Details

sample36.0ms

Algorithm

intervals

Results

15.0ms	70×	body	1280	valid
7.0ms	46×	body	640	valid
3.0ms	120×	body	80	valid
1.0ms	16×	body	320	valid
0.0ms	4×	body	160	valid

simplify62.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	31	5
3	54	5
4	119	5
5	333	5
6	1646	5
7	5001	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(+ 1.0 (exp (* -2.0 x)))
1.2b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
7×	`add-log-exp`
6×	`flip3-+` `flip-+`
5×	`add-exp-log` `add-cbrt-cube` `div-inv`
4×	`associate-/r*`
3×	`pow1` `expm1-log1p-u` `fma-def` `log1p-expm1-u` `associate-/l*`
2×	`difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `flip--` `distribute-lft-out--`

Counts

3 → 141

Calls

3 calls:

9.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
43.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series130.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
16.0ms	(+ 1.0 (exp (* -2.0 x)))
78.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	398	1645
1	1287	1235
2	5001	1212

prune259.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.33333333333333337 (pow x 3))
9.4b	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-r`
7×	`add-exp-log`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `cube-prod` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

2 → 43

Calls

2 calls:

7.0ms	(* 0.33333333333333337 (pow x 3))
0.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series132.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(* 0.33333333333333337 (pow x 3))
97.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify189.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	142	195
1	582	172
2	3698	172
3	5002	172

prune128.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.0b	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.5b	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
1.2b	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite377.0ms

Algorithm

rewrite-expression-head

Rules

1732×	`times-frac`
1496×	`*-un-lft-identity`
1020×	`add-sqr-sqrt`
997×	`sqrt-prod`
996×	`add-cube-cbrt`
585×	`prod-diff`
249×	`distribute-lft-out`
195×	`fma-neg`
84×	`sqrt-div` `associate-/r/`
43×	`flip3-+` `flip-+`
42×	`div-inv`
30×	`associate-/l*`
14×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`difference-of-squares`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-def`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `sum-log` `flip--` `associate-/l/` `distribute-lft-out--`

Counts

4 → 1108

Calls

4 calls:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
26.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
7.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
230.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series199.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ 1.0 (exp (* -2.0 x)))
40.0ms	(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
63.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
80.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify221.0ms

Algorithm

egg-herbie

Counts

1120 → 1120

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1609	25904
1	5001	17295

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3)))
0.0b	(pow (exp (* -2.0 x)) 3)
1.6b	(- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))
1.7b	(fma (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3))) (+ (* 1.0 1.0) (- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))) (- 1.0))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

61×	`*-un-lft-identity`
27×	`times-frac`
21×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`distribute-lft-out`
19×	`unpow-prod-down` `cube-prod`
9×	`associate-/r*`
7×	`add-cbrt-cube` `add-log-exp`
6×	`add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `sum-cubes` `log1p-expm1-u`
3×	`pow-unpow` `pow-pow` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `cube-mult` `pow-to-exp` `sub-neg` `exp-prod` `flip3--` `exp-to-pow` `distribute-rgt-out--` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `unpow3` `div-exp` `prod-diff` `pow-exp` `clear-num` `flip--` `flip-+` `fma-udef` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 109

Calls

4 calls:

28.0ms	(/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3)))
2.0ms	(pow (exp (* -2.0 x)) 3)
6.0ms	(- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))
0.0ms	(fma (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3))) (+ (* 1.0 1.0) (- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))) (- 1.0))

series443.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3)))
40.0ms	(pow (exp (* -2.0 x)) 3)
76.0ms	(- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))
253.0ms	(fma (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3))) (+ (* 1.0 1.0) (- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))) (- 1.0))

simplify84.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	454	1172
1	2072	1040
2	5001	1021

prune311.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes195.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.2b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	40
1	46	40

end0.0ms

sample882.0ms

Algorithm

intervals

Results

374.0ms	1738×	body	1280	valid
174.0ms	1231×	body	640	valid
108.0ms	4140×	body	80	valid
54.0ms	581×	body	320	valid
24.0ms	310×	body	160	valid