Details

sample329.0ms

Algorithm

intervals

Results

28.0ms	371×	body	80	nan
20.0ms	224×	body	80	valid
15.0ms	202×	body	80	overflowed
6.0ms	36×	body	160	valid

simplify71.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.4b

localize20.0ms

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))
6.8b	(- (exp (* 2.0 x)) 1.0)
7.0b	(- (exp x) 1.0)

rewrite48.0ms

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:

14.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
16.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series202.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
57.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
31.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

simplify58.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (39.0ms)

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

prune390.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
0.1b	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
6.8b	(fma (- 1.0) 1.0 (exp (+ x x)))
6.8b	(- (exp (* 2.0 x)) 1.0)

rewrite44.0ms

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:

7.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
19.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (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)

series252.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
117.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
43.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
26.0ms	(- (exp (* 2.0 x)) 1.0)

simplify111.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (82.0ms)

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

prune654.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (+ (exp x) 1.0))
0.1b	(* (fma (- 1.0) 1.0 (exp (+ x x))) (/ 1 (+ (exp x) 1.0)))
6.8b	(fma (- 1.0) 1.0 (exp (+ x x)))
6.8b	(- (exp (* 2.0 x)) 1.0)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
26×	`times-frac`
18×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`prod-diff`
7×	`pow1` `distribute-lft-out`
6×	`add-log-exp`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `associate-/r*` `associate-/r/` `log1p-expm1-u`
3×	`fma-neg` `associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `cbrt-unprod` `flip-+` `div-inv`
1×	`sub-neg` `flip3--` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `flip--` `fma-udef` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 120

Calls

4 calls:

7.0ms	(/ 1 (+ (exp x) 1.0))
18.0ms	(* (fma (- 1.0) 1.0 (exp (+ x x))) (/ 1 (+ (exp x) 1.0)))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series163.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ 1 (+ (exp x) 1.0))
67.0ms	(* (fma (- 1.0) 1.0 (exp (+ x x))) (/ 1 (+ (exp x) 1.0)))
46.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
26.0ms	(- (exp (* 2.0 x)) 1.0)

simplify56.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	425	1014
1	1673	836
2	5002	790

prune357.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))))
0.1b	(expm1 (log1p (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))))
6.8b	(fma (- 1.0) 1.0 (exp (+ x x)))
6.8b	(- (exp (* 2.0 x)) 1.0)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
6×	`add-log-exp`
5×	`expm1-log1p-u`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg`
1×	`sub-neg` `log1p-udef` `expm1-log1p` `flip3--` `diff-log` `log1p-expm1` `flip--` `fma-udef` `distribute-lft-out--` `expm1-udef` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

0.0ms	(log1p (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))))
0.0ms	(expm1 (log1p (/ (- (exp (* 2.0 x)) 1.0) (/ (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)

series581.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(log1p (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))))
285.0ms	(expm1 (log1p (/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))))
44.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
26.0ms	(- (exp (* 2.0 x)) 1.0)

simplify39.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	315	802
1	1051	652
2	5001	648

prune249.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes36.0ms

Accuracy

99.3% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 2.7b

bsearch117.0ms

Steps

Iters	Range		Point
8	4.542041637378999e-19	1.2289470995845548e-16	5.521403901107718e-17
9	-0.09294265133275766	-5.033370145566524e-07	-1.273190028162842e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	17
1	37	17

end0.0ms

sample2.5s

Algorithm

intervals

Results

966.0ms	12775×	body	80	nan
599.0ms	7418×	body	80	valid
487.0ms	6583×	body	80	overflowed
119.0ms	714×	body	160	valid