Details

sample163.0ms

Algorithm

intervals

Results

83.0ms	1762×	body	80	nan
14.0ms	257×	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

prune10.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.3b

Counts

2 → 1

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ (log (+ x y)) (log z)) t)
0.2b	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
0.6b	(+ (log (+ x y)) (log z))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
28×	`pow1`
25×	`log-pow` `distribute-lft-out`
21×	`prod-diff`
19×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
7×	`log-prod` `fma-neg`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`associate-+l-` `log-div` `associate-+l+` `fma-def`
3×	`add-exp-log` `expm1-log1p-u` `associate-+r+` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`associate--l-` `diff-log` `sum-log`
1×	`+-commutative` `sub-neg` `flip3--` `associate--l+` `flip--` `fma-udef` `difference-of-squares`

Counts

3 → 92

Calls

3 calls:

9.0ms	(- (+ (log (+ x y)) (log z)) t)
1.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
7.0ms	(+ (log (+ x y)) (log z))

series333.0ms

Counts

3 → 9

Calls

3 calls:

166.0ms	(- (+ (log (+ x y)) (log z)) t)
94.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
73.0ms	(+ (log (+ x y)) (log z))

simplify41.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	388	866
1	1209	661
2	5001	650

prune275.0ms

Filtered

101 candidates to 61 candidates (60.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	93	8	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	8	102

Merged error: 0.1b

Counts

102 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
0.5b	(* (cbrt (+ x y)) (cbrt (+ x y)))
0.5b	(+ (log (* (cbrt (+ x y)) (cbrt (+ x y)))) (+ (log (cbrt (+ x y))) (log z)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
46×	`pow1`
35×	`distribute-lft-out`
32×	`cbrt-prod`
31×	`log-pow`
30×	`cbrt-div`
23×	`add-sqr-sqrt`
16×	`flip3-+` `flip-+`
15×	`add-cube-cbrt`
14×	`pow1/3`
12×	`fma-def`
10×	`associate-+l-` `log-div`
9×	`swap-sqr` `pow-prod-down`
8×	`frac-times`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
5×	`add-log-exp`
4×	`expm1-log1p-u` `associate-r/` `associate-l/` `pow-sqr` `pow-prod-up` `add-cbrt-cube` `log1p-expm1-u` `unswap-sqr`
3×	`sum-log`
2×	`pow2` `associate-+r-` `pow-plus`
1×	`+-commutative` `associate-+l+` `associate-+r+` `log-prod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 140

Calls

4 calls:

3.0ms	(cbrt (+ x y))
3.0ms	(cbrt (+ x y))
10.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))
21.0ms	(+ (log (* (cbrt (+ x y)) (cbrt (+ x y)))) (+ (log (cbrt (+ x y))) (log z)))

series625.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(cbrt (+ x y))
128.0ms	(cbrt (+ x y))
161.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))
212.0ms	(+ (log (* (cbrt (+ x y)) (cbrt (+ x y)))) (+ (log (cbrt (+ x y))) (log z)))

simplify54.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	446	1192
1	1635	1018
2	5001	925

prune546.0ms

Filtered

152 candidates to 104 candidates (68.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	152	8	160

Merged error: 0.1b

Counts

160 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

140×	`*-un-lft-identity`
117×	`distribute-lft-out`
91×	`pow1`
87×	`log-pow`
39×	`prod-diff`
30×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
16×	`log-prod`
13×	`fma-neg`
12×	`associate-+r+`
11×	`fma-def` `distribute-lft-out--`
10×	`associate-+l-` `add-log-exp`
7×	`sum-log`
6×	`log-div` `sqrt-prod`
5×	`associate-+l+` `flip3-+` `flip-+`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`diff-log`
2×	`+-commutative` `associate--l-`
1×	`sub-neg` `flip3--` `associate--l+` `flip--` `fma-udef` `difference-of-squares`

Counts

4 → 166

Calls

4 calls:

17.0ms	(- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t)
1.0ms	(fma (log t) (- a 0.5) (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t))
8.0ms	(+ (log (+ x y)) (log (sqrt z)))
12.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))

series591.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t)
116.0ms	(fma (log t) (- a 0.5) (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t))
140.0ms	(+ (log (+ x y)) (log (sqrt z)))
167.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))

simplify69.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	595	1938
1	1968	1430
2	5001	1386

prune402.0ms

Filtered

178 candidates to 89 candidates (50.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	178	8	186

Merged error: 0.1b

Counts

186 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))) (cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))))
0.6b	(+ (log (+ x y)) (log z))
0.6b	(+ (log (+ x y)) (log z))
0.6b	(+ (log (+ x y)) (log z))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
26×	`pow1`
21×	`add-cube-cbrt` `log-prod`
16×	`cbrt-prod`
15×	`log-pow` `distribute-lft-out`
12×	`associate-+l+` `fma-def`
9×	`associate-+r+`
6×	`add-exp-log` `associate-+l-` `log-div` `flip3-+` `pow1/3` `swap-sqr` `associate-r` `associate-l` `flip-+`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`+-commutative` `sum-log`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 132

Calls

4 calls:

6.0ms	(* (cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))) (cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))))
7.0ms	(+ (log (+ x y)) (log z))
7.0ms	(+ (log (+ x y)) (log z))
7.0ms	(+ (log (+ x y)) (log z))

series934.0ms

Counts

4 → 12

Calls

4 calls:

720.0ms	(* (cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))) (cbrt (fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))))
72.0ms	(+ (log (+ x y)) (log z))
73.0ms	(+ (log (+ x y)) (log z))
69.0ms	(+ (log (+ x y)) (log z))

simplify84.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	706	1687
1	2773	1534
2	5002	1423

prune581.0ms

Filtered

144 candidates to 105 candidates (72.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	139	5	144
Fresh	3	2	5
Picked	1	0	1
Done	0	2	2
Total	143	9	152

Merged error: 0.1b

Counts

152 → 9

regimes636.0ms

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	21	16
1	21	16

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.6s	57386×	body	80	nan
444.0ms	8023×	body	80	valid