Details

sample32.0ms

Algorithm

intervals

Results

12.0ms	267×	body	80	valid
3.0ms	83×	body	80	overflowed
3.0ms	8×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	1×	body	1280	valid
1.0ms	6×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	19	5
2	19	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 0.5b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.5b	(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:

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

series133.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+ 1.0 (exp x))
61.0ms	(- (log (+ 1.0 (exp x))) (* x y))
64.0ms	(log (+ 1.0 (exp x)))

simplify50.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (45.0ms)

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

prune115.0ms

Filtered

54 candidates to 40 candidates (74.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	51	3	54
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	51	4	55

Merged error: 0.2b

Counts

55 → 4

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 1/2 (pow x 2))
0.0b	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
6.1b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
9×	`add-exp-log`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
6×	`log-prod`
5×	`add-cbrt-cube`
4×	`pow1` `unpow-prod-down` `log-div` `add-log-exp` `unswap-sqr`
3×	`associate-l` `prod-exp` `associate--l+`
2×	`associate--l-` `flip3-+` `flip-+` `unpow2` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `pow-exp` `log-pow` `*-commutative` `flip--` `cbrt-unprod`

Counts

3 → 58

Calls

3 calls:

5.0ms	(* 1/2 (pow x 2))
8.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
6.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series156.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(* 1/2 (pow x 2))
73.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
54.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	344	470
1	1288	435
2	5002	426

prune145.0ms

Filtered

67 candidates to 50 candidates (74.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	67	4	71

Merged error: 0.2b

Counts

71 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(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)
15.5b	(/ (- (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))))

rewrite39.0ms

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)))
6.0ms	(pow (log (+ 1.0 (exp x))) 3)
19.0ms	(/ (- (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))))

series546.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(log (+ 1.0 (exp x)))
124.0ms	(* (log (+ (exp x) 1.0)) (+ (log (+ 1.0 (exp x))) (* x y)))
120.0ms	(pow (log (+ 1.0 (exp x))) 3)
237.0ms	(/ (- (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))))

simplify127.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (101.0ms)

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

prune480.0ms

Filtered

147 candidates to 97 candidates (66.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	146	5	151

Merged error: 0.2b

Counts

151 → 5

localize44.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (log (+ (exp x) 1.0)) (+ (log (+ 1.0 (exp x))) (* x y)))
0.7b	(pow (log (+ (exp x) 1.0)) 2)
11.0b	(* (+ (* (* x y) (+ (* x y) (log (+ 1.0 (exp x))))) (pow (log (+ (exp x) 1.0)) 2)) (/ (- (log (+ 1.0 (exp x))) (* x y)) (+ (* (log (+ (exp x) 1.0)) (+ (log (+ 1.0 (exp x))) (* x y))) (* (* x y) (* x y)))))
11.0b	(/ (- (log (+ 1.0 (exp x))) (* x y)) (+ (* (log (+ (exp x) 1.0)) (+ (log (+ 1.0 (exp x))) (* x y))) (* (* x y) (* x y))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
18×	`associate-r`
14×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`pow1`
7×	`associate-l`
5×	`flip3-+` `flip-+`
4×	`unpow-prod-down` `associate-/r/` `add-log-exp`
3×	`pow-unpow` `associate-r/` `prod-exp` `associate-/r` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `div-exp` `pow-prod-down` `associate-l/` `log-pow` `-commutative` `div-inv` `associate-/l/`
1×	`distribute-rgt-in` `pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `distribute-lft-in` `div-sub` `pow-exp` `clear-num` `flip--` `unpow2` `sqr-pow`

Counts

4 → 112

Calls

4 calls:

6.0ms	(* (log (+ (exp x) 1.0)) (+ (log (+ 1.0 (exp x))) (* x y)))
3.0ms	(pow (log (+ (exp x) 1.0)) 2)
23.0ms	(* (+ (* (* x y) (+ (* x y) (log (+ 1.0 (exp x))))) (pow (log (+ (exp x) 1.0)) 2)) (/ (- (log (+ 1.0 (exp x))) (* x y)) (+ (* (log (+ (exp x) 1.0)) (+ (log (+ 1.0 (exp x))) (* x y))) (* (* x y) (* x y)))))
14.0ms	(/ (- (log (+ 1.0 (exp x))) (* x y)) (+ (* (log (+ (exp x) 1.0)) (+ (log (+ 1.0 (exp x))) (* x y))) (* (* x y) (* x y))))

series525.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (log (+ (exp x) 1.0)) (+ (log (+ 1.0 (exp x))) (* x y)))
85.0ms	(pow (log (+ (exp x) 1.0)) 2)
61.0ms	(* (+ (* (* x y) (+ (* x y) (log (+ 1.0 (exp x))))) (pow (log (+ (exp x) 1.0)) 2)) (/ (- (log (+ 1.0 (exp x))) (* x y)) (+ (* (log (+ (exp x) 1.0)) (+ (log (+ 1.0 (exp x))) (* x y))) (* (* x y) (* x y)))))
255.0ms	(/ (- (log (+ 1.0 (exp x))) (* x y)) (+ (* (log (+ (exp x) 1.0)) (+ (log (+ 1.0 (exp x))) (* x y))) (* (* x y) (* x y))))

simplify136.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (108.0ms)

Iter	Nodes	Cost
0	693	3034
1	3967	2712
2	5001	2687

prune401.0ms

Filtered

124 candidates to 92 candidates (74.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	124	5	129

Merged error: 0.2b

Counts

129 → 5

regimes81.0ms

Accuracy

0% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	5
1	10	5

end0.0ms

sample914.0ms

Algorithm

intervals

Results

393.0ms	8398×	body	80	valid
102.0ms	2449×	body	80	overflowed
78.0ms	136×	body	1280	valid
75.0ms	244×	body	640	valid
37.0ms	182×	body	320	valid
12.0ms	109×	body	160	valid

Details

sample32.0ms

simplify5.0ms

prune2.0ms

localize8.0ms

rewrite13.0ms

series133.0ms

simplify50.0ms

prune115.0ms

localize11.0ms

rewrite22.0ms

series156.0ms

simplify44.0ms

prune145.0ms

localize20.0ms

rewrite39.0ms

series546.0ms

simplify127.0ms

prune480.0ms

localize44.0ms

rewrite49.0ms

series525.0ms

simplify136.0ms

prune401.0ms

regimes81.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample914.0ms

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