Details

sample100.0ms

Algorithm

intervals

Results

62.0ms	178×	body	1280	valid
14.0ms	288×	body	80	valid
8.0ms	42×	body	640	valid
3.0ms	19×	body	320	valid
1.0ms	11×	body	160	valid

simplify228.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	5
1	26	5
2	41	5
3	55	5
4	67	5
5	104	5
6	161	5
7	344	5
8	1454	5
9	5001	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.0b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`prod-diff`
16×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`add-log-exp`
5×	`fma-def`
4×	`frac-add`
3×	`flip3--` `fma-neg` `flip--` `distribute-lft-out--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `expm1-log1p-u` `sub-neg` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+`

Counts

2 → 65

Calls

2 calls:

5.0ms	(- (exp x) 2.0)
28.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series70.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(- (exp x) 2.0)
54.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify37.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	282	506
1	1008	381
2	5001	367

prune161.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
0.1b	(* 1/12 (pow x 4))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
7×	`add-exp-log` `associate-r`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube`
3×	`associate-l` `prod-exp` `unswap-sqr`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

2 → 37

Calls

2 calls:

0.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
5.0ms	(* 1/12 (pow x 4))

series159.0ms

Counts

2 → 6

Calls

2 calls:

123.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
36.0ms	(* 1/12 (pow x 4))

simplify67.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	122	183
1	427	166
2	1923	165
3	5002	164

prune102.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (- (exp x) 2.0) (- (exp x) 2.0)) (* (exp (- x)) (exp (- x)))) (- (- (exp x) 2.0) (exp (- x))))
0.0b	(* (exp (- x)) (exp (- x)))
0.0b	(* (- (exp x) 2.0) (- (exp x) 2.0))
3.9b	(- (* (- (exp x) 2.0) (- (exp x) 2.0)) (* (exp (- x)) (exp (- x))))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

148×	`frac-sub`
144×	`frac-times`
121×	`exp-neg`
119×	`flip3--` `*-un-lft-identity` `flip--`
104×	`neg-sub0` `exp-diff`
88×	`add-sqr-sqrt`
76×	`exp-prod`
74×	`associate-/l/`
72×	`associate-r/` `associate-l/`
66×	`add-cube-cbrt`
37×	`prod-diff`
24×	`distribute-rgt-neg-in` `times-frac`
22×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
21×	`distribute-lft-out--`
20×	`distribute-lft-neg-in`
18×	`pow1`
17×	`un-div-inv` `difference-of-squares`
16×	`pow-prod-down`
14×	`pow-sqr` `pow-prod-up`
10×	`swap-sqr` `add-cbrt-cube`
8×	`add-exp-log` `neg-mul-1` `associate-r` `associate-l`
6×	`associate-/r*` `associate-/r/` `add-log-exp`
5×	`sub-neg`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
2×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 379

Calls

4 calls:

75.0ms	(/ (- (* (- (exp x) 2.0) (- (exp x) 2.0)) (* (exp (- x)) (exp (- x)))) (- (- (exp x) 2.0) (exp (- x))))
26.0ms	(* (exp (- x)) (exp (- x)))
28.0ms	(* (- (exp x) 2.0) (- (exp x) 2.0))
25.0ms	(- (* (- (exp x) 2.0) (- (exp x) 2.0)) (* (exp (- x)) (exp (- x))))

series299.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ (- (* (- (exp x) 2.0) (- (exp x) 2.0)) (* (exp (- x)) (exp (- x)))) (- (- (exp x) 2.0) (exp (- x))))
15.0ms	(* (exp (- x)) (exp (- x)))
32.0ms	(* (- (exp x) 2.0) (- (exp x) 2.0))
87.0ms	(- (* (- (exp x) 2.0) (- (exp x) 2.0)) (* (exp (- x)) (exp (- x))))

simplify78.0ms

Algorithm

egg-herbie

Counts

391 → 391

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1451	6429
1	5002	5668

prune882.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp (- x)) 2)
0.0b	(pow (- (exp x) 2.0) 2)
3.9b	(- (pow (- (exp x) 2.0) 2) (pow (exp (- x)) 2))
4.4b	(fma (- (exp (- x))) (exp (- x)) (pow (exp (- x)) 2))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

95×	`unpow-prod-down`
85×	`add-sqr-sqrt`
80×	`prod-diff`
76×	`*-un-lft-identity`
49×	`add-cube-cbrt`
29×	`unpow2` `sqr-pow`
26×	`difference-of-squares`
14×	`distribute-lft-out--`
12×	`pow-pow`
10×	`exp-prod` `fma-neg`
6×	`pow1` `pow-unpow` `add-log-exp`
5×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
2×	`pow-to-exp` `pow-exp`
1×	`neg-mul-1` `sub-neg` `flip3--` `diff-log` `flip--` `fma-udef`

Counts

4 → 185

Calls

4 calls:

5.0ms	(pow (exp (- x)) 2)
6.0ms	(pow (- (exp x) 2.0) 2)
77.0ms	(- (pow (- (exp x) 2.0) 2) (pow (exp (- x)) 2))
0.0ms	(fma (- (exp (- x))) (exp (- x)) (pow (exp (- x)) 2))

series225.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(pow (exp (- x)) 2)
33.0ms	(pow (- (exp x) 2.0) 2)
84.0ms	(- (pow (- (exp x) 2.0) 2) (pow (exp (- x)) 2))
92.0ms	(fma (- (exp (- x))) (exp (- x)) (pow (exp (- x)) 2))

simplify69.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	603	3250
1	1735	2036
2	5001	2004

prune345.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes25.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	5
1	11	5

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.9s	5564×	body	1280	valid
397.0ms	8040×	body	80	valid
259.0ms	1274×	body	640	valid
86.0ms	648×	body	320	valid
33.0ms	333×	body	160	valid