Details

analyze70.0ms

Algorithm: search

sample24.0ms

Algorithm

intervals

Results

11.0ms	236×	body	80	valid
3.0ms	9×	body	640	valid
1.0ms	2×	body	1280	valid
1.0ms	5×	body	320	valid
0.0ms	4×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	19	5
2	19	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: 0.3b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.0b	(+ 1.0 (exp x))
0.3b	(log (+ 1.0 (exp x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`log-prod`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `log-div` `associate--l+`
3×	`flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `sum-log` `log-pow` `flip--`

Counts

3 → 45

Calls

3 calls:

6.0ms	(- (log (+ 1.0 (exp x))) (* x y))
3.0ms	(+ 1.0 (exp x))
4.0ms	(log (+ 1.0 (exp x)))

series22.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify50.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	207	322
1	584	301
2	1729	298
3	5001	297

prune85.0ms

Filtered

40 candidates to 54 candidates (-35.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	51	3	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	3	55

Merged error: 0b

Counts

55 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (sqrt (+ 1.0 (exp x)))) (* x y))
0.9b	(log (sqrt (+ 1.0 (exp x))))
0.9b	(log (sqrt (+ 1.0 (exp x))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

21×	`log-prod`
18×	`*-un-lft-identity`
12×	`sqrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`pow1`
7×	`associate--l+` `add-log-exp`
6×	`add-exp-log` `log-div` `sqrt-div` `log-pow`
4×	`flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
2×	`associate--l-` `sqrt-pow1` `pow1/2` `rem-log-exp`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `sum-log` `flip--`

Counts

4 → 73

Calls

4 calls:

3.0ms	(+ 1.0 (exp x))
7.0ms	(- (log (sqrt (+ 1.0 (exp x)))) (* x y))
4.0ms	(log (sqrt (+ 1.0 (exp x))))
4.0ms	(log (sqrt (+ 1.0 (exp x))))

series47.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(+ 1.0 (exp x))
15.0ms	(- (log (sqrt (+ 1.0 (exp x)))) (* x y))
14.0ms	(log (sqrt (+ 1.0 (exp x))))
16.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify60.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	227	617
1	620	580
2	1867	562
3	5002	554

prune155.0ms

Filtered

62 candidates to 85 candidates (-37.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	85	3	88

Merged error: 0b

Counts

88 → 3

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
0.0b	(+ (* 1/2 (pow x 2)) (+ x 2.0))
7.3b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
6×	`log-prod`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `log-div`
3×	`flip3-+` `associate--l+` `sum-log` `add-cbrt-cube` `flip-+`
2×	`associate--l-`
1×	`+-commutative` `sub-neg` `associate-+r+` `flip3--` `diff-log` `rem-log-exp` `log-pow` `flip--`

Counts

3 → 44

Calls

3 calls:

8.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
6.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
6.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series17.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
3.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
4.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify130.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	292	480
1	1010	443
2	4638	436
3	5002	436

prune99.0ms

Filtered

43 candidates to 53 candidates (-23.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	53	3	56

Merged error: 0b

Counts

56 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (+ 1.0 (exp x)))
0.6b	(* (log (+ (exp x) 1.0)) (+ (log (+ 1.0 (exp x))) (* x y)))
0.7b	(pow (log (+ 1.0 (exp x))) 3)
13.8b	(/ (- (pow (log (+ 1.0 (exp x))) 3) (pow (* x y) 3)) (+ (* (log (+ (exp x) 1.0)) (+ (log (+ 1.0 (exp x))) (* x y))) (* (* x y) (* x y))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
39×	`times-frac`
38×	`*-un-lft-identity`
32×	`difference-of-squares`
28×	`add-cube-cbrt`
25×	`sqr-pow`
13×	`associate-/l*`
12×	`unpow-prod-down` `cube-prod`
11×	`pow1`
10×	`add-exp-log`
9×	`add-cbrt-cube`
4×	`difference-cubes` `log-prod` `associate-l` `log-pow` `distribute-lft-out--` `add-log-exp`
3×	`pow-unpow` `flip3-+` `associate-r` `associate-/r*` `flip-+`
2×	`log-div` `associate-*r/` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `distribute-rgt-in` `cube-mult` `pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `distribute-lft-in` `unpow3` `div-sub` `div-exp` `rem-log-exp` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 135

Calls

4 calls:

3.0ms	(log (+ 1.0 (exp x)))
6.0ms	(* (log (+ (exp x) 1.0)) (+ (log (+ 1.0 (exp x))) (* x y)))
3.0ms	(pow (log (+ 1.0 (exp x))) 3)
20.0ms	(/ (- (pow (log (+ 1.0 (exp x))) 3) (pow (* x y) 3)) (+ (* (log (+ (exp x) 1.0)) (+ (log (+ 1.0 (exp x))) (* x y))) (* (* x y) (* x y))))

series90.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(log (+ 1.0 (exp x)))
23.0ms	(* (log (+ (exp x) 1.0)) (+ (log (+ 1.0 (exp x))) (* x y)))
16.0ms	(pow (log (+ 1.0 (exp x))) 3)
40.0ms	(/ (- (pow (log (+ 1.0 (exp x))) 3) (pow (* x y) 3)) (+ (* (log (+ (exp x) 1.0)) (+ (log (+ 1.0 (exp x))) (* x y))) (* (* x y) (* x y))))

simplify121.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	693	3202
1	3329	3080
2	5001	3030

prune362.0ms

Filtered

97 candidates to 147 candidates (-51.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	147	3	150

Merged error: 0b

Counts

150 → 3

regimes77.0ms

Accuracy

0% (0.8b remaining)

Error of 1.1b against oracle of 0.3b and baseline of 1.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	11
1	13	11

end0.0ms

analyze64.0ms

Algorithm: search

sample682.0ms

Algorithm

intervals

Results

338.0ms	7345×	body	80	valid
77.0ms	245×	body	640	valid
74.0ms	135×	body	1280	valid
29.0ms	157×	body	320	valid
13.0ms	118×	body	160	valid
2.0ms	40×	body	80	invalid
0.0ms	9×	body	80	overflowed

Details

analyze70.0ms

sample24.0ms

simplify4.0ms

prune3.0ms

localize7.0ms

rewrite13.0ms

series22.0ms

simplify50.0ms

prune85.0ms

localize10.0ms

rewrite21.0ms

series47.0ms

simplify60.0ms

prune155.0ms

localize11.0ms

rewrite22.0ms

series17.0ms

simplify130.0ms

prune99.0ms

localize19.0ms

rewrite37.0ms

series90.0ms

simplify121.0ms

prune362.0ms

regimes77.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze64.0ms

sample682.0ms

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