Details

sample35.0ms

Algorithm

intervals

Results

13.0ms	60×	body	1280	valid
7.0ms	46×	body	640	valid
3.0ms	118×	body	80	valid
2.0ms	25×	body	320	valid
0.0ms	7×	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: 32.7b

localize7.0ms

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)))
2.8b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite58.0ms

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:

6.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
39.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series131.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
16.0ms	(+ 1.0 (exp (* -2.0 x)))
79.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (36.0ms)

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

prune277.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.33333333333333337 (pow x 3))
8.8b	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite8.0ms

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:

6.0ms	(* 0.33333333333333337 (pow x 3))
0.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series129.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(* 0.33333333333333337 (pow x 3))
94.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify191.0ms

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

prune141.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
2.8b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
2.8b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
2.8b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

254×	`*-un-lft-identity`
205×	`add-sqr-sqrt`
162×	`add-cube-cbrt` `prod-diff`
151×	`times-frac`
54×	`fma-neg`
36×	`distribute-lft-out`
32×	`cbrt-prod`
24×	`associate-/r/`
14×	`difference-of-squares`
12×	`cbrt-div` `flip3-+` `flip-+` `div-inv`
11×	`pow1` `swap-sqr`
10×	`add-log-exp`
9×	`flip3--` `associate-r` `associate-l` `flip--` `distribute-lft-out--`
6×	`add-exp-log` `pow1/3`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `diff-log`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 328

Calls

4 calls:

131.0ms	(* (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
41.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
41.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
39.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series454.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(* (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
79.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
77.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
81.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify87.0ms

Algorithm

egg-herbie

Counts

340 → 340

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	472	4999
1	1486	3759
2	5001	3576

prune692.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
2.8b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
2.9b	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
2.9b	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

398×	`sqrt-prod`
387×	`*-un-lft-identity`
306×	`prod-diff`
298×	`add-sqr-sqrt`
265×	`add-cube-cbrt`
221×	`times-frac`
60×	`fma-neg`
56×	`distribute-lft-out`
36×	`associate-/r/`
19×	`flip3-+` `flip-+`
18×	`div-inv`
14×	`difference-of-squares`
10×	`add-log-exp`
5×	`cbrt-prod` `distribute-lft-out--`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 444

Calls

4 calls:

22.0ms	(cbrt (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
41.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
54.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
54.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series759.0ms

Counts

4 → 12

Calls

4 calls:

446.0ms	(cbrt (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
77.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
113.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
122.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify128.0ms

Algorithm

egg-herbie

Counts

456 → 456

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	803	9180
1	2402	6960
2	5001	6481

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes387.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.7b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	77
1	58	77

end0.0ms

sample888.0ms

Algorithm

intervals

Results

367.0ms	1703×	body	1280	valid
176.0ms	1249×	body	640	valid
111.0ms	4072×	body	80	valid
64.0ms	656×	body	320	valid
19.0ms	320×	body	160	valid