Details

sample35.0ms

Algorithm

intervals

Results

14.0ms	61×	body	1280	valid
6.0ms	40×	body	640	valid
4.0ms	123×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	11×	body	160	valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 31.0b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 124

Calls

2 calls:

5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
13.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series127.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
85.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	376	1556
1	1170	1155
2	5001	1121

prune291.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
0.1b	(* 0.33333333333333337 (pow x 3))
8.7b	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

1.0ms	(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
11.0ms	(* 0.33333333333333337 (pow x 3))
1.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series194.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
42.0ms	(* 0.33333333333333337 (pow x 3))
105.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify210.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	170	298
1	655	262
2	4021	262
3	5002	262

prune159.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

160×	`*-un-lft-identity`
116×	`add-sqr-sqrt`
108×	`prod-diff`
106×	`add-cube-cbrt`
98×	`times-frac`
59×	`log-prod`
56×	`exp-sum`
25×	`distribute-lft-out`
18×	`fma-neg`
16×	`associate-/r/`
8×	`flip3-+` `flip-+` `div-inv`
7×	`log-pow`
6×	`exp-prod`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-/r*` `difference-of-squares`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
2×	`sub-neg` `distribute-lft-out--`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `exp-diff` `diff-log` `div-exp` `rem-log-exp` `clear-num` `flip--`

Counts

3 → 201

Calls

3 calls:

5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
16.0ms	(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
16.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series197.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
79.0ms	(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
83.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify64.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	515	2850
1	1388	2049
2	5002	1637

prune307.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`fma-def`
9×	`distribute-lft-out`
6×	`add-log-exp`
4×	`add-exp-log` `associate-/r*` `associate-/r/` `add-cbrt-cube`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `sum-log` `log1p-expm1-u` `div-inv`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+r-` `distribute-rgt-neg-in` `frac-2neg` `div-exp` `unsub-neg` `neg-log` `clear-num`

Counts

2 → 72

Calls

2 calls:

8.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
15.0ms	(+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (- 1.0))

series117.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
81.0ms	(+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (- 1.0))

simplify96.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	258	437
1	893	406
2	3778	396
3	5001	395

prune168.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes254.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	25
1	35	25

end0.0ms

sample935.0ms

Algorithm

intervals

Results

388.0ms	1721×	body	1280	valid
188.0ms	1279×	body	640	valid
123.0ms	4085×	body	80	valid
64.0ms	603×	body	320	valid
20.0ms	312×	body	160	valid