Details

sample172.0ms

Algorithm

intervals

Results

70.0ms	1294×	body	80	nan
24.0ms	393×	body	80	valid
5.0ms	13×	body	640	valid
4.0ms	9×	body	160	valid
2.0ms	11×	body	320	valid
1.0ms	1×	body	1280	valid

simplify40.0ms

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: 3.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(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)))
6.8b	(log (- 1.0 z))

rewrite70.0ms

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:

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

series450.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
67.0ms	(* y (- (log z) t))
187.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
48.0ms	(log (- 1.0 z))

simplify93.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (76.0ms)

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

prune665.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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	(* 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)))

rewrite819.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 300

Calls

4 calls:

109.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
495.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
16.0ms	(* y (- (log z) t))
179.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series597.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
104.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
76.0ms	(* 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)))

simplify151.0ms

Algorithm

egg-herbie

Counts

312 → 312

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	1091	5982
1	4469	4426
2	5001	4420

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (fma y (- (log z) t) (* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a)) (* (fma (- b) 1 (* b 1)) a)))
0.0b	(* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a)
0.1b	(fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1)))
0.6b	(fma y (- (log z) t) (* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`exp-prod` `associate-r` `associate-l`
2×	`fma-udef` `rem-exp-log`
1×	`exp-sum` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 55

Calls

4 calls:

5.0ms	(exp (+ (fma y (- (log z) t) (* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a)) (* (fma (- b) 1 (* b 1)) a)))
3.0ms	(* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a)
0.0ms	(fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1)))
0.0ms	(fma y (- (log z) t) (* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a))

series3.3s

Counts

4 → 12

Calls

4 calls:

2.1s	(exp (+ (fma y (- (log z) t) (* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a)) (* (fma (- b) 1 (* b 1)) a)))
426.0ms	(* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a)
291.0ms	(fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1)))
532.0ms	(fma y (- (log z) t) (* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a))

simplify110.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	311	1950
1	971	1656
2	4399	1645
3	5001	1644

prune524.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1)))
0.6b	(fma y (- (log z) t) (* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a))
0.6b	(fma y (- (log z) t) (* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a))
0.6b	(fma y (- (log z) t) (* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

4 → 40

Calls

4 calls:

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

series1.9s

Counts

4 → 12

Calls

4 calls:

288.0ms	(fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1)))
522.0ms	(fma y (- (log z) t) (* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a))
542.0ms	(fma y (- (log z) t) (* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a))
524.0ms	(fma y (- (log z) t) (* (fma (+ (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (sqrt (log 1.0)) (sqrt (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z)))) (- (* b 1))) a))

simplify57.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	153	1424
1	455	1200
2	1772	1193
3	5002	1190

prune533.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes166.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	105
1	59	105
2	59	105

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.2s	40731×	body	80	nan
764.0ms	12420×	body	80	valid
135.0ms	395×	body	640	valid
83.0ms	383×	body	320	valid
53.0ms	73×	body	1280	valid
39.0ms	297×	body	160	valid