Details

sample184.0ms

Algorithm

intervals

Results

66.0ms	1200×	body	80	nan
22.0ms	380×	body	80	valid
4.0ms	12×	body	640	valid
3.0ms	13×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	2×	body	1280	valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.1b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.3b	(log (- 1.0 z))

rewrite104.0ms

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:

40.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
25.0ms	(* y (- (log z) t))
31.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.0ms	(log (- 1.0 z))

series423.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
68.0ms	(* y (- (log z) t))
179.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
43.0ms	(log (- 1.0 z))

simplify73.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (58.0ms)

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

prune415.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite938.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

164.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
592.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
24.0ms	(* y (- (log z) t))
151.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series546.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
94.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
69.0ms	(* y (- (log z) t))
229.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify86.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	645	1743
1	2810	1639
2	5002	1630

prune566.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite360.0ms

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:

25.0ms	(* y (- (log z) t))
24.0ms	(* y (- (log z) t))
150.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
153.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series598.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* y (- (log z) t))
65.0ms	(* y (- (log z) t))
234.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
229.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify70.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (51.0ms)

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

prune911.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (+ (* (- (log z) t) y) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 3)
0.3b	(+ (* (- (log z) t) y) (* 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)))
28.5b	(cbrt (pow (+ (* (- (log z) t) y) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 3))

rewrite356.0ms

Algorithm

rewrite-expression-head

Rules

38×	`associate--l+`
28×	`associate-+r+`
20×	`associate-*r/`
19×	`distribute-rgt-in` `distribute-lft-in`
18×	`log-prod`
16×	`add-sqr-sqrt` `add-cube-cbrt` `flip3--` `*-un-lft-identity` `frac-add` `flip--`
12×	`cube-div` `cbrt-prod` `associate-*l/`
10×	`sub-neg` `associate-+l+`
8×	`add-log-exp`
6×	`unpow-prod-down` `cbrt-div` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow-unpow`
2×	`+-commutative` `cube-mult` `unpow3` `sum-log` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 124

Calls

4 calls:

25.0ms	(pow (+ (* (- (log z) t) y) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 3)
151.0ms	(+ (* (- (log z) t) y) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
152.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
23.0ms	(cbrt (pow (+ (* (- (log z) t) y) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 3))

series6.2s

Counts

4 → 12

Calls

4 calls:

5.6s	(pow (+ (* (- (log z) t) y) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 3)
203.0ms	(+ (* (- (log z) t) y) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
229.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
199.0ms	(cbrt (pow (+ (* (- (log z) t) y) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 3))

simplify98.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	748	3315
1	2941	3206
2	5002	3198

prune903.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes176.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	16
1	32	16

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.1s	41637×	body	80	nan
746.0ms	12718×	body	80	valid
118.0ms	350×	body	640	valid
77.0ms	370×	body	320	valid
44.0ms	62×	body	1280	valid
38.0ms	308×	body	160	valid