Details

sample197.0ms

Algorithm

intervals

Results

87.0ms	1477×	body	80	nan
29.0ms	450×	body	80	valid
2.0ms	33×	body	80	overflowed
1.0ms	4×	body	320	valid
1.0ms	1×	body	1280	valid
1.0ms	2×	body	640	valid
0.0ms	1×	body	160	valid

simplify39.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (- (log (- 1.0 z)) b))
0.1b	(* y (- (log z) t))
1.0b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
6.0b	(log (- 1.0 z))

rewrite70.0ms

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:

20.0ms	(* a (- (log (- 1.0 z)) b))
14.0ms	(* y (- (log z) t))
20.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

series365.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* a (- (log (- 1.0 z)) b))
70.0ms	(* y (- (log z) t))
181.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
42.0ms	(log (- 1.0 z))

simplify106.0ms

Algorithm

egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 2 (85.0ms)

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

prune697.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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)))

rewrite968.0ms

Algorithm

rewrite-expression-head

Rules

168×	`prod-diff`
156×	`*-un-lft-identity`
144×	`add-sqr-sqrt`
110×	`add-cube-cbrt`
108×	`distribute-rgt-in` `distribute-lft-in`
92×	`associate--l+`
74×	`associate-+r+`
48×	`pow1`
38×	`log-pow`
34×	`associate-+l+`
31×	`distribute-lft-out--`
24×	`log-prod`
17×	`associate-r`
14×	`difference-of-squares`
12×	`sub-neg` `associate-*r/`
10×	`add-cbrt-cube`
9×	`add-exp-log` `associate-l`
6×	`flip3--` `flip--` `add-log-exp`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `exp-sum` `sum-log` `flip-+`

Counts

4 → 306

Calls

4 calls:

302.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
464.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
17.0ms	(* y (- (log z) t))
163.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series645.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(* x (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))))
102.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
73.0ms	(* y (- (log z) t))
240.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify149.0ms

Algorithm

egg-herbie

Counts

318 → 318

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	1119	6148
1	4676	4554
2	5001	4552

prune1.1s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(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))
0.2b	(pow (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))) 3)
30.4b	(cbrt (pow (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))) 3))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
28×	`add-cube-cbrt`
24×	`prod-diff`
17×	`distribute-rgt-in` `distribute-lft-in`
14×	`pow1`
12×	`cbrt-prod`
7×	`add-exp-log` `log-pow` `add-cbrt-cube`
6×	`unpow-prod-down` `log-prod` `cube-prod` `associate-r` `associate--l+`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-l`
2×	`cube-mult` `sub-neg` `unpow3` `associate-*r/` `distribute-lft-out--` `sqr-pow`
1×	`pow-to-exp` `flip3--` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `rem-cbrt-cube` `cbrt-unprod` `fma-udef` `rem-cube-cbrt` `difference-of-squares` `unswap-sqr`

Counts

4 → 117

Calls

4 calls:

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)))
15.0ms	(* y (- (log z) t))
1.0ms	(pow (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))) 3)
1.0ms	(cbrt (pow (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))) 3))

series6.9s

Counts

4 → 12

Calls

4 calls:

215.0ms	(fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t)))
76.0ms	(* y (- (log z) t))
6.3s	(pow (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))) 3)
217.0ms	(cbrt (pow (fma (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a (* y (- (log z) t))) 3))

simplify71.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	465	1703
1	1952	1427
2	5003	1414

prune464.0ms

Pruning

2 alts after pruning (1 fresh and 1 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)))

rewrite380.0ms

Algorithm

rewrite-expression-head

Rules

216×	`prod-diff`
182×	`*-un-lft-identity`
172×	`add-sqr-sqrt`
148×	`associate-+r+`
142×	`distribute-rgt-in` `distribute-lft-in`
140×	`add-cube-cbrt`
104×	`associate--l+`
68×	`associate-+l+`
58×	`pow1`
50×	`log-pow`
36×	`log-prod`
28×	`distribute-lft-out--`
20×	`associate-*r/`
16×	`sub-neg`
14×	`difference-of-squares`
12×	`associate-r`
10×	`flip3--` `flip--`
8×	`add-exp-log` `frac-add` `add-cbrt-cube` `add-log-exp`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`+-commutative` `fma-def` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 370

Calls

4 calls:

14.0ms	(* y (- (log z) t))
14.0ms	(* y (- (log z) t))
161.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))
162.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series611.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* y (- (log z) t))
76.0ms	(* 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)))
229.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify136.0ms

Algorithm

egg-herbie

Counts

382 → 382

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	899	6250
1	3403	4818
2	5001	4806

prune2.0s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes144.0ms

Accuracy

0% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	16
1	30	16

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.5s	43082×	body	80	nan
869.0ms	13153×	body	80	valid
59.0ms	825×	body	80	overflowed
40.0ms	103×	body	640	valid
27.0ms	113×	body	320	valid
19.0ms	26×	body	1280	valid
16.0ms	111×	body	160	valid