Details

sample174.0ms

Algorithm

intervals

Results

73.0ms	1245×	body	80	nan
25.0ms	395×	body	80	valid
7.0ms	20×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	2×	body	1280	valid
0.0ms	3×	body	160	valid

simplify37.0ms

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: 2.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (- (log (- 1.0 z)) b))
0.1b	(* y (- (log z) t))
1.0b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.9b	(log (- 1.0 z))

rewrite36.0ms

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:

9.0ms	(* a (- (log (- 1.0 z)) b))
7.0ms	(* y (- (log z) t))
12.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

series393.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* a (- (log (- 1.0 z)) b))
76.0ms	(* y (- (log z) t))
193.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
47.0ms	(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

prune466.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

Calls

4 calls:

24.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
19.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
7.0ms	(* y (- (log z) t))
21.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series642.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
104.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
74.0ms	(* 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)))

simplify87.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	677	1907
1	3019	1768
2	5001	1757

prune588.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

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:

7.0ms	(* y (- (log z) t))
7.0ms	(* y (- (log z) t))
22.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
21.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series631.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* y (- (log z) t))
73.0ms	(* y (- (log z) t))
244.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
246.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify75.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (50.0ms)

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

prune909.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize32.0ms

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)
1.0b	(+ (* (- (log z) t) y) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
1.0b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
31.3b	(cbrt (pow (+ (* (- (log z) t) y) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 3))

rewrite71.0ms

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:

10.0ms	(pow (+ (* (- (log z) t) y) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 3)
21.0ms	(+ (* (- (log z) t) y) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
21.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
13.0ms	(cbrt (pow (+ (* (- (log z) t) y) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 3))

series6.6s

Counts

4 → 12

Calls

4 calls:

5.9s	(pow (+ (* (- (log z) t) y) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 3)
213.0ms	(+ (* (- (log z) t) y) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
238.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
219.0ms	(cbrt (pow (+ (* (- (log z) t) y) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))) 3))

simplify90.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (62.0ms)

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

prune927.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes159.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	36
1	42	36

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.3s	40219×	body	80	nan
804.0ms	12447×	body	80	valid
145.0ms	403×	body	640	valid
81.0ms	364×	body	320	valid
60.0ms	82×	body	1280	valid
37.0ms	268×	body	160	valid