Details

sample271.0ms

Algorithm

intervals

Results

122.0ms	1969×	body	80	nan
18.0ms	256×	body	80	valid

simplify112.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	5198	16

prune15.0ms

Filtered

1 candidates to 1 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: 0.3b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (- a 0.5) (log t)) t)
0.1b	(+ (log (+ x y)) (+ (log z) (- (* (- a 0.5) (log t)) t)))
0.1b	(* (- a 0.5) (log t))
0.2b	(+ (log z) (- (* (- a 0.5) (log t)) t))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

7.0ms	(- (* (- a 0.5) (log t)) t)
16.0ms	(+ (log (+ x y)) (+ (log z) (- (* (- a 0.5) (log t)) t)))
7.0ms	(* (- a 0.5) (log t))
10.0ms	(+ (log z) (- (* (- a 0.5) (log t)) t))

series97.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (* (- a 0.5) (log t)) t)
55.0ms	(+ (log (+ x y)) (+ (log z) (- (* (- a 0.5) (log t)) t)))
10.0ms	(* (- a 0.5) (log t))
21.0ms	(+ (log z) (- (* (- a 0.5) (log t)) t))

simplify70.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5038	1480

prune184.0ms

Filtered

82 candidates to 112 candidates (-36.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	104	8	112
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	106	8	114

Merged error: 0.0b

Counts

114 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (+ (log z) (* (- a 0.5) (* 2 (log (cbrt t))))) (- (* (- a 0.5) (log (cbrt t))) t))
0.2b	(+ (log z) (* (- a 0.5) (* 2 (log (cbrt t)))))
0.6b	(cbrt t)
0.6b	(cbrt t)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

39×	`log-prod`
38×	`associate-+r+`
30×	`distribute-rgt-in` `distribute-lft-in`
24×	`cbrt-prod`
21×	`*-un-lft-identity`
19×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`add-log-exp`
12×	`associate--l+`
7×	`sum-log`
4×	`pow1` `add-exp-log` `associate-+l+` `flip3-+` `frac-add` `add-cbrt-cube` `flip-+`
2×	`+-commutative` `flip3--` `pow1/3` `diff-log` `flip--`
1×	`associate-+r-` `sub-neg` `distribute-lft-out`

Counts

4 → 95

Calls

4 calls:

15.0ms	(+ (+ (log z) (* (- a 0.5) (* 2 (log (cbrt t))))) (- (* (- a 0.5) (log (cbrt t))) t))
7.0ms	(+ (log z) (* (- a 0.5) (* 2 (log (cbrt t)))))
1.0ms	(cbrt t)
1.0ms	(cbrt t)

series162.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(+ (+ (log z) (* (- a 0.5) (* 2 (log (cbrt t))))) (- (* (- a 0.5) (log (cbrt t))) t))
66.0ms	(+ (log z) (* (- a 0.5) (* 2 (log (cbrt t)))))
23.0ms	(cbrt t)
24.0ms	(cbrt t)

simplify53.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4990	1704
1	4990	1704

prune192.0ms

Filtered

86 candidates to 107 candidates (-24.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	107	8	115

Merged error: 0.0b

Counts

115 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (+ (log z) (* (- a 0.5) (* 2 (log (cbrt t))))) (- (* (- a 0.5) (log (pow t 1/3))) t))
0.2b	(+ (log z) (* (- a 0.5) (* 2 (log (cbrt t)))))
0.6b	(cbrt t)
5.0b	(pow t 1/3)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

41×	`log-prod`
40×	`associate-+r+`
31×	`distribute-rgt-in` `distribute-lft-in`
22×	`*-un-lft-identity`
20×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`cbrt-prod` `add-log-exp`
14×	`associate--l+`
9×	`unpow-prod-down`
7×	`sum-log`
5×	`pow1` `add-exp-log`
4×	`associate-+l+` `flip3-+` `frac-add` `add-cbrt-cube` `flip-+`
3×	`pow-unpow` `sqr-pow`
2×	`+-commutative` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `associate-+r-` `sub-neg` `pow-pow` `unpow1/3` `pow1/3` `pow-exp` `distribute-lft-out`

Counts

4 → 104

Calls

4 calls:

16.0ms	(+ (+ (log z) (* (- a 0.5) (* 2 (log (cbrt t))))) (- (* (- a 0.5) (log (pow t 1/3))) t))
7.0ms	(+ (log z) (* (- a 0.5) (* 2 (log (cbrt t)))))
1.0ms	(cbrt t)
2.0ms	(pow t 1/3)

series176.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(+ (+ (log z) (* (- a 0.5) (* 2 (log (cbrt t))))) (- (* (- a 0.5) (log (pow t 1/3))) t))
65.0ms	(+ (log z) (* (- a 0.5) (* 2 (log (cbrt t)))))
23.0ms	(cbrt t)
24.0ms	(pow t 1/3)

simplify47.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5592	1696

prune219.0ms

Filtered

86 candidates to 116 candidates (-34.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	116	8	124

Merged error: 0.0b

Counts

124 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (log (sqrt (+ x y))) (+ (- (* (- a 0.5) (log t)) t) (+ (log z) (log (sqrt (+ x y))))))
0.1b	(+ (- (* (- a 0.5) (log t)) t) (+ (log z) (log (sqrt (+ x y)))))
0.1b	(* (- a 0.5) (log t))
0.5b	(+ (log z) (log (sqrt (+ x y))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

63×	`*-un-lft-identity`
45×	`distribute-lft-out`
29×	`pow1` `log-prod`
23×	`log-pow`
21×	`add-log-exp`
19×	`add-sqr-sqrt`
18×	`associate-+l+` `sum-log`
15×	`add-cube-cbrt`
13×	`associate-+r-`
9×	`associate-+r+` `flip3-+` `flip-+`
8×	`log-div` `sqrt-div` `sqrt-prod`
6×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `associate--l+` `add-cbrt-cube`
5×	`associate-l`
4×	`associate-+l-` `diff-log` `associate-r` `frac-add`
3×	`+-commutative` `flip3--` `flip--`
2×	`associate-*l/`
1×	`sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 131

Calls

4 calls:

21.0ms	(+ (log (sqrt (+ x y))) (+ (- (* (- a 0.5) (log t)) t) (+ (log z) (log (sqrt (+ x y))))))
16.0ms	(+ (- (* (- a 0.5) (log t)) t) (+ (log z) (log (sqrt (+ x y)))))
7.0ms	(* (- a 0.5) (log t))
11.0ms	(+ (log z) (log (sqrt (+ x y))))

series131.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ (log (sqrt (+ x y))) (+ (- (* (- a 0.5) (log t)) t) (+ (log z) (log (sqrt (+ x y))))))
40.0ms	(+ (- (* (- a 0.5) (log t)) t) (+ (log z) (log (sqrt (+ x y)))))
10.0ms	(* (- a 0.5) (log t))
26.0ms	(+ (log z) (log (sqrt (+ x y))))

simplify50.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5022	2561

prune166.0ms

Filtered

97 candidates to 143 candidates (-47.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	141	2	143
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	143	8	151

Merged error: 0.0b

Counts

151 → 8

regimes847.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	28
1	48	28

end0.0ms

sample7.5s

Algorithm

intervals

Results

3.4s	55908×	body	80	nan
574.0ms	8030×	body	80	valid

Details

sample271.0ms

simplify112.0ms

prune15.0ms

localize16.0ms

rewrite44.0ms

series97.0ms

simplify70.0ms

prune184.0ms

localize21.0ms

rewrite32.0ms

series162.0ms

simplify53.0ms

prune192.0ms

localize30.0ms

rewrite32.0ms

series176.0ms

simplify47.0ms

prune219.0ms

localize19.0ms

rewrite61.0ms

series131.0ms

simplify50.0ms

prune166.0ms

regimes847.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample7.5s

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