Details

sample328.0ms

Algorithm

intervals

Results

23.0ms	416×	body	80	nan
16.0ms	243×	body	80	valid
12.0ms	232×	body	80	overflowed
3.0ms	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.2b

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))
4.3b	(- (exp (* 2.0 x)) 1.0)
4.4b	(- (exp x) 1.0)

rewrite60.0ms

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)))
26.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
8.0ms	(- (exp x) 1.0)

series200.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(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)
22.0ms	(- (exp x) 1.0)

simplify58.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (40.0ms)

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

prune404.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 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)
4.3b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.3b	(- (exp (* 2.0 x)) 1.0)

rewrite20.0ms

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)
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series238.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(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)
47.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
25.0ms	(- (exp (* 2.0 x)) 1.0)

simplify44.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (36.0ms)

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

prune277.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (fma (- 1.0) 1.0 (exp (+ x x))) 3)
0.3b	(cbrt (pow (fma (- 1.0) 1.0 (exp (+ x x))) 3))
4.3b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.3b	(- (exp (* 2.0 x)) 1.0)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

1.0ms	(pow (fma (- 1.0) 1.0 (exp (+ x x))) 3)
1.0ms	(cbrt (pow (fma (- 1.0) 1.0 (exp (+ x x))) 3))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series183.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow (fma (- 1.0) 1.0 (exp (+ x x))) 3)
46.0ms	(cbrt (pow (fma (- 1.0) 1.0 (exp (+ x x))) 3))
40.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
30.0ms	(- (exp (* 2.0 x)) 1.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	294	698
1	1075	592
2	5001	584

prune288.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
0.2b	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
0.3b	(/ (pow x 2) (sqrt 2.0))
0.4b	(/ x (sqrt 2.0))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

177×	`times-frac`
176×	`add-sqr-sqrt`
151×	`*-un-lft-identity`
149×	`add-cube-cbrt`
78×	`prod-diff`
67×	`sqrt-prod`
52×	`associate-l`
41×	`distribute-rgt-in` `unpow-prod-down` `distribute-lft-in`
21×	`add-exp-log`
15×	`unpow2` `sqr-pow`
13×	`add-cbrt-cube`
12×	`associate-/r*`
11×	`associate-/l*`
9×	`div-inv` `add-log-exp` `unswap-sqr`
7×	`div-exp`
6×	`pow1` `associate-r`
4×	`expm1-log1p-u` `associate-*r/` `prod-exp` `log1p-expm1-u`
3×	`cbrt-undiv` `sum-log`
2×	`frac-times` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `frac-add` `pow-exp` `clear-num` `flip--` `cbrt-unprod` `flip-+` `difference-of-squares`
1×	`+-commutative` `associate-+r+` `fma-def` `pow-prod-down` `associate-l/` `-commutative` `distribute-lft-out--`

Counts

4 → 308

Calls

4 calls:

14.0ms	(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
56.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
5.0ms	(/ (pow x 2) (sqrt 2.0))
3.0ms	(/ x (sqrt 2.0))

series284.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
67.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
64.0ms	(/ (pow x 2) (sqrt 2.0))
59.0ms	(/ x (sqrt 2.0))

simplify74.0ms

Algorithm

egg-herbie

Counts

320 → 320

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1334	4318
1	5001	3447

prune587.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes24.0ms

Accuracy

74.4% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 2.8b

bsearch55.0ms

Steps

Iters	Range		Point
7	-7.225379688545694e-13	-5.3975284999429435e-15	-5.602562757292874e-14

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	24
1	39	24

end0.0ms

sample1.9s

Algorithm

intervals

Results

693.0ms	12778×	body	80	nan
424.0ms	7427×	body	80	valid
339.0ms	6672×	body	80	overflowed
93.0ms	700×	body	160	valid