Details

sample32.0ms

Algorithm

intervals

Results

12.0ms	56×	body	1280	valid
5.0ms	36×	body	640	valid
4.0ms	133×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	12×	body	160	valid

simplify62.0ms

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: 28.8b

localize6.0ms

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

rewrite27.0ms

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))))
12.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series139.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(+ 1.0 (exp (* -2.0 x)))
41.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
81.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify52.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (37.0ms)

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

prune269.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
2.7b	(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

116×	`*-un-lft-identity`
88×	`times-frac`
70×	`add-sqr-sqrt`
58×	`add-cube-cbrt`
26×	`distribute-lft-out`
24×	`swap-sqr`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-r` `associate-l`
12×	`associate-/r/`
11×	`pow1`
8×	`associate-/r*`
6×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `div-inv` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`pow2` `frac-times` `sub-neg` `flip3--` `pow-plus` `fma-neg` `diff-log` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `difference-of-squares`

Counts

4 → 177

Calls

4 calls:

5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
21.0ms	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
12.0ms	(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

series210.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
42.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
43.0ms	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
89.0ms	(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

simplify82.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	571	1982
1	2701	1720
2	5001	1646

prune429.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(cbrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3))
0.0b	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
2.8b	(- (cbrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)) 1.0)

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

246×	`*-un-lft-identity`
216×	`cbrt-prod`
179×	`add-sqr-sqrt`
164×	`add-cube-cbrt`
158×	`times-frac`
135×	`prod-diff`
110×	`unpow-prod-down` `cube-prod`
45×	`fma-neg`
40×	`distribute-lft-out`
26×	`associate-/r/`
13×	`flip3-+` `flip-+` `div-inv`
9×	`add-exp-log` `add-cbrt-cube`
7×	`difference-of-squares` `sqr-pow`
6×	`cube-mult` `unpow3` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`pow-unpow` `associate-/l*`
2×	`cbrt-undiv` `cube-div` `div-exp` `pow-exp` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `cbrt-div` `flip3--` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `clear-num` `flip--` `rem-cbrt-cube` `distribute-lft-out--`

Counts

4 → 349

Calls

4 calls:

5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
8.0ms	(cbrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3))
7.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
31.0ms	(- (cbrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)) 1.0)

series221.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
37.0ms	(cbrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3))
58.0ms	(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
84.0ms	(- (cbrt (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)) 1.0)

simplify106.0ms

Algorithm

egg-herbie

Counts

361 → 361

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	735	4681
1	2819	2948
2	5001	2752

prune433.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
0.0b	(cbrt (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))))
0.3b	(cbrt (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
3.1b	(fma (cbrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (cbrt (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) (- 1.0))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

96×	`*-un-lft-identity`
76×	`times-frac`
60×	`add-sqr-sqrt`
48×	`add-cube-cbrt`
24×	`swap-sqr`
21×	`distribute-lft-out`
19×	`cbrt-prod`
18×	`associate-r` `associate-l`
16×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`associate-/r/`
5×	`flip3-+` `flip-+` `div-inv`
4×	`cbrt-undiv` `expm1-log1p-u` `cbrt-div` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`frac-times` `pow1/3` `associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `fma-udef`

Counts

4 → 143

Calls

4 calls:

18.0ms	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
9.0ms	(cbrt (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))))
5.0ms	(cbrt (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
1.0ms	(fma (cbrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (cbrt (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) (- 1.0))

series912.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
220.0ms	(cbrt (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))))
171.0ms	(cbrt (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
478.0ms	(fma (cbrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (cbrt (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) (- 1.0))

simplify81.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	695	2017
1	2866	1758
2	5002	1657

prune415.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes316.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.5b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	27
1	38	27

end0.0ms

sample876.0ms

Algorithm

intervals

Results

350.0ms	1679×	body	1280	valid
180.0ms	1278×	body	640	valid
115.0ms	4070×	body	80	valid
61.0ms	634×	body	320	valid
20.0ms	339×	body	160	valid