Details

sample31.0ms

Algorithm

intervals

Results

12.0ms	54×	body	1280	valid
5.0ms	33×	body	640	valid
3.0ms	135×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	10×	body	160	valid

simplify61.0ms

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: 28.4b

localize11.0ms

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))))
3.0b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite29.0ms

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:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
13.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series139.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(+ 1.0 (exp (* -2.0 x)))
37.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
83.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify51.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (36.0ms)

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

prune250.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (exp (* -2.0 x))))
0.5b	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.5b	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
28.9b	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
42×	`times-frac`
40×	`add-sqr-sqrt`
37×	`add-cube-cbrt`
36×	`sqrt-prod`
14×	`associate-/r*`
10×	`add-exp-log`
9×	`distribute-lft-out`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`sqrt-div` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `flip3-+` `div-exp` `flip-+`
2×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `div-inv`
1×	`rem-sqrt-square` `rec-exp` `1-exp` `fma-udef` `hypot-def` `inv-pow`

Counts

4 → 129

Calls

4 calls:

4.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
6.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
7.0ms	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
1.0ms	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

series381.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt (+ 1.0 (exp (* -2.0 x))))
70.0ms	(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
46.0ms	(/ 1 (sqrt (+ 1.0 (exp (* -2.0 x)))))
219.0ms	(fma (/ 1 (sqrt (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (- 1.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	382	1270
1	1331	1133
2	5002	1081

prune291.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

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

rewrite12.0ms

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)))))
9.0ms	(* 0.33333333333333337 (pow x 3))
1.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series184.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(fma 1.0 x (- (fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))))
37.0ms	(* 0.33333333333333337 (pow x 3))
98.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify197.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 1 (5.0ms)

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

prune157.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp (* -2.0 x)) 3)
0.0b	(/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3)))
3.1b	(- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))
3.2b	(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))

rewrite28.0ms

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:

3.0ms	(pow (exp (* -2.0 x)) 3)
14.0ms	(/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3)))
6.0ms	(- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))
1.0ms	(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))

series439.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(pow (exp (* -2.0 x)) 3)
77.0ms	(/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3)))
76.0ms	(- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))
248.0ms	(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))

simplify73.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	454	1170
1	2072	1040
2	5001	1015

prune304.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes104.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 29.4b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	26
1	40	26

end0.0ms

sample883.0ms

Algorithm

intervals

Results

376.0ms	1762×	body	1280	valid
171.0ms	1230×	body	640	valid
107.0ms	4099×	body	80	valid
57.0ms	625×	body	320	valid
20.0ms	284×	body	160	valid