Details

sample184.0ms

Algorithm

intervals

Results

92.0ms	1855×	body	80	nan
15.0ms	257×	body	80	valid

simplify67.0ms

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

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (log (+ x y)) (log z)) t)
0.1b	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
0.1b	(* (- a 0.5) (log t))
0.6b	(+ (log (+ x y)) (log z))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

91×	`*-un-lft-identity`
48×	`pow1`
43×	`add-sqr-sqrt`
42×	`prod-diff` `log-pow`
41×	`distribute-lft-out`
35×	`add-cube-cbrt`
28×	`associate-+l+`
19×	`log-prod`
14×	`add-log-exp`
13×	`fma-def`
11×	`distribute-lft-out--`
9×	`associate-+r+`
7×	`fma-neg`
6×	`add-exp-log` `distribute-rgt-in` `flip3--` `distribute-lft-in` `associate-*l/` `sum-log` `add-cbrt-cube` `flip--`
5×	`associate-+l-` `associate-l`
4×	`expm1-log1p-u` `log-div` `flip3-+` `diff-log` `associate-r` `frac-add` `flip-+` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`+-commutative` `associate--l-` `sub-neg` `associate--l+`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 172

Calls

4 calls:

9.0ms	(- (+ (log (+ x y)) (log z)) t)
16.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
7.0ms	(* (- a 0.5) (log t))
8.0ms	(+ (log (+ x y)) (log z))

series522.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(- (+ (log (+ x y)) (log z)) t)
205.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
64.0ms	(* (- a 0.5) (log t))
77.0ms	(+ (log (+ x y)) (log z))

simplify79.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	706	1592
1	2722	1253
2	5001	1237

prune551.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
0.5b	(fma 2 (log (cbrt z)) (log (+ x y)))
0.5b	(cbrt z)
0.5b	(cbrt z)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

5.0ms	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
1.0ms	(fma 2 (log (cbrt z)) (log (+ x y)))
1.0ms	(cbrt z)
1.0ms	(cbrt z)

series700.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(+ (fma 2 (log (cbrt z)) (log (+ x y))) (log (cbrt z)))
146.0ms	(fma 2 (log (cbrt z)) (log (+ x y)))
184.0ms	(cbrt z)
189.0ms	(cbrt z)

simplify72.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	203	445
1	573	409
2	2204	368
3	5002	358

prune417.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (fma 2 (log (* (cbrt 1) (pow z 1/3))) (log (+ x y))) (log (cbrt z)))
0.5b	(fma 2 (log (* (cbrt 1) (pow z 1/3))) (log (+ x y)))
0.5b	(cbrt z)
5.1b	(pow z 1/3)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`pow1` `cbrt-prod` `associate-+r+` `log-prod`
5×	`add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`unpow-prod-down` `pow-unpow` `fma-def`
2×	`fma-udef` `distribute-lft-out`
1×	`+-commutative` `pow-to-exp` `associate-+l+` `pow-pow` `flip3-+` `unpow1/3` `pow1/3` `pow-exp` `sum-log` `log-pow` `flip-+` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

5.0ms	(+ (fma 2 (log (* (cbrt 1) (pow z 1/3))) (log (+ x y))) (log (cbrt z)))
1.0ms	(fma 2 (log (* (cbrt 1) (pow z 1/3))) (log (+ x y)))
1.0ms	(cbrt z)
2.0ms	(pow z 1/3)

series696.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(+ (fma 2 (log (* (cbrt 1) (pow z 1/3))) (log (+ x y))) (log (cbrt z)))
133.0ms	(fma 2 (log (* (cbrt 1) (pow z 1/3))) (log (+ x y)))
185.0ms	(cbrt z)
182.0ms	(pow z 1/3)

simplify169.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	269	532
1	874	474
2	4953	394
3	5001	394

prune453.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (pow (fma 2/3 (log z) (log (+ x y))) 3))
0.5b	(fma 2/3 (log z) (log (+ x y)))
0.5b	(cbrt z)
0.7b	(pow (fma 2/3 (log z) (log (+ x y))) 3)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `pow1/3` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow-exp` `rem-cbrt-cube` `fma-udef` `rem-cube-cbrt`

Counts

4 → 71

Calls

4 calls:

2.0ms	(cbrt (pow (fma 2/3 (log z) (log (+ x y))) 3))
1.0ms	(fma 2/3 (log z) (log (+ x y)))
1.0ms	(cbrt z)
2.0ms	(pow (fma 2/3 (log z) (log (+ x y))) 3)

series670.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (pow (fma 2/3 (log z) (log (+ x y))) 3))
94.0ms	(fma 2/3 (log z) (log (+ x y)))
182.0ms	(cbrt z)
300.0ms	(pow (fma 2/3 (log z) (log (+ x y))) 3)

simplify168.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	206	518
1	670	482
2	4409	466
3	5002	466

prune365.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes668.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	31	15
1	31	15

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.8s	57213×	body	80	nan
484.0ms	8037×	body	80	valid