Details

sample232.0ms

Algorithm

intervals

Results

137.0ms	1762×	body	80	nan
23.0ms	257×	body	80	valid

simplify66.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

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))

rewrite47.0ms

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:

36.0ms	(- (+ (log (+ x y)) (log z)) t)
0.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
7.0ms	(+ (log (+ x y)) (log z))

series318.0ms

Counts

3 → 9

Calls

3 calls:

160.0ms	(- (+ (log (+ x y)) (log z)) t)
88.0ms	(fma (log t) (- a 0.5) (- (+ (log (+ x y)) (log z)) t))
70.0ms	(+ (log (+ x y)) (log z))

simplify39.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (30.0ms)

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

prune281.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

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)))

rewrite98.0ms

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:

2.0ms	(cbrt (+ x y))
2.0ms	(cbrt (+ x y))
23.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))
65.0ms	(+ (log (* (cbrt (+ x y)) (cbrt (+ x y)))) (+ (log (cbrt (+ x y))) (log z)))

series625.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(cbrt (+ x y))
128.0ms	(cbrt (+ x y))
163.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))
208.0ms	(+ (log (* (cbrt (+ x y)) (cbrt (+ x y)))) (+ (log (cbrt (+ x y))) (log z)))

simplify53.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (41.0ms)

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

prune625.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (cbrt (+ x y)))
0.2b	(fma (log t) (- a 0.5) (- (* 1 (fma 3 (log (cbrt (+ x y))) (log z))) t))
0.5b	(cbrt (+ x y))
0.6b	(fma 3 (log (cbrt (+ x y))) (log z))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `flip3-+` `pow1/3` `log-pow` `flip-+` `fma-udef` `distribute-lft-out`
1×	`rem-log-exp`

Counts

4 → 57

Calls

4 calls:

3.0ms	(log (cbrt (+ x y)))
0.0ms	(fma (log t) (- a 0.5) (- (* 1 (fma 3 (log (cbrt (+ x y))) (log z))) t))
2.0ms	(cbrt (+ x y))
0.0ms	(fma 3 (log (cbrt (+ x y))) (log z))

series494.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(log (cbrt (+ x y)))
136.0ms	(fma (log t) (- a 0.5) (- (* 1 (fma 3 (log (cbrt (+ x y))) (log z))) t))
127.0ms	(cbrt (+ x y))
121.0ms	(fma 3 (log (cbrt (+ x y))) (log z))

simplify84.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	314	507
1	859	453
2	3658	439
3	5001	439

prune342.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

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)))

rewrite273.0ms

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:

222.0ms	(- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t)
0.0ms	(fma (log t) (- a 0.5) (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t))
8.0ms	(+ (log (+ x y)) (log (sqrt z)))
34.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))

series605.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t)
124.0ms	(fma (log t) (- a 0.5) (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t))
144.0ms	(+ (log (+ x y)) (log (sqrt z)))
171.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))

simplify68.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 2 (46.0ms)

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

prune444.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes439.0ms

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	19	12
1	19	12

end0.0ms

sample7.2s

Algorithm

intervals

Results

4.4s	57386×	body	80	nan
737.0ms	8023×	body	80	valid