Details

sample34.0ms

Algorithm

intervals

Results

13.0ms	268×	body	80	valid
4.0ms	94×	body	80	overflowed
2.0ms	4×	body	1280	valid
2.0ms	6×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	5×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	19	5
2	23	5
3	23	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: 1.3b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.0b	(+ 1.0 (exp x))
1.2b	(log (+ 1.0 (exp x)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod`
6×	`pow1` `add-log-exp`
4×	`add-exp-log` `log-div` `fma-neg` `prod-diff` `associate--l+`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `log-pow` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `sum-log` `flip--`

Counts

3 → 62

Calls

3 calls:

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

series130.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(- (log (+ 1.0 (exp x))) (* x y))
8.0ms	(+ 1.0 (exp x))
60.0ms	(log (+ 1.0 (exp x)))

simplify60.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	236	404
1	702	369
2	2284	367
3	5002	340

prune159.0ms

Filtered

71 candidates to 54 candidates (76.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	66	5	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	5	72

Merged error: 0.6b

Counts

72 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log (+ (pow 1.0 3) (pow (exp x) 3))) (log (+ (* 1.0 1.0) (- (* (exp x) (exp x)) (* 1.0 (exp x))))))
1.0b	(log (+ (pow 1.0 3) (pow (exp x) 3)))
5.9b	(- (* (exp x) (exp x)) (* 1.0 (exp x)))
6.1b	(log (+ (* 1.0 1.0) (- (* (exp x) (exp x)) (* 1.0 (exp x)))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
24×	`log-prod`
19×	`pow1` `add-sqr-sqrt`
17×	`add-cube-cbrt` `prod-diff`
15×	`log-pow`
10×	`distribute-lft-out`
9×	`associate--l+`
8×	`unpow-prod-down` `log-div` `cube-prod`
6×	`add-exp-log` `add-log-exp`
5×	`fma-neg`
4×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out--`
3×	`associate--r+`
2×	`associate--l-` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `sum-cubes` `flip--` `associate--r-`
1×	`distribute-rgt-out--` `difference-of-squares`

Counts

4 → 110

Calls

4 calls:

22.0ms	(- (log (+ (pow 1.0 3) (pow (exp x) 3))) (log (+ (* 1.0 1.0) (- (* (exp x) (exp x)) (* 1.0 (exp x))))))
10.0ms	(log (+ (pow 1.0 3) (pow (exp x) 3)))
6.0ms	(- (* (exp x) (exp x)) (* 1.0 (exp x)))
8.0ms	(log (+ (* 1.0 1.0) (- (* (exp x) (exp x)) (* 1.0 (exp x)))))

series470.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(- (log (+ (pow 1.0 3) (pow (exp x) 3))) (log (+ (* 1.0 1.0) (- (* (exp x) (exp x)) (* 1.0 (exp x))))))
92.0ms	(log (+ (pow 1.0 3) (pow (exp x) 3)))
44.0ms	(- (* (exp x) (exp x)) (* 1.0 (exp x)))
114.0ms	(log (+ (* 1.0 1.0) (- (* (exp x) (exp x)) (* 1.0 (exp x)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	472	2306
1	1585	1771
2	5001	1753

prune332.0ms

Filtered

122 candidates to 79 candidates (64.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	122	5	127

Merged error: 0.6b

Counts

127 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.0b	(+ 1.0 (exp x))
0.8b	(expm1 (log1p (- (log (+ 1.0 (exp x))) (* x y))))
1.2b	(log (+ 1.0 (exp x)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
9×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`log-prod`
7×	`pow1` `add-log-exp`
5×	`add-exp-log`
4×	`expm1-log1p-u` `log-div` `fma-neg` `prod-diff` `associate--l+` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `log-pow` `flip-+` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sub-neg` `expm1-log1p` `flip3--` `diff-log` `rem-log-exp` `sum-log` `flip--` `expm1-udef`

Counts

4 → 73

Calls

4 calls:

6.0ms	(- (log (+ 1.0 (exp x))) (* x y))
3.0ms	(+ 1.0 (exp x))
1.0ms	(expm1 (log1p (- (log (+ 1.0 (exp x))) (* x y))))
3.0ms	(log (+ 1.0 (exp x)))

series742.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (log (+ 1.0 (exp x))) (* x y))
8.0ms	(+ 1.0 (exp x))
611.0ms	(expm1 (log1p (- (log (+ 1.0 (exp x))) (* x y))))
66.0ms	(log (+ 1.0 (exp x)))

simplify87.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (80.0ms)

Iter	Nodes	Cost
0	379	576
1	1094	528
2	3883	520
3	5001	507

prune212.0ms

Filtered

85 candidates to 67 candidates (78.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	85	5	90

Merged error: 0.6b

Counts

90 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.7b	(pow (- (log (+ (exp x) 1.0)) (* x y)) 3)
1.2b	(log (+ (exp x) 1.0))
11.3b	(cbrt (pow (- (log (+ (exp x) 1.0)) (* x y)) 3))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
12×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt`
6×	`pow1` `add-exp-log` `unpow-prod-down` `cube-prod` `add-log-exp`
5×	`add-cbrt-cube`
4×	`cube-div` `expm1-log1p-u` `log-prod` `log1p-expm1-u`
3×	`pow-unpow` `fma-def`
2×	`cube-mult` `log-div` `cbrt-div` `flip3--` `flip3-+` `unpow3` `flip--` `flip-+` `distribute-lft-out` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `pow-pow` `pow1/3` `rem-log-exp` `pow-exp` `sum-log` `log-pow` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 86

Calls

4 calls:

4.0ms	(+ (exp x) 1.0)
4.0ms	(pow (- (log (+ (exp x) 1.0)) (* x y)) 3)
4.0ms	(log (+ (exp x) 1.0))
4.0ms	(cbrt (pow (- (log (+ (exp x) 1.0)) (* x y)) 3))

series266.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (exp x) 1.0)
138.0ms	(pow (- (log (+ (exp x) 1.0)) (* x y)) 3)
59.0ms	(log (+ (exp x) 1.0))
60.0ms	(cbrt (pow (- (log (+ (exp x) 1.0)) (* x y)) 3))

simplify51.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	393	758
1	1524	700
2	5001	690

prune206.0ms

Filtered

98 candidates to 64 candidates (65.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	98	5	103

Merged error: 0.6b

Counts

103 → 5

regimes54.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	17
1	22	17

end0.0ms

sample902.0ms

Algorithm

intervals

Results

400.0ms	8473×	body	80	valid
98.0ms	2429×	body	80	overflowed
74.0ms	237×	body	640	valid
61.0ms	111×	body	1280	valid
34.0ms	182×	body	320	valid
12.0ms	108×	body	160	valid