (exp x) 1.0)
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series234.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(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)
43.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
28.0ms	(- (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

prune286.0ms

Filtered

85 candidates to 65 candidates (76.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
22×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sqrt-pow1` `fma-neg` `sqrt-prod` `associate-/l*`
2×	`flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `exp-prod` `exp-to-pow` `frac-2neg` `pow1/2` `diff-log` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 94

Calls

4 calls:

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

series249.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(sqrt (exp (* 2.0 x)))
117.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
14.0ms	(- (exp x) 1.0)
90.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

simplify39.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	305	1109
1	943	913
2	5001	891

prune304.0ms

Filtered

106 candidates to 77 candidates (72.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma 0.4999999999999998 (pow x 2) (fma 1.0 x 2.0))
29.1b	(sqrt (fma 0.4999999999999998 (pow x 2) (fma 1.0 x 2.0)))

rewrite3.0ms

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:

1.0ms	(fma 0.4999999999999998 (pow x 2) (fma 1.0 x 2.0))
2.0ms	(sqrt (fma 0.4999999999999998 (pow x 2) (fma 1.0 x 2.0)))

series103.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(fma 0.4999999999999998 (pow x 2) (fma 1.0 x 2.0))
81.0ms	(sqrt (fma 0.4999999999999998 (pow x 2) (fma 1.0 x 2.0)))

simplify69.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	140	185
1	460	173
2	2403	165
3	5001	162

prune79.0ms

Filtered

31 candidates to 25 candidates (80.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes26.0ms

Accuracy

91.3% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 2.8b

bsearch81.0ms

Steps

Iters	Range		Point
9	5.168885000514563e-20	2.1397042541860684e-14	1.2926370682794756e-15
6	-3.484100988050835e-05	-2.6892755714465704e-06	-9.511249813039962e-06

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	28
1	35	28

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	6899×	body	10240	exit
385.0ms	12756×	body	80	nan
252.0ms	7397×	body	80	valid
54.0ms	721×	body	160	valid