Details

sample236.0ms

Algorithm

intervals

Results

112.0ms	1336×	body	80	nan
40.0ms	402×	body	80	valid
5.0ms	10×	body	640	valid
4.0ms	13×	body	320	valid
2.0ms	9×	body	160	valid
2.0ms	2×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.2b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
8.6b	(log (- 1.0 z))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

18.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
14.0ms	(* y (- (log z) t))
13.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
2.0ms	(log (- 1.0 z))

series445.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
71.0ms	(* y (- (log z) t))
188.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
43.0ms	(log (- 1.0 z))

simplify69.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	630	971
1	2443	914
2	5001	902

prune416.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
0.1b	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
0.2b	(* 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)))

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

85×	`add-sqr-sqrt`
80×	`times-frac`
74×	`associate-r`
56×	`unpow-prod-down`
50×	`*-un-lft-identity`
47×	`add-cube-cbrt`
29×	`add-exp-log`
28×	`associate--l+`
24×	`unpow2` `sqr-pow`
18×	`log-prod` `unswap-sqr`
17×	`distribute-rgt-in` `distribute-lft-in`
14×	`associate-+r+`
11×	`associate-*r/` `prod-exp` `add-cbrt-cube`
10×	`associate-+l+`
9×	`pow1` `div-exp` `add-log-exp`
8×	`sub-neg`
6×	`pow-to-exp` `associate-l` `pow-exp`
5×	`flip3--` `flip--`
4×	`frac-add`
3×	`exp-prod` `cbrt-unprod`
2×	`pow-prod-down` `sum-log` `*-commutative` `rem-exp-log` `distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `exp-sum` `log-pow` `flip-+` `div-inv` `difference-of-squares`

Counts

4 → 195

Calls

4 calls:

27.0ms	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
103.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
14.0ms	(* y (- (log z) t))
96.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series528.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
166.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
72.0ms	(* y (- (log z) t))
237.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify116.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	1062	1909
1	4620	1720
2	5002	1718

prune855.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt`
80×	`times-frac`
74×	`associate-r`
59×	`unpow-prod-down`
51×	`*-un-lft-identity`
48×	`add-cube-cbrt`
30×	`add-exp-log`
28×	`associate--l+`
25×	`sqr-pow`
24×	`unpow2`
18×	`log-prod` `unswap-sqr`
17×	`distribute-rgt-in` `distribute-lft-in`
14×	`associate-+r+`
11×	`associate-*r/` `prod-exp` `add-cbrt-cube`
10×	`pow1` `associate-+l+`
9×	`div-exp`
8×	`sub-neg` `pow-exp`
7×	`pow-to-exp`
6×	`associate-l` `add-log-exp`
5×	`flip3--` `flip--`
4×	`frac-add`
3×	`pow-unpow` `cbrt-unprod`
2×	`pow-prod-down` `*-commutative` `distribute-lft-out--`
1×	`cbrt-undiv` `unpow-prod-up` `+-commutative` `e-exp-1` `pow-pow` `flip3-+` `sum-log` `log-pow` `flip-+` `div-inv` `difference-of-squares`

Counts

4 → 201

Calls

4 calls:

25.0ms	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
89.0ms	(pow E (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
12.0ms	(* y (- (log z) t))
95.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series532.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
175.0ms	(pow E (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
70.0ms	(* y (- (log z) t))
237.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify53.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1117	2064
1	5001	1889

prune877.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y (- (log z) t))
0.2b	(* 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)))
0.3b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

56×	`associate--l+`
36×	`log-prod`
34×	`distribute-rgt-in` `distribute-lft-in`
28×	`add-sqr-sqrt` `associate-+r+`
26×	`*-un-lft-identity`
20×	`add-cube-cbrt` `associate-+l+` `associate-*r/`
16×	`sub-neg`
12×	`associate-r`
10×	`pow1` `flip3--` `flip--`
8×	`add-exp-log` `frac-add` `add-cbrt-cube` `add-log-exp`
6×	`associate-l`
4×	`distribute-lft-out--`
2×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `log-pow` `*-commutative` `cbrt-unprod` `flip-+` `difference-of-squares` `unswap-sqr`

Counts

4 → 144

Calls

4 calls:

14.0ms	(* y (- (log z) t))
13.0ms	(* y (- (log z) t))
96.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
97.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series625.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* y (- (log z) t))
74.0ms	(* y (- (log z) t))
242.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
236.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify71.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	494	2014
1	2047	1920
2	5003	1910

prune881.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes213.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	34
1	39	34
2	39	34

end0.0ms

sample7.0s

Algorithm

intervals

Results

3.4s	40735×	body	80	nan
1.3s	12496×	body	80	valid
195.0ms	381×	body	640	valid
125.0ms	378×	body	320	valid
70.0ms	78×	body	1280	valid
51.0ms	240×	body	160	valid