Details

sample219.0ms

Algorithm

intervals

Results

101.0ms	1161×	body	80	nan
39.0ms	375×	body	80	valid
5.0ms	15×	body	320	valid
5.0ms	9×	body	640	valid
2.0ms	2×	body	1280	valid
1.0ms	6×	body	160	valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	10
1	62	10
2	137	10
3	344	10
4	1155	10
5	5001	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (- (log (- 1.0 z)) b))
0.1b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
6.9b	(log (- 1.0 z))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

96×	`prod-diff`
91×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
73×	`add-cube-cbrt`
72×	`distribute-rgt-in` `distribute-lft-in`
38×	`associate-+r+`
37×	`log-prod`
35×	`pow1`
34×	`associate-+l+`
32×	`associate--l+`
27×	`log-pow`
12×	`associate-r/` `associate-r*`
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×	`expm1-log1p-u` `frac-add` `log1p-expm1-u`
2×	`log-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `rem-log-exp` `sum-log` `flip-+`

Counts

4 → 230

Calls

4 calls:

18.0ms	(* a (- (log (- 1.0 z)) b))
15.0ms	(* y (- (log z) t))
21.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

series393.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* a (- (log (- 1.0 z)) b))
74.0ms	(* y (- (log z) t))
196.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
43.0ms	(log (- 1.0 z))

simplify112.0ms

Algorithm

egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	959	2405
1	3910	1813
2	5001	1810

prune874.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log z) t)
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))
0.5b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite688.0ms

Algorithm

rewrite-expression-head

Rules

180×	`prod-diff`
166×	`*-un-lft-identity`
151×	`add-sqr-sqrt`
117×	`add-cube-cbrt`
108×	`distribute-rgt-in` `distribute-lft-in`
95×	`associate--l+`
74×	`associate-+r+`
51×	`pow1`
43×	`log-pow`
34×	`associate-+l+`
33×	`distribute-lft-out--`
27×	`log-prod`
15×	`difference-of-squares`
13×	`sub-neg` `associate-r`
12×	`associate-*r/`
8×	`add-exp-log` `add-cbrt-cube`
7×	`flip3--` `flip--` `add-log-exp`
6×	`associate-l`
4×	`expm1-log1p-u` `fma-neg` `frac-add` `log1p-expm1-u`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `diff-log` `sum-log` `flip-+`

Counts

4 → 321

Calls

4 calls:

4.0ms	(- (log z) t)
478.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
15.0ms	(* y (- (log z) t))
172.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series486.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- (log z) t)
112.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
68.0ms	(* y (- (log z) t))
248.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify150.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	1036	5948
1	4185	4321
2	5001	4314

prune1.1s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
18×	`pow1`
17×	`distribute-rgt-in` `distribute-lft-in`
12×	`log-pow`
9×	`log-prod` `associate--l+`
8×	`add-log-exp`
6×	`add-exp-log` `associate-r` `add-cbrt-cube`
4×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u` `distribute-lft-out--`
3×	`sub-neg` `exp-prod` `associate-l`
2×	`flip3--` `associate-*r/` `flip--` `rem-exp-log` `difference-of-squares`
1×	`diff-log` `exp-sum` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 120

Calls

4 calls:

8.0ms	(exp (+ (* y (log 1)) (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t)))))
4.0ms	(- (log z) t)
15.0ms	(* y (- (log z) t))
0.0ms	(fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(exp (+ (* y (log 1)) (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t)))))
64.0ms	(- (log z) t)
74.0ms	(* y (- (log z) t))
218.0ms	(fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t)))

simplify51.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	393	1290
1	1407	934
2	5001	899

prune511.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
18×	`pow1`
17×	`distribute-rgt-in` `distribute-lft-in`
14×	`associate-r`
12×	`add-exp-log` `log-pow`
9×	`log-prod` `associate--l+`
8×	`add-cbrt-cube`
6×	`associate-l`
5×	`prod-exp` `add-log-exp`
4×	`expm1-log1p-u` `unpow-prod-down` `fma-neg` `log1p-expm1-u` `distribute-lft-out--` `unswap-sqr`
3×	`sub-neg`
2×	`flip3--` `associate-r/` `pow-exp` `-commutative` `flip--` `cbrt-unprod` `difference-of-squares` `sqr-pow`
1×	`unpow-prod-up` `pow-to-exp` `e-exp-1` `diff-log` `pow-prod-down` `fma-udef`

Counts

4 → 134

Calls

4 calls:

7.0ms	(* x (pow E (+ (* y (log 1)) (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))))))
4.0ms	(- (log z) t)
15.0ms	(* y (- (log z) t))
0.0ms	(fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t)))

series597.0ms

Counts

4 → 12

Calls

4 calls:

242.0ms	(* x (pow E (+ (* y (log 1)) (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))))))
57.0ms	(- (log z) t)
74.0ms	(* y (- (log z) t))
224.0ms	(fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t)))

simplify63.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	524	1620
1	2059	1245
2	5001	1220

prune543.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes206.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	17
1	37	17

end0.0ms

sample7.2s

Algorithm

intervals

Results

3.4s	40671×	body	80	nan
1.3s	12464×	body	80	valid
173.0ms	326×	body	640	valid
134.0ms	380×	body	320	valid
72.0ms	75×	body	1280	valid
67.0ms	298×	body	160	valid