Details

analyze2.0ms

Algorithm: search

sample35.0ms

Algorithm

intervals

Results

12.0ms	49×	body	1280	valid
8.0ms	46×	body	640	valid
4.0ms	135×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	10×	body	160	valid

simplify57.0ms

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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 28.7b

Counts

2 → 1

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

rewrite18.0ms

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:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
9.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series15.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(+ 1.0 (exp (* -2.0 x)))
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
7.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify89.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	251	494
1	731	465
2	2771	460
3	5002	460

prune116.0ms

Filtered

50 candidates to 69 candidates (-38.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	2	70

Merged error: 0.0b

Counts

70 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
14×	`times-frac`
8×	`add-log-exp`
7×	`log-pow`
6×	`add-exp-log` `exp-prod` `add-cbrt-cube`
5×	`pow1` `log-prod` `distribute-lft-out`
4×	`associate-/r*` `difference-of-squares`
3×	`associate-/l*`
2×	`sub-neg` `flip3-+` `exp-sum` `associate-/r/` `flip-+` `distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `log-div` `flip3--` `frac-2neg` `exp-diff` `diff-log` `div-exp` `rem-log-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

4 → 81

Calls

4 calls:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
10.0ms	(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
11.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series22.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(+ 1.0 (exp (* -2.0 x)))
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
7.0ms	(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
7.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify95.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	291	672
1	849	622
2	3009	617
3	5002	617

prune154.0ms

Filtered

65 candidates to 93 candidates (-43.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	93	2	95

Merged error: 0.0b

Counts

95 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
18×	`*-un-lft-identity` `log-pow`
16×	`log-prod`
14×	`sqrt-pow1`
12×	`exp-prod`
10×	`add-cube-cbrt` `sqrt-prod`
8×	`pow1` `add-log-exp` `difference-of-squares`
6×	`add-exp-log`
4×	`sub-neg` `times-frac` `exp-sum` `add-cbrt-cube` `distribute-lft-out--`
2×	`log-div` `flip3--` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 82

Calls

4 calls:

11.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
9.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
11.0ms	(log (sqrt (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))))
11.0ms	(log (sqrt (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))))

series67.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
7.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
26.0ms	(log (sqrt (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))))
26.0ms	(log (sqrt (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))))

simplify45.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	190	930
1	394	846
2	1193	836
3	5001	832

prune260.0ms

Filtered

66 candidates to 94 candidates (-42.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	94	2	96

Merged error: 0.0b

Counts

96 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 2) (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
2.8b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
2.8b	(log (sqrt (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))))
3.3b	(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

153×	`add-sqr-sqrt`
77×	`times-frac`
57×	`sqrt-prod`
46×	`associate-l`
44×	`difference-of-squares`
40×	`*-un-lft-identity`
26×	`add-cube-cbrt`
10×	`add-exp-log`
9×	`log-pow` `add-cbrt-cube`
8×	`pow1` `log-prod` `add-log-exp`
7×	`sqrt-pow1`
6×	`exp-prod` `distribute-lft-out--`
4×	`associate-r`
3×	`sub-neg`
2×	`frac-times` `flip3--` `flip3-+` `diff-log` `associate-*r/` `exp-sum` `prod-exp` `flip--` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`cbrt-undiv` `distribute-rgt-in` `log-div` `distribute-lft-in` `pow1/2` `exp-diff` `sqrt-div` `div-exp` `rem-log-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `distribute-lft-out`

Counts

4 → 136

Calls

4 calls:

52.0ms	(* (/ (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 2) (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
9.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
11.0ms	(log (sqrt (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))))
24.0ms	(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series82.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (/ (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 2) (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
10.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
27.0ms	(log (sqrt (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))))
12.0ms	(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify74.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	715	2579
1	2724	2378
2	5001	2366

prune546.0ms

Filtered

87 candidates to 148 candidates (-70.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	147	3	150

Merged error: 0b

Counts

150 → 3

regimes385.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	36
1	51	36

end0.0ms

analyze2.0ms

Algorithm: search

sample1.0s

Algorithm

intervals

Results

427.0ms	1742×	body	1280	valid
214.0ms	1237×	body	640	valid
150.0ms	4142×	body	80	valid
69.0ms	597×	body	320	valid
21.0ms	282×	body	160	valid

Details

analyze2.0ms

sample35.0ms

simplify57.0ms

prune7.0ms

localize7.0ms

rewrite18.0ms

series15.0ms

simplify89.0ms

prune116.0ms

localize9.0ms

rewrite31.0ms

series22.0ms

simplify95.0ms

prune154.0ms

localize12.0ms

rewrite45.0ms

series67.0ms

simplify45.0ms

prune260.0ms

localize20.0ms

rewrite103.0ms

series82.0ms

simplify74.0ms

prune546.0ms

regimes385.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

analyze2.0ms

sample1.0s

Profiling