Details

sample76.0ms

Algorithm

intervals

Results

49.0ms	170×	body	1280	valid
8.0ms	44×	body	640	valid
6.0ms	245×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	14×	body	160	valid

simplify229.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 29.4b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.9b	(+ (- (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:

8.0ms	(- (exp x) 2.0)
25.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series66.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(- (exp x) 2.0)
53.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify40.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (29.0ms)

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

prune165.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

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)))
6.0ms	(* 1/12 (pow x 4))

series158.0ms

Counts

2 → 6

Calls

2 calls:

123.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
35.0ms	(* 1/12 (pow x 4))

simplify65.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 3 (62.0ms)

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

prune108.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 2.0)
0.0b	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
0.0b	(* (+ (exp x) 2.0) (exp x))
4.5b	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`add-sqr-sqrt` `add-cbrt-cube`
9×	`add-exp-log` `add-cube-cbrt`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `associate-l` `associate-*l/` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `times-frac` `associate-r` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `-commutative` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

4.0ms	(+ (exp x) 2.0)
10.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
16.0ms	(* (+ (exp x) 2.0) (exp x))
0.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

series337.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ (exp x) 2.0)
217.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (* (+ (exp x) 2.0) (exp x)))
22.0ms	(* (+ (exp x) 2.0) (exp x))
91.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

simplify40.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	312	834
1	1220	713
2	5001	710

prune246.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (+ (exp x) 2.0))
0.0b	(- (log (/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (+ (exp x) 2.0))) x)
0.3b	(exp (- (log (/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (+ (exp x) 2.0))) x))
4.5b	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
49×	`add-sqr-sqrt`
45×	`add-cube-cbrt`
36×	`log-prod` `times-frac` `associate--l+`
32×	`exp-sum`
24×	`prod-diff`
13×	`pow1`
10×	`distribute-lft-out`
9×	`log-pow`
7×	`add-log-exp`
6×	`add-exp-log` `exp-prod` `associate-/r/` `add-cbrt-cube`
4×	`expm1-log1p-u` `fma-neg` `associate-/r*` `log1p-expm1-u` `distribute-lft-out--`
3×	`flip3-+` `flip-+` `div-inv` `associate-/l*`
2×	`sub-neg` `diff-log` `rem-exp-log` `difference-of-squares`
1×	`cbrt-undiv` `associate--l-` `log-div` `flip3--` `frac-2neg` `exp-diff` `div-exp` `clear-num` `flip--` `fma-udef`

Counts

4 → 147

Calls

4 calls:

7.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (+ (exp x) 2.0))
10.0ms	(- (log (/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (+ (exp x) 2.0))) x)
18.0ms	(exp (- (log (/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (+ (exp x) 2.0))) x))
0.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

series663.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (+ (exp x) 2.0))
271.0ms	(- (log (/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (+ (exp x) 2.0))) x)
168.0ms	(exp (- (log (/ (fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (+ (exp x) 2.0))) x))
94.0ms	(fma (exp x) (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))

simplify70.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	581	2993
1	1902	2620
2	5002	2540

prune443.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes17.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	5
1	11	5

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.7s	5684×	body	1280	valid
201.0ms	1203×	body	640	valid
199.0ms	7841×	body	80	valid
65.0ms	635×	body	320	valid
20.0ms	306×	body	160	valid