Details

sample291.0ms

Algorithm

intervals

Results

147.0ms	1270×	body	80	nan
45.0ms	371×	body	80	valid
6.0ms	16×	body	320	valid
6.0ms	11×	body	640	valid
4.0ms	4×	body	1280	valid
1.0ms	6×	body	160	valid

simplify38.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
0.1b	(* y (- (log z) t))
1.3b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
6.1b	(log (- 1.0 z))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

72×	`prod-diff`
69×	`add-sqr-sqrt`
66×	`*-un-lft-identity`
57×	`add-cube-cbrt`
53×	`distribute-rgt-in` `distribute-lft-in`
38×	`associate-+r+`
34×	`associate-+l+`
28×	`pow1`
27×	`log-prod`
22×	`associate--l+`
20×	`log-pow`
10×	`associate-r/` `associate-r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`sub-neg` `flip3--` `associate-l` `flip--` `add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u` `difference-of-squares`
2×	`log-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `rem-log-exp` `exp-sum` `sum-log` `flip-+`

Counts

4 → 188

Calls

4 calls:

52.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
15.0ms	(* y (- (log z) t))
20.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

series131.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))))
13.0ms	(* y (- (log z) t))
41.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

simplify98.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	947	2029
1	3790	1591
2	5001	1590

prune1.9s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
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))
1.3b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite699.0ms

Algorithm

rewrite-expression-head

Rules

208×	`add-sqr-sqrt`
188×	`*-un-lft-identity`
168×	`prod-diff`
142×	`add-cube-cbrt`
108×	`distribute-rgt-in` `distribute-lft-in`
92×	`associate--l+`
81×	`associate-r`
80×	`times-frac`
74×	`associate-+r+`
56×	`unpow-prod-down`
48×	`pow1`
38×	`log-pow`
34×	`associate-+l+`
31×	`add-exp-log` `distribute-lft-out--`
24×	`log-prod` `unpow2` `sqr-pow`
19×	`unswap-sqr`
14×	`difference-of-squares`
13×	`associate-*r/` `add-cbrt-cube`
12×	`sub-neg` `prod-exp`
9×	`div-exp` `associate-l`
6×	`pow-to-exp` `flip3--` `pow-exp` `flip--` `add-log-exp`
4×	`expm1-log1p-u` `frac-add` `cbrt-unprod` `log1p-expm1-u`
3×	`pow-prod-down` `*-commutative`
1×	`cbrt-undiv` `+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+` `div-inv`

Counts

4 → 397

Calls

4 calls:

26.0ms	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
467.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
15.0ms	(* y (- (log z) t))
166.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series100.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
22.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
13.0ms	(* y (- (log z) t))
62.0ms	(+ (* 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

409 → 409

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1521	6345
1	5001	4737

prune4.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))))
0.6b	(cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))))
0.6b	(cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))))
0.6b	(cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

58×	`cbrt-prod`
52×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
22×	`pow1` `distribute-lft-out--`
18×	`cbrt-div`
15×	`add-cube-cbrt` `swap-sqr`
11×	`log-pow`
9×	`flip3--` `pow1/3` `associate-r` `associate-l` `flip--`
7×	`difference-of-squares`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 119

Calls

4 calls:

185.0ms	(* (cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))))
22.0ms	(cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))))
22.0ms	(cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))))
24.0ms	(cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))))

series71.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))))
16.0ms	(cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))))
19.0ms	(cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))))
17.0ms	(cbrt (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))))

simplify71.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	527	2977
1	1967	2821
2	5001	2531

prune3.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b

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

0.1b

(* y (- (log z) t))

0.8b

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`prod-diff`
23×	`add-cube-cbrt`
17×	`distribute-rgt-in` `distribute-lft-in`
14×	`pow1`
10×	`associate-r`
7×	`log-pow` `add-cbrt-cube`
6×	`add-exp-log` `log-prod` `associate-l` `associate--l+`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`flip3--` `exp-sum` `flip--` `fma-udef` `difference-of-squares`

Counts

3 → 90

Calls

3 calls:

28.0ms

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

15.0ms

(* y (- (log z) t))

2.0ms

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

series160.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms

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

13.0ms

(* y (- (log z) t))

48.0ms

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

simplify55.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	443	1211
1	1734	917
2	5001	898

prune1.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes523.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	42
1	53	42
2	53	42

end0.0ms

sample8.0s

Algorithm

intervals

Results

4.1s	40957×	body	80	nan
1.4s	12519×	body	80	valid
191.0ms	354×	body	640	valid
144.0ms	409×	body	320	valid
75.0ms	79×	body	1280	valid
62.0ms	276×	body	160	valid