Details

sample374.0ms

Algorithm

intervals

Results

200.0ms	1429×	body	80	nan
69.0ms	426×	body	80	valid
9.0ms	14×	body	640	valid
7.0ms	17×	body	320	valid
5.0ms	4×	body	1280	valid
4.0ms	13×	body	160	valid

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
0.0b	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.2b	(* y (- (log z) t))
6.3b	(log (- 1.0 z))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 182

Calls

4 calls:

22.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
19.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
18.0ms	(* y (- (log z) t))
3.0ms	(log (- 1.0 z))

series454.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
139.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
75.0ms	(* y (- (log z) t))
48.0ms	(log (- 1.0 z))

simplify97.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	904	1913
1	3501	1501
2	5001	1500

prune646.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

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))
0.0b	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
0.2b	(* y (- (log z) t))

rewrite652.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
96×	`prod-diff`
90×	`add-sqr-sqrt`
68×	`add-cube-cbrt`
54×	`distribute-rgt-in` `distribute-lft-in`
49×	`associate--l+`
33×	`pow1`
25×	`log-pow`
21×	`distribute-lft-out--`
15×	`log-prod`
13×	`associate-r`
9×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`sub-neg`
6×	`associate-l`
4×	`expm1-log1p-u` `fma-neg` `associate-*r/` `log1p-expm1-u`
3×	`exp-prod` `flip3--` `flip--`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`
1×	`diff-log` `exp-sum` `sum-log`

Counts

4 → 210

Calls

4 calls:

5.0ms	(- (log z) t)
502.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
112.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
19.0ms	(* y (- (log z) t))

series406.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (log z) t)
103.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
173.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
67.0ms	(* y (- (log z) t))

simplify95.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	741	3682
1	2875	2500
2	5001	2306

prune594.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite352.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

Calls

4 calls:

111.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
100.0ms	(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))
120.0ms	(pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3)
16.0ms	(* y (- (log z) t))

series732.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
174.0ms	(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))
318.0ms	(pow (exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))) 3)
72.0ms	(* y (- (log z) t))

simplify69.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	512	2107
1	2093	1792
2	5002	1734

prune562.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity`
7×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `unpow-prod-down` `pow-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `exp-prod` `fma-udef`
1×	`unpow-prod-up` `cbrt-prod` `pow-to-exp` `pow1/3` `pow-exp` `exp-lft-sqr` `sqr-pow`

Counts

4 → 55

Calls

4 calls:

3.0ms	(cbrt (* (pow (exp 2) (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))) (pow E (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))))
2.0ms	(pow (exp 2) (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))
0.0ms	(fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))
0.0ms	(fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))

series1.5s

Counts

4 → 12

Calls

4 calls:

840.0ms	(cbrt (* (pow (exp 2) (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))) (pow E (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))))
228.0ms	(pow (exp 2) (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))
229.0ms	(fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))
235.0ms	(fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))

simplify85.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	227	1292
1	663	1154
2	2641	1102
3	5001	1015

prune424.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

regimes161.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	31
1	38	31
2	38	31

end0.0ms

sample10.4s

Algorithm

intervals

Results

5.7s	41664×	body	80	nan
2.0s	12748×	body	80	valid
231.0ms	377×	body	640	valid
167.0ms	400×	body	320	valid
80.0ms	79×	body	1280	valid
79.0ms	275×	body	160	valid