Details

sample316.0ms

Algorithm

intervals

Results

22.0ms	331×	body	80	nan
16.0ms	241×	body	80	valid
13.0ms	202×	body	80	overflowed
3.0ms	21×	body	160	valid

simplify70.0ms

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: 4.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.8b	(- (exp (* 2.0 x)) 1.0)
5.0b	(- (exp x) 1.0)

rewrite59.0ms

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:

17.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
22.0ms	(sqrt (/ (- (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:

58.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
91.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
24.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

simplify57.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (40.0ms)

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

prune410.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize12.0ms

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))
5.0b	(- (exp x) 1.0)
5.0b	(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:

8.0ms	(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))

series369.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(sqrt (/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0)))
115.0ms	(/ (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))

simplify46.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (32.0ms)

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

prune368.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (expm1 (log1p (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)))) (- (exp x) 1.0)))
0.0b	(/ (expm1 (log1p (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)))) (- (exp x) 1.0))
5.0b	(- (exp x) 1.0)
5.0b	(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-sub` `div-exp` `clear-num` `fma-udef` `expm1-udef`

Counts

4 → 113

Calls

4 calls:

8.0ms	(sqrt (/ (expm1 (log1p (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)))) (- (exp x) 1.0)))
7.0ms	(/ (expm1 (log1p (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))

series608.0ms

Counts

4 → 12

Calls

4 calls:

281.0ms	(sqrt (/ (expm1 (log1p (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)))) (- (exp x) 1.0)))
229.0ms	(/ (expm1 (log1p (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)))) (- (exp x) 1.0))
13.0ms	(- (exp x) 1.0)
84.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

simplify50.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	368	1966
1	1095	1666
2	5001	1610

prune414.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (expm1 (log1p (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)))) (/ 1 (- (exp x) 1.0))))
0.0b	(* (expm1 (log1p (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)))) (/ 1 (- (exp x) 1.0)))
5.0b	(- (exp x) 1.0)
5.0b	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
21×	`add-cube-cbrt` `associate-r`
17×	`times-frac`
13×	`add-exp-log`
9×	`pow1` `prod-diff` `add-cbrt-cube`
6×	`add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`fma-neg` `associate-l` `unswap-sqr`
2×	`flip3--` `sqrt-pow1` `sqrt-div` `associate-*r/` `div-exp` `pow-prod-down` `associate-/r/` `un-div-inv` `flip--` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `pow1/2` `diff-log` `1-exp` `sqrt-prod` `*-commutative` `fma-udef` `div-inv`

Counts

4 → 99

Calls

4 calls:

6.0ms	(sqrt (* (expm1 (log1p (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)))) (/ 1 (- (exp x) 1.0))))
20.0ms	(* (expm1 (log1p (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)))) (/ 1 (- (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))

series607.0ms

Counts

4 → 12

Calls

4 calls:

289.0ms	(sqrt (* (expm1 (log1p (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)))) (/ 1 (- (exp x) 1.0))))
220.0ms	(* (expm1 (log1p (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)))) (/ 1 (- (exp x) 1.0)))
14.0ms	(- (exp x) 1.0)
84.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	430	1307
1	1651	966
2	5002	911

prune333.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes32.0ms

Accuracy

66.9% (1.2b remaining)

Error of 1.3b against oracle of 0.1b and baseline of 3.6b

bsearch46.0ms

Steps

Iters	Range		Point
7	-7.610621345753375e-17	-6.875149561731272e-19	-5.697781248128253e-17

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	18
1	24	18

end0.0ms

sample2.1s

Algorithm

intervals

Results

762.0ms	12246×	body	80	nan
480.0ms	7360×	body	80	valid
410.0ms	6523×	body	80	overflowed
104.0ms	760×	body	160	valid