Details

sample205.0ms

Algorithm

intervals

Results

91.0ms	1312×	body	80	nan
30.0ms	408×	body	80	valid
5.0ms	20×	body	320	valid
5.0ms	13×	body	640	valid
3.0ms	4×	body	1280	valid
2.0ms	10×	body	160	valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	10
1	58	10
2	129	10
3	318	10
4	1073	10
5	5001	10

prune4.0ms

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: 2.5b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log z) t)
0.1b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
6.4b	(log (- 1.0 z))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

30×	`log-prod`
26×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`associate--l+`
17×	`distribute-rgt-in` `distribute-lft-in`
14×	`add-cube-cbrt` `associate-+r+`
10×	`associate-+l+` `associate-*r/`
9×	`pow1`
7×	`add-exp-log` `sub-neg` `flip3--` `flip--` `distribute-lft-out--` `add-log-exp`
6×	`associate-r` `add-cbrt-cube`
5×	`difference-of-squares`
4×	`frac-add`
3×	`associate-l` `log-pow`
2×	`log-div`
1×	`+-commutative` `flip3-+` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

4.0ms	(- (log z) t)
7.0ms	(* y (- (log z) t))
11.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
3.0ms	(log (- 1.0 z))

series373.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (log z) t)
68.0ms	(* y (- (log z) t))
197.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
43.0ms	(log (- 1.0 z))

simplify65.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	593	882
1	2248	832
2	5001	824

prune374.0ms

Filtered

118 candidates to 84 candidates (71.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	2	119

Merged error: 0.3b

Counts

119 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
0.0b	(- (log z) t)
0.1b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

87×	`add-sqr-sqrt`
80×	`times-frac`
74×	`associate-r`
56×	`unpow-prod-down`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt`
31×	`associate--l+`
29×	`add-exp-log`
24×	`unpow2` `sqr-pow`
21×	`log-prod`
18×	`unswap-sqr`
17×	`distribute-rgt-in` `distribute-lft-in`
14×	`associate-+r+`
11×	`associate-*r/` `prod-exp` `add-cbrt-cube`
10×	`pow1` `associate-+l+`
9×	`sub-neg` `div-exp`
7×	`add-log-exp`
6×	`pow-to-exp` `flip3--` `associate-l` `pow-exp` `flip--`
4×	`frac-add` `distribute-lft-out--`
3×	`cbrt-unprod`
2×	`pow-prod-down` `log-pow` `*-commutative` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+` `div-inv`

Counts

4 → 200

Calls

4 calls:

18.0ms	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
4.0ms	(- (log z) t)
7.0ms	(* y (- (log z) t))
23.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* 1/2 (/ (pow z 2) (pow 1.0 2)))
56.0ms	(- (log z) t)
71.0ms	(* 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)))

simplify112.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1014	1728
1	4349	1558
2	5001	1558

prune813.0ms

Filtered

212 candidates to 137 candidates (64.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	210	2	212
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	211	3	214

Merged error: 0.0b

Counts

214 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (exp (neg (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))))))
0.0b	(+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))
0.0b	(* 0.5 (* a (pow z 2)))
8.7b	(* a (pow z 2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log`
18×	`add-sqr-sqrt`
13×	`associate-r` `add-cbrt-cube`
11×	`prod-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-l`
8×	`pow1`
6×	`add-log-exp`
5×	`cbrt-unprod` `unswap-sqr`
4×	`unpow-prod-down`
3×	`*-commutative`
2×	`exp-neg` `pow-to-exp` `associate-*r/` `pow-prod-down` `pow-exp` `unpow2` `sqr-pow`
1×	`+-commutative` `neg-sub0` `distribute-neg-in` `flip3-+` `exp-diff` `exp-sum` `sum-log` `un-div-inv` `flip-+`

Counts

4 → 79

Calls

4 calls:

12.0ms	(* x (exp (neg (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))))))
5.0ms	(+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))
6.0ms	(* 0.5 (* a (pow z 2)))
6.0ms	(* a (pow z 2))

series244.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* x (exp (neg (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))))))
92.0ms	(+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))
33.0ms	(* 0.5 (* a (pow z 2)))
34.0ms	(* a (pow z 2))

simplify53.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	329	636
1	1429	538
2	5001	529

prune244.0ms

Filtered

91 candidates to 58 candidates (63.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	90	4	94

Merged error: 0.0b

Counts

94 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))))
0.0b	(+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))
0.0b	(* 0.5 (* a (pow z 2)))
8.7b	(* a (pow z 2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
15×	`add-sqr-sqrt`
12×	`add-log-exp`
11×	`add-cbrt-cube`
10×	`prod-exp`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
6×	`pow1` `associate-l`
4×	`unpow-prod-down` `sum-log` `cbrt-unprod` `unswap-sqr`
3×	`exp-prod` `rem-exp-log`
2×	`pow-to-exp` `pow-exp` `*-commutative` `unpow2` `sqr-pow`
1×	`+-commutative` `flip3-+` `exp-sum` `pow-prod-down` `flip-+`

Counts

4 → 71

Calls

4 calls:

8.0ms	(exp (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))))
5.0ms	(+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))
6.0ms	(* 0.5 (* a (pow z 2)))
6.0ms	(* a (pow z 2))

series206.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(exp (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))))
92.0ms	(+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))
32.0ms	(* 0.5 (* a (pow z 2)))
33.0ms	(* a (pow z 2))

simplify47.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	280	492
1	1179	433
2	5002	427

prune205.0ms

Filtered

83 candidates to 53 candidates (63.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	84	3	87

Merged error: 0.0b

Counts

87 → 3

regimes163.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	16
1	32	16

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.9s	41615×	body	80	nan
970.0ms	12552×	body	80	valid
169.0ms	413×	body	640	valid
104.0ms	395×	body	320	valid
52.0ms	65×	body	1280	valid
51.0ms	316×	body	160	valid

Details

sample205.0ms

simplify40.0ms

prune4.0ms

localize18.0ms

rewrite30.0ms

series373.0ms

simplify65.0ms

prune374.0ms

localize22.0ms

rewrite62.0ms

series422.0ms

simplify112.0ms

prune813.0ms

localize15.0ms

rewrite30.0ms

series244.0ms

simplify53.0ms

prune244.0ms

localize14.0ms

rewrite26.0ms

series206.0ms

simplify47.0ms

prune205.0ms

regimes163.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.2s

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