Details

sample108.0ms

Algorithm

intervals

Results

44.0ms	741×	body	80	nan
12.0ms	183×	body	80	valid
11.0ms	30×	body	640	valid
5.0ms	7×	body	1280	valid
5.0ms	22×	body	320	valid
2.0ms	14×	body	160	valid

simplify134.0ms

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

prune3.0ms

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: 8.1b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.0b	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
0.2b	(* (- x 1.0) (log y))
3.8b	(log (- 1.0 y))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

9.0ms	(* (- z 1.0) (log (- 1.0 y)))
11.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
7.0ms	(* (- x 1.0) (log y))
3.0ms	(log (- 1.0 y))

series310.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (- z 1.0) (log (- 1.0 y)))
162.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
57.0ms	(* (- x 1.0) (log y))
48.0ms	(log (- 1.0 y))

simplify53.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	498	803
1	1805	714
2	5001	701

prune276.0ms

Filtered

106 candidates to 75 candidates (70.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	96	10	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	10	107

Merged error: 0.0b

Counts

107 → 10

localize24.0ms

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

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)))))))
12.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
12.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
8.0ms	(* (- x 1.0) (log y))

series535.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
247.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
68.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
61.0ms	(* (- x 1.0) (log y))

simplify124.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	888	2535
1	4674	2460
2	5001	2448

prune621.0ms

Filtered

141 candidates to 107 candidates (75.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	140	11	151

Merged error: 0.0b

Counts

151 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (- x 1.0) (log y)) (* (* (- 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))))))))
0.2b	(* (- 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)))))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

98×	`associate-*l/`
88×	`frac-times`
84×	`flip3--` `flip--`
52×	`frac-add`
31×	`flip3-+` `flip-+`
29×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
26×	`associate-*r/`
20×	`associate-r`
16×	`pow1`
13×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
12×	`log-prod` `sqrt-prod`
11×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
6×	`associate-+l+` `add-log-exp` `difference-of-squares`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
4×	`sub-neg` `associate-+r+`
3×	`log-pow` `*-commutative` `distribute-lft-out`
2×	`unswap-sqr`
1×	`+-commutative` `sum-log`

Counts

4 → 190

Calls

4 calls:

14.0ms	(+ (* (- x 1.0) (log y)) (* (* (- 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))))))))
7.0ms	(* (- 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)))))))
25.0ms	(* (* (- 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)))))))

series968.0ms

Counts

4 → 12

Calls

4 calls:

450.0ms	(+ (* (- x 1.0) (log y)) (* (* (- 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))))))))
60.0ms	(* (- x 1.0) (log y))
154.0ms	(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
303.0ms	(* (* (- 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)))))))

simplify175.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (63.0ms)

Iter	Nodes	Cost
0	1672	8394
1	5002	8001

prune1.2s

Filtered

202 candidates to 165 candidates (81.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	202	11	213

Merged error: 0.0b

Counts

213 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (+ (log (sqrt (- 1.0 y))) (log (sqrt (- 1.0 y))))))
0.2b	(* (- x 1.0) (log y))
3.8b	(log (sqrt (- 1.0 y)))
3.8b	(log (sqrt (- 1.0 y)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

28×	`log-prod`
22×	`add-sqr-sqrt` `associate-*l/`
20×	`*-un-lft-identity`
17×	`flip3--` `flip--`
16×	`frac-add`
14×	`add-cube-cbrt`
11×	`pow1`
10×	`sqrt-prod`
8×	`add-exp-log` `frac-times`
7×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `log-pow` `flip-+`
6×	`associate-+l+` `add-cbrt-cube` `add-log-exp`
5×	`associate-l`
4×	`log-div` `sqrt-div` `associate-r/` `associate-r*`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`associate-+r+` `sqrt-pow1` `pow1/2` `rem-log-exp`
1×	`+-commutative` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

11.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (+ (log (sqrt (- 1.0 y))) (log (sqrt (- 1.0 y))))))
7.0ms	(* (- x 1.0) (log y))
4.0ms	(log (sqrt (- 1.0 y)))
4.0ms	(log (sqrt (- 1.0 y)))

series612.0ms

Counts

4 → 12

Calls

4 calls:

258.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (+ (log (sqrt (- 1.0 y))) (log (sqrt (- 1.0 y))))))
58.0ms	(* (- x 1.0) (log y))
149.0ms	(log (sqrt (- 1.0 y)))
146.0ms	(log (sqrt (- 1.0 y)))

simplify198.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (183.0ms)

Iter	Nodes	Cost
0	860	1447
1	4063	1274
2	5002	1203

prune381.0ms

Filtered

118 candidates to 91 candidates (77.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	8	8
Picked	1	0	1
Done	0	2	2
Total	118	11	129

Merged error: 0.0b

Counts

129 → 11

regimes317.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	15
1	28	15

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.5s	24104×	body	80	nan
393.0ms	5914×	body	80	valid
275.0ms	769×	body	640	valid
185.0ms	274×	body	1280	valid
145.0ms	639×	body	320	valid
62.0ms	441×	body	160	valid

Details

sample108.0ms

simplify134.0ms

prune3.0ms

localize13.0ms

rewrite33.0ms

series310.0ms

simplify53.0ms

prune276.0ms

localize24.0ms

rewrite49.0ms

series535.0ms

simplify124.0ms

prune621.0ms

localize23.0ms

rewrite84.0ms

series968.0ms

simplify175.0ms

prune1.2s

localize15.0ms

rewrite31.0ms

series612.0ms

simplify198.0ms

prune381.0ms

regimes317.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.3s

Profiling