Details

sample176.0ms

Algorithm

intervals

Results

75.0ms	1314×	body	80	nan
24.0ms	398×	body	80	valid
5.0ms	15×	body	640	valid
2.0ms	10×	body	320	valid
1.0ms	7×	body	160	valid
1.0ms	1×	body	1280	valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	10
1	58	10
2	129	10
3	318	10
4	1073	10
5	5001	10

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (- (log (- 1.0 z)) b))
0.1b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.6b	(log (- 1.0 z))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

37×	`log-prod`
35×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
32×	`associate--l+`
24×	`distribute-rgt-in` `distribute-lft-in`
17×	`add-cube-cbrt`
14×	`associate-+r+`
12×	`associate-r/` `associate-r*`
11×	`pow1`
10×	`associate-+l+`
9×	`add-exp-log` `distribute-lft-out--`
8×	`sub-neg` `add-cbrt-cube`
7×	`flip3--` `flip--` `difference-of-squares`
6×	`associate-l` `add-log-exp`
4×	`frac-add`
3×	`log-pow`
2×	`log-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3-+` `rem-log-exp` `sum-log` `flip-+`

Counts

4 → 125

Calls

4 calls:

20.0ms	(* a (- (log (- 1.0 z)) b))
14.0ms	(* y (- (log z) t))
14.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

series390.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* a (- (log (- 1.0 z)) b))
75.0ms	(* y (- (log z) t))
194.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
44.0ms	(log (- 1.0 z))

simplify75.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	678	1058
1	2743	995
2	5002	986

prune478.0ms

Filtered

137 candidates to 95 candidates (69.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
0.0b	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
0.1b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite605.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 220

Calls

4 calls:

441.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
28.0ms	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
13.0ms	(* y (- (log z) t))
108.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
55.0ms	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
72.0ms	(* y (- (log z) t))
241.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify47.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1080	2186
1	5001	1935

prune1.1s

Filtered

232 candidates to 147 candidates (63.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))
0.0b	(* 0.5 (* a (pow z 2)))
0.0b	(+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))
7.7b	(* a (pow z 2))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
14×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-log-exp`
10×	`prod-exp`
9×	`associate-r`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `associate-l`
4×	`unpow-prod-down` `sum-log` `cbrt-unprod` `unswap-sqr`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `flip-+` `unpow2` `sqr-pow`
1×	`associate-+r+` `pow-prod-down`

Counts

4 → 70

Calls

4 calls:

17.0ms	(+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))
8.0ms	(* 0.5 (* a (pow z 2)))
6.0ms	(+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))
6.0ms	(* a (pow z 2))

series224.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))
33.0ms	(* 0.5 (* a (pow z 2)))
93.0ms	(+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))
31.0ms	(* a (pow z 2))

simplify53.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	329	506
1	1469	461
2	5002	452

prune229.0ms

Filtered

82 candidates to 53 candidates (64.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes127.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	16
1	32	16

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.2s	40081×	body	80	nan
755.0ms	12257×	body	80	valid
130.0ms	379×	body	640	valid
92.0ms	429×	body	320	valid
58.0ms	81×	body	1280	valid
35.0ms	253×	body	160	valid