Details

sample189.0ms

Algorithm

intervals

Results

81.0ms	1310×	body	80	nan
27.0ms	403×	body	80	valid
6.0ms	16×	body	640	valid
3.0ms	12×	body	320	valid
1.0ms	1×	body	1280	valid
1.0ms	7×	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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 1.7b

Counts

2 → 1

localize16.0ms

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))
0.8b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.0b	(log (- 1.0 z))

rewrite53.0ms

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:

9.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
12.0ms	(* y (- (log z) t))
18.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.0ms	(log (- 1.0 z))

series462.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
92.0ms	(* y (- (log z) t))
191.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
41.0ms	(log (- 1.0 z))

simplify94.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (76.0ms)

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

prune654.0ms

Filtered

194 candidates to 126 candidates (64.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	188	6	194
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	189	6	195

Merged error: 0.0b

Counts

195 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
0.0b	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
0.1b	(* y (- (log z) t))
0.8b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
128×	`*-un-lft-identity`
108×	`prod-diff`
107×	`add-cube-cbrt`
80×	`times-frac`
74×	`associate-+r+` `associate-r`
71×	`distribute-rgt-in` `distribute-lft-in`
56×	`unpow-prod-down`
52×	`associate--l+`
34×	`associate-+l+`
33×	`pow1`
29×	`add-exp-log`
25×	`log-pow`
24×	`unpow2` `sqr-pow`
18×	`log-prod` `unswap-sqr`
14×	`distribute-lft-out--`
11×	`associate-*r/` `prod-exp` `add-cbrt-cube`
9×	`div-exp` `add-log-exp`
8×	`sub-neg`
7×	`difference-of-squares`
6×	`pow-to-exp` `associate-l` `pow-exp`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u`
3×	`exp-prod` `cbrt-unprod`
2×	`pow-prod-down` `sum-log` `*-commutative` `rem-exp-log`
1×	`cbrt-undiv` `+-commutative` `fma-def` `flip3-+` `exp-sum` `flip-+` `div-inv`

Counts

4 → 312

Calls

4 calls:

22.0ms	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
20.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
9.0ms	(* y (- (log z) t))
35.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series530.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
167.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
72.0ms	(* y (- (log z) t))
238.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify70.0ms

Algorithm

egg-herbie

Counts

324 → 324

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1481	4058
1	5001	3215

prune1.5s

Filtered

324 candidates to 197 candidates (60.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	321	3	324
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	326	4	330

Merged error: 0.0b

Counts

330 → 4

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`prod-diff`
11×	`pow1`
6×	`add-cbrt-cube` `add-log-exp`
5×	`add-exp-log` `log-pow`
4×	`expm1-log1p-u` `fma-neg` `associate-r` `log1p-expm1-u`
3×	`log-prod` `exp-prod` `associate-l` `associate--l+` `fma-udef`
2×	`exp-sum` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `rem-exp-log` `difference-of-squares` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

5.0ms	(* x (exp (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))))
5.0ms	(- (log z) t)
2.0ms	(exp (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a)))
1.0ms	(fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))

series687.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(* x (exp (fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))))
55.0ms	(- (log z) t)
178.0ms	(exp (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	(fma y (- (log z) t) (* (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)) a))

simplify43.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	356	1091
1	1140	883
2	5002	876

prune418.0ms

Filtered

93 candidates to 66 candidates (71.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	92	5	97

Merged error: 0.0b

Counts

97 → 5

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp (fma y (- (log z) t) (* a (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b))))) 3)
0.0b	(cbrt (pow (exp (fma y (- (log z) t) (* a (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b))))) 3))
0.0b	(exp (fma y (- (log z) t) (* a (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)))))
0.6b	(fma y (- (log z) t) (* a (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `cube-prod`
6×	`exp-prod` `fma-udef`
5×	`pow1` `exp-sum` `add-cbrt-cube` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `pow-pow` `log1p-expm1-u`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-exp-log` `rem-cube-cbrt`

Counts

4 → 79

Calls

4 calls:

4.0ms	(pow (exp (fma y (- (log z) t) (* a (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b))))) 3)
3.0ms	(cbrt (pow (exp (fma y (- (log z) t) (* a (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b))))) 3))
2.0ms	(exp (fma y (- (log z) t) (* a (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)))))
1.0ms	(fma y (- (log z) t) (* a (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b))))

series878.0ms

Counts

4 → 12

Calls

4 calls:

296.0ms	(pow (exp (fma y (- (log z) t) (* a (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b))))) 3)
174.0ms	(cbrt (pow (exp (fma y (- (log z) t) (* a (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b))))) 3))
174.0ms	(exp (fma y (- (log z) t) (* a (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b)))))
234.0ms	(fma y (- (log z) t) (* a (- (log 1.0) (+ (fma 1/2 (/ (pow z 2) (pow 1.0 2)) (* 1.0 z)) b))))

simplify199.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	243	1551
1	812	1449
2	4899	1441
3	5001	1441

prune397.0ms

Filtered

91 candidates to 58 candidates (63.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	92	4	96

Merged error: 0.0b

Counts

96 → 4

regimes201.0ms

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	27	14
1	27	14

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.5s	41528×	body	80	nan
857.0ms	12572×	body	80	valid
142.0ms	379×	body	640	valid
95.0ms	405×	body	320	valid
60.0ms	80×	body	1280	valid
39.0ms	272×	body	160	valid