Details

sample34.0ms

Algorithm

intervals

Results

11.0ms	50×	body	1280	valid
6.0ms	46×	body	640	valid
3.0ms	129×	body	80	valid
2.0ms	22×	body	320	valid
1.0ms	9×	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	30	5
3	52	5
4	114	5
5	322	5
6	1627	5
7	5002	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
2.6b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
13×	`times-frac`
12×	`add-cube-cbrt`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
4×	`associate-/r*`
3×	`pow1` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `flip--` `div-inv` `distribute-lft-out--`

Counts

3 → 60

Calls

3 calls:

6.0ms	(+ 1.0 (exp (* -2.0 x)))
15.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
67.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series123.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(+ 1.0 (exp (* -2.0 x)))
34.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
74.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify91.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	251	494
1	731	465
2	2785	460
3	5001	460

prune144.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3)
0.0b	(cbrt (pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3))
2.6b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`cbrt-prod`
17×	`times-frac`
12×	`unpow-prod-down` `cube-prod`
10×	`difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`cube-div` `associate-/r*` `distribute-lft-out`
3×	`pow-unpow` `flip3--` `flip--` `associate-/l*`
2×	`cube-mult` `cbrt-div` `unpow3` `associate-/r/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `pow1/3` `diff-log` `div-exp` `pow-exp` `clear-num` `rem-cbrt-cube` `flip-+` `div-inv` `rem-cube-cbrt`

Counts

4 → 108

Calls

4 calls:

13.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
73.0ms	(pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3)
62.0ms	(cbrt (pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3))
66.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series293.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
111.0ms	(pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3)
73.0ms	(cbrt (pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3))
72.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	382	1080
1	1422	1033
2	5002	1019

prune230.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))) 3)
0.0b	(cbrt (pow (* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))) 3))
0.3b	(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
3.1b	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite538.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `sqrt-prod`
16×	`cube-div`
12×	`frac-times` `difference-of-squares`
11×	`associate-r`
10×	`flip3--` `flip--`
9×	`pow1` `add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
8×	`cbrt-prod` `add-cube-cbrt` `cbrt-div`
6×	`associate-r/` `associate-l/` `add-log-exp`
5×	`associate-l`
4×	`times-frac` `distribute-lft-out--`
3×	`sub-neg` `pow-unpow`
2×	`distribute-rgt-in` `cube-mult` `unpow-prod-down` `pow-pow` `distribute-lft-in` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `pow1/3` `diff-log` `*-commutative` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

107.0ms	(pow (* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))) 3)
8.0ms	(cbrt (pow (* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))) 3))
340.0ms	(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
78.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

491.0ms	(pow (* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))) 3)
361.0ms	(cbrt (pow (* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))) 3))
354.0ms	(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
109.0ms	(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify99.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	633	2584
1	3433	2118
2	5001	2087

prune384.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
0.1b	(* 0.33333333333333337 (pow x 3))
0.7b	(* 5.551115123125783e-17 (pow x 4))
6.6b	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `cube-prod` `sqr-pow`
2×	`pow-to-exp` `diff-log` `pow-exp` `sum-log` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `sub-neg` `flip3--` `flip3-+` `unpow3` `flip--` `flip-+` `associate--r+`

Counts

4 → 81

Calls

4 calls:

15.0ms	(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
13.0ms	(* 0.33333333333333337 (pow x 3))
15.0ms	(* 5.551115123125783e-17 (pow x 4))
9.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
35.0ms	(* 0.33333333333333337 (pow x 3))
39.0ms	(* 5.551115123125783e-17 (pow x 4))
102.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

simplify52.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	344	493
1	1475	459
2	5001	459

prune189.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes268.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 29.4b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	33
1	43	33

end0.0ms

sample899.0ms

Algorithm

intervals

Results

340.0ms	1669×	body	1280	valid
179.0ms	1316×	body	640	valid
109.0ms	4088×	body	80	valid
54.0ms	615×	body	320	valid
18.0ms	312×	body	160	valid