Details

sample244.0ms

Algorithm

intervals

Results

141.0ms	1911×	body	80	nan
24.0ms	258×	body	80	valid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	9
1	61	8
2	161	8
3	393	8
4	984	8
5	2256	8
6	4095	8
7	5001	8

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 2 expressions with local error:

0.2b	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
0.5b	(+ (log (+ x y)) (log z))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
7×	`pow1` `log-prod`
5×	`add-sqr-sqrt` `add-cube-cbrt` `log-pow` `distribute-lft-out`
4×	`associate-+l+` `fma-def`
3×	`associate-+r+`
2×	`add-exp-log` `expm1-log1p-u` `associate-+l-` `log-div` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`
1×	`+-commutative` `sum-log` `fma-udef`

Counts

2 → 40

Calls

2 calls:

0.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
7.0ms	(+ (log (+ x y)) (log z))

series157.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
68.0ms	(+ (log (+ x y)) (log z))

simplify53.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	262	323
1	662	288
2	2590	282
3	5001	278

prune192.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
57×	`prod-diff`
46×	`add-sqr-sqrt`
42×	`add-cube-cbrt`
27×	`associate-+r+`
26×	`associate-+l+`
23×	`pow1`
22×	`distribute-rgt-in` `distribute-lft-in`
18×	`log-pow`
17×	`distribute-lft-out`
10×	`add-log-exp`
7×	`log-prod`
6×	`associate-*r/`
5×	`add-exp-log` `sub-neg` `flip3--` `fma-def` `associate-r` `sum-log` `add-cbrt-cube` `flip--`
4×	`associate-l` `frac-add`
3×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u`
2×	`+-commutative` `associate-+l-` `log-div` `diff-log`
1×	`associate-+r-` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 144

Calls

3 calls:

59.0ms	(+ (* (log t) (- a 0.5)) (- (+ (log (+ x y)) (log z)) t))
12.0ms	(* (log t) (- a 0.5))
7.0ms	(+ (log (+ x y)) (log z))

series263.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(+ (* (log t) (- a 0.5)) (- (+ (log (+ x y)) (log z)) t))
93.0ms	(* (log t) (- a 0.5))
71.0ms	(+ (log (+ x y)) (log z))

simplify85.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	773	1594
1	3106	1268
2	5003	1265

prune484.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (sqrt (+ x y)))
0.2b	(fma (log t) (- a 0.5) (- (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t))
0.4b	(+ (log (sqrt (+ x y))) (log z))
0.5b	(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
27×	`pow1`
26×	`log-pow`
25×	`distribute-lft-out`
24×	`log-prod`
14×	`associate-+l+`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`fma-def` `sqrt-prod`
8×	`log-div` `sqrt-div`
6×	`associate-+l-` `flip3-+` `flip-+`
5×	`add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `associate-+r+` `sum-log` `add-cbrt-cube` `log1p-expm1-u`
3×	`sqrt-pow1` `pow1/2`
2×	`+-commutative` `associate-+r-`
1×	`rem-log-exp` `fma-udef`

Counts

4 → 109

Calls

4 calls:

3.0ms	(log (sqrt (+ x y)))
0.0ms	(fma (log t) (- a 0.5) (- (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t))
8.0ms	(+ (log (sqrt (+ x y))) (log z))
23.0ms	(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(log (sqrt (+ x y)))
130.0ms	(fma (log t) (- a 0.5) (- (+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z))) t))
110.0ms	(+ (log (sqrt (+ x y))) (log z))
123.0ms	(+ (log (sqrt (+ x y))) (+ (log (sqrt (+ x y))) (log z)))

simplify41.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	497	975
1	1412	857
2	5001	831

prune518.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (log t) (- a 0.5) (- (+ (log (sqrt (sqrt (+ x y)))) (+ (log (sqrt (sqrt (+ x y)))) (+ (log (sqrt (+ x y))) (log z)))) t))
0.3b	(+ (log (sqrt (sqrt (+ x y)))) (+ (log (sqrt (+ x y))) (log z)))
0.3b	(+ (log (sqrt (sqrt (+ x y)))) (+ (log (sqrt (sqrt (+ x y)))) (+ (log (sqrt (+ x y))) (log z))))
0.4b	(+ (log (sqrt (+ x y))) (log z))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

84×	`*-un-lft-identity`
83×	`distribute-lft-out`
67×	`log-pow`
66×	`pow1`
30×	`log-prod`
27×	`associate-+l+`
26×	`sqrt-prod`
22×	`fma-def`
18×	`sqrt-div`
16×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`associate-+l-` `log-div`
10×	`sum-log`
9×	`sqrt-pow1` `flip3-+` `flip-+`
8×	`associate-+r-`
7×	`add-log-exp`
5×	`associate-+r+` `pow1/2`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`+-commutative`
1×	`fma-udef`

Counts

4 → 154

Calls

4 calls:

0.0ms	(fma (log t) (- a 0.5) (- (+ (log (sqrt (sqrt (+ x y)))) (+ (log (sqrt (sqrt (+ x y)))) (+ (log (sqrt (+ x y))) (log z)))) t))
25.0ms	(+ (log (sqrt (sqrt (+ x y)))) (+ (log (sqrt (+ x y))) (log z)))
65.0ms	(+ (log (sqrt (sqrt (+ x y)))) (+ (log (sqrt (sqrt (+ x y)))) (+ (log (sqrt (+ x y))) (log z))))
13.0ms	(+ (log (sqrt (+ x y))) (log z))

series1.2s

Counts

4 → 12

Calls

4 calls:

211.0ms	(fma (log t) (- a 0.5) (- (+ (log (sqrt (sqrt (+ x y)))) (+ (log (sqrt (sqrt (+ x y)))) (+ (log (sqrt (+ x y))) (log z)))) t))
437.0ms	(+ (log (sqrt (sqrt (+ x y)))) (+ (log (sqrt (+ x y))) (log z)))
457.0ms	(+ (log (sqrt (sqrt (+ x y)))) (+ (log (sqrt (sqrt (+ x y)))) (+ (log (sqrt (+ x y))) (log z))))
120.0ms	(+ (log (sqrt (+ x y))) (log z))

simplify66.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	729	1902
1	2456	1704
2	5003	1658

prune706.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes616.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	19
1	23	19

end0.0ms

sample7.2s

Algorithm

intervals

Results

4.3s	56957×	body	80	nan
726.0ms	8027×	body	80	valid