Details

analyze347.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	74.9%	25.1%	3
0%	74.9%	25.1%	4
0%	74.9%	25.1%	5
0%	62.4%	37.6%	6
0%	31.2%	68.8%	7
0%	31.2%	68.8%	8
0%	31.2%	68.8%	9
0%	28.1%	71.9%	10
6.1%	20.4%	73.5%	11
6.1%	20.4%	73.5%	12
7.7%	18.8%	73.5%	13
9.2%	16.6%	74.3%	14

sample64.0ms

Algorithm

intervals

Results

14.0ms	170×	body	80	valid
13.0ms	11×	body	1280	valid
12.0ms	29×	body	640	valid
9.0ms	33×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	8×	body	80	nan
0.0ms	2×	body	80	invalid

simplify141.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	9
1	49	9
2	118	9
3	256	9
4	533	9
5	1250	9
6	2637	9
7	4297	9
8	4573	9
9	4588	9
10	4588	9

prune4.0ms

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: 8.3b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
0.0b	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
0.1b	(* (- x 1.0) (log y))
5.7b	(log (- 1.0 y))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

27×	`log-prod`
25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
13×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in` `add-log-exp`
10×	`associate-+r+` `associate-*l/`
8×	`pow1`
7×	`add-exp-log` `flip3--` `flip--`
6×	`associate-+l+` `add-cbrt-cube`
5×	`associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`associate-r` `frac-add`
2×	`log-div` `diff-log` `sum-log` `log-pow`
1×	`+-commutative` `sub-neg` `flip3-+` `rem-log-exp` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

11.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
10.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
6.0ms	(* (- x 1.0) (log y))
3.0ms	(log (- 1.0 y))

series75.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
38.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
10.0ms	(* (- x 1.0) (log y))
3.0ms	(log (- 1.0 y))

simplify64.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	675	991
1	2434	927
2	5001	887

prune198.0ms

Filtered

80 candidates to 104 candidates (-30.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	98	6	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	6	105

Merged error: 0.0b

Counts

105 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.0b	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0b	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.1b	(* (- x 1.0) (log y))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt`
80×	`times-frac`
78×	`associate-r`
57×	`*-un-lft-identity`
56×	`unpow-prod-down`
50×	`add-cube-cbrt`
31×	`add-exp-log`
27×	`flip3--` `flip--`
24×	`log-prod` `associate-*l/` `unpow2` `sqr-pow`
19×	`unswap-sqr`
16×	`distribute-rgt-in` `distribute-lft-in` `frac-add`
13×	`associate-l` `add-cbrt-cube`
12×	`pow1` `frac-times` `prod-exp` `associate--l+`
10×	`associate-+r+`
9×	`div-exp`
7×	`associate-*r/`
6×	`pow-to-exp` `associate-+l+` `pow-exp` `add-log-exp`
4×	`sub-neg` `cbrt-unprod` `distribute-lft-out--`
3×	`pow-prod-down` `*-commutative` `difference-of-squares`
2×	`log-pow`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `sum-log` `flip-+` `div-inv`

Counts

4 → 223

Calls

4 calls:

11.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
19.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
14.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
7.0ms	(* (- x 1.0) (log y))

series70.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
5.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
13.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
10.0ms	(* (- x 1.0) (log y))

simplify58.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1359	2834
1	5001	2680

prune721.0ms

Filtered

162 candidates to 235 candidates (-45.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	233	2	235
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	233	8	241

Merged error: 0.0b

Counts

241 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.1b	(* (- x 1.0) (log y))
0.2b	(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.4b	(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
88×	`associate-r`
80×	`times-frac`
59×	`*-un-lft-identity`
56×	`unpow-prod-down`
45×	`add-cube-cbrt`
36×	`add-exp-log`
32×	`frac-times`
24×	`unpow2` `sqr-pow`
22×	`flip3--` `flip--`
19×	`unswap-sqr`
18×	`pow1` `associate-*l/` `add-cbrt-cube`
15×	`prod-exp`
14×	`associate-l`
12×	`flip3-+` `sqrt-prod` `flip-+`
11×	`associate-*r/`
9×	`div-exp`
7×	`cbrt-unprod`
6×	`distribute-rgt-in` `pow-to-exp` `log-prod` `distribute-lft-in` `pow-prod-down` `pow-exp` `difference-of-squares`
5×	`distribute-lft-out--`
4×	`*-commutative` `add-log-exp`
3×	`log-pow` `distribute-lft-out`
2×	`sub-neg`
1×	`cbrt-undiv` `div-inv`

Counts

4 → 227

Calls

4 calls:

21.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
6.0ms	(* (- x 1.0) (log y))
13.0ms	(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
21.0ms	(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series82.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
13.0ms	(* (- x 1.0) (log y))
24.0ms	(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
39.0ms	(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify61.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1329	3335
1	5002	2950

prune1.3s

Filtered

163 candidates to 239 candidates (-46.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	239	8	247

Merged error: 0.0b

Counts

247 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow y 2))
0.0b	(+ (* 1.0 (* z y)) (* 0.5 (* z (pow y 2))))
0.1b	(* (- x 1.0) (log y))
7.1b	(* z (pow y 2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
20×	`associate-r`
16×	`add-exp-log` `*-un-lft-identity`
14×	`add-cube-cbrt`
11×	`associate-l`
10×	`add-cbrt-cube`
9×	`unswap-sqr`
8×	`unpow-prod-down`
7×	`pow1` `prod-exp`
6×	`log-prod` `add-log-exp`
4×	`unpow2` `sqr-pow`
3×	`distribute-rgt-in` `distribute-lft-in` `*-commutative` `cbrt-unprod`
2×	`pow-to-exp` `associate-*l/` `pow-exp`
1×	`+-commutative` `flip3--` `flip3-+` `pow-prod-down` `sum-log` `log-pow` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 94

Calls

4 calls:

6.0ms	(* 0.5 (pow y 2))
6.0ms	(+ (* 1.0 (* z y)) (* 0.5 (* z (pow y 2))))
7.0ms	(* (- x 1.0) (log y))
6.0ms	(* z (pow y 2))

series35.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 0.5 (pow y 2))
13.0ms	(+ (* 1.0 (* z y)) (* 0.5 (* z (pow y 2))))
10.0ms	(* (- x 1.0) (log y))
8.0ms	(* z (pow y 2))

simplify59.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	431	548
1	1797	471
2	5001	443

prune198.0ms

Filtered

69 candidates to 106 candidates (-53.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	106	8	114

Merged error: 0.0b

Counts

114 → 8

regimes597.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	15
1	28	15

end0.0ms

analyze427.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	74.9%	25.1%	3
0%	74.9%	25.1%	4
0%	74.9%	25.1%	5
0%	62.4%	37.6%	6
0%	31.2%	68.8%	7
0%	31.2%	68.8%	8
0%	31.2%	68.8%	9
0%	28.1%	71.9%	10
6.1%	20.4%	73.5%	11
6.1%	20.4%	73.5%	12
7.7%	18.8%	73.5%	13
9.2%	16.6%	74.3%	14

sample1.4s

Algorithm

intervals

Results

443.0ms	5847×	body	80	valid
292.0ms	740×	body	640	valid
197.0ms	273×	body	1280	valid
180.0ms	725×	body	320	valid
65.0ms	415×	body	160	valid
23.0ms	264×	body	80	nan
3.0ms	36×	body	80	invalid

Details

analyze347.0ms

sample64.0ms

simplify141.0ms

prune4.0ms

localize13.0ms

rewrite138.0ms

series75.0ms

simplify64.0ms

prune198.0ms

localize19.0ms

rewrite63.0ms

series70.0ms

simplify58.0ms

prune721.0ms

localize23.0ms

rewrite74.0ms

series82.0ms

simplify61.0ms

prune1.3s

localize19.0ms

rewrite28.0ms

series35.0ms

simplify59.0ms

prune198.0ms

regimes597.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze427.0ms

sample1.4s

Profiling