Details

sample216.0ms

Algorithm

intervals

Results

84.0ms	1546×	body	80	nan
26.0ms	447×	body	80	valid
2.0ms	38×	body	80	overflowed
2.0ms	5×	body	640	valid
1.0ms	5×	body	160	valid
1.0ms	3×	body	320	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: 1.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (+ (* y (- (log z) t)) (* 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))

rewrite107.0ms

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:

42.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
26.0ms	(* y (- (log z) t))
30.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.0ms	(log (- 1.0 z))

series414.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
68.0ms	(* y (- (log z) t))
170.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
43.0ms	(log (- 1.0 z))

simplify66.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (56.0ms)

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

prune414.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize28.0ms

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))
0.1b	(exp (+ (* y (- (log z) t)) (* 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)))

rewrite1.0s

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:

651.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
179.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
26.0ms	(* y (- (log z) t))
164.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series542.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
158.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
69.0ms	(* y (- (log z) t))
221.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify81.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (64.0ms)

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

prune577.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
0.1b	(* y (- (log z) t))
0.3b	(cbrt (pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3))
1.0b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite528.0ms

Algorithm

rewrite-expression-head

Rules

28×	`associate--l+`
20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
18×	`log-prod`
17×	`distribute-rgt-in` `distribute-lft-in`
16×	`add-cube-cbrt`
14×	`cbrt-prod` `associate-+r+`
10×	`associate-+l+` `associate-*r/`
9×	`add-log-exp`
8×	`sub-neg`
7×	`pow1`
6×	`add-exp-log` `associate-r` `add-cbrt-cube`
5×	`flip3--` `flip--`
4×	`unpow-prod-down` `cube-prod` `frac-add`
3×	`exp-prod` `associate-l` `exp-sum`
2×	`sum-log` `rem-exp-log` `distribute-lft-out--`
1×	`+-commutative` `cube-mult` `flip3-+` `pow1/3` `unpow3` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `flip-+` `difference-of-squares` `unswap-sqr` `sqr-pow`

Counts

4 → 108

Calls

4 calls:

179.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
26.0ms	(* y (- (log z) t))
154.0ms	(cbrt (pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3))
165.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series600.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
63.0ms	(* y (- (log z) t))
158.0ms	(cbrt (pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3))
220.0ms	(+ (* 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

120 → 120

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	624	1859
1	2577	1812
2	5003	1803

prune578.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3))
0.2b	(sqrt (pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3))
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)))

rewrite669.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

169.0ms	(sqrt (pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3))
169.0ms	(sqrt (pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3))
161.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
164.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series1.6s

Counts

4 → 12

Calls

4 calls:

564.0ms	(sqrt (pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3))
565.0ms	(sqrt (pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3))
226.0ms	(+ (* 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)))

simplify72.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	553	2874
1	2048	2766
2	5002	2766

prune1.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes247.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	58
1	41	58

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.3s	43625×	body	80	nan
799.0ms	13369×	body	80	valid
51.0ms	851×	body	80	overflowed
38.0ms	109×	body	640	valid
23.0ms	108×	body	320	valid
19.0ms	27×	body	1280	valid
17.0ms	128×	body	160	valid