Details

sample37.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

11.0ms	48×	body	1280	valid
7.0ms	42×	body	640	valid
4.0ms	133×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	14×	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

prune3.0ms

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

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(+ 1.0 (exp (* -2.0 x)))
3.8b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite23.0ms

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:

9.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
10.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series15.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
2.0ms	(+ 1.0 (exp (* -2.0 x)))
8.0ms	(- (/ 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

prune119.0ms

Filtered

50 candidates to 69 candidates (-38.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	66	3	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	3	70

Merged error: 0.0b

Counts

70 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 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))
3.8b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
18×	`cbrt-prod`
12×	`unpow-prod-down` `cube-prod`
10×	`add-cube-cbrt` `difference-of-squares`
8×	`add-log-exp`
5×	`pow1` `add-exp-log` `times-frac` `add-cbrt-cube` `distribute-lft-out--`
4×	`cube-div`
3×	`pow-unpow` `flip3--` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `sub-neg` `pow-pow` `flip3-+` `pow1/3` `diff-log` `pow-exp` `sum-log` `rem-cbrt-cube` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 87

Calls

4 calls:

5.0ms	(+ 1.0 (exp (* -2.0 x)))
10.0ms	(pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3)
10.0ms	(cbrt (pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3))
10.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series29.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(+ 1.0 (exp (* -2.0 x)))
13.0ms	(pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3)
7.0ms	(cbrt (pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3))
7.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	345	909
1	1226	864
2	5001	849

prune132.0ms

Filtered

55 candidates to 99 candidates (-80.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	99	3	102

Merged error: 0.0b

Counts

102 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(+ 1.0 (exp (* -2.0 x)))
3.8b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
3.9b	(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))

rewrite30.0ms

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:

5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
9.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
10.0ms	(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))

series22.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
2.0ms	(+ 1.0 (exp (* -2.0 x)))
7.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
8.0ms	(log (exp (- (/ 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	851	622
2	3011	617
3	5001	617

prune147.0ms

Filtered

64 candidates to 93 candidates (-45.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	93	3	96

Merged error: 0.0b

Counts

96 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 0.33333333333333337 (pow x 3))
0.4b	(* 5.551115123125783e-17 (pow x 4))
8.6b	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`associate-r`
13×	`add-exp-log`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`add-log-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `flip3-+` `unpow3` `sum-log` `flip-+`

Counts

3 → 67

Calls

3 calls:

6.0ms	(* 0.33333333333333337 (pow x 3))
5.0ms	(* 5.551115123125783e-17 (pow x 4))
4.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

series16.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(* 0.33333333333333337 (pow x 3))
4.0ms	(* 5.551115123125783e-17 (pow x 4))
9.0ms	(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

simplify43.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	268	323
1	1157	293
2	5001	293

prune98.0ms

Filtered

47 candidates to 76 candidates (-61.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	76	3	79

Merged error: 0.0b

Counts

79 → 3

regimes489.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.0b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	23
1	36	23

end0.0ms

sample1.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

420.0ms	1737×	body	1280	valid
198.0ms	1211×	body	640	valid
135.0ms	4138×	body	80	valid
66.0ms	601×	body	320	valid
22.0ms	313×	body	160	valid

Details

sample37.0ms

simplify57.0ms

prune3.0ms

localize6.0ms

rewrite23.0ms

series15.0ms

simplify89.0ms

prune119.0ms

localize9.0ms

rewrite37.0ms

series29.0ms

simplify42.0ms

prune132.0ms

localize11.0ms

rewrite30.0ms

series22.0ms

simplify95.0ms

prune147.0ms

localize10.0ms

rewrite16.0ms

series16.0ms

simplify43.0ms

prune98.0ms

regimes489.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling