Details

sample30.0ms

Algorithm

intervals

Results

9.0ms	257×	body	80	valid
6.0ms	247×	body	80	nan

simplify78.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (10.0ms)

Iter	Nodes	Cost
0	21	6
1	63	6
2	212	6
3	725	5
4	1882	5
5	3231	5
6	4574	5
7	5001	5

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

66.0ms	(- (+ (- x (* (+ y 0.5) (log y))) y) z)
3.0ms	(- x (* (+ y 0.5) (log y)))
10.0ms	(+ (- x (* (+ y 0.5) (log y))) y)
11.0ms	(* (+ y 0.5) (log y))

series368.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (+ (- x (* (+ y 0.5) (log y))) y) z)
42.0ms	(- x (* (+ y 0.5) (log y)))
41.0ms	(+ (- x (* (+ y 0.5) (log y))) y)
234.0ms	(* (+ y 0.5) (log y))

simplify71.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	539	1002
1	2085	847
2	5002	829

prune306.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ x (fma (- (+ y 0.5)) (log y) y)) z)
0.0b	(+ x (fma (- (+ y 0.5)) (log y) y))
0.1b	(fma (- (+ y 0.5)) (log y) y)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `prod-diff`
10×	`add-log-exp`
6×	`distribute-lft-out`
4×	`fma-neg`
3×	`pow1` `add-exp-log` `expm1-log1p-u` `fma-def` `add-cbrt-cube` `log1p-expm1-u`
2×	`diff-log` `sum-log` `fma-udef` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `associate-+r+` `flip3--` `flip3-+` `associate--l+` `flip--` `flip-+` `difference-of-squares`

Counts

3 → 63

Calls

3 calls:

25.0ms	(- (+ x (fma (- (+ y 0.5)) (log y) y)) z)
3.0ms	(+ x (fma (- (+ y 0.5)) (log y) y))
0.0ms	(fma (- (+ y 0.5)) (log y) y)

series371.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(- (+ x (fma (- (+ y 0.5)) (log y) y)) z)
43.0ms	(+ x (fma (- (+ y 0.5)) (log y) y))
282.0ms	(fma (- (+ y 0.5)) (log y) y)

simplify38.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	305	659
1	941	532
2	5001	525

prune192.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (log (cbrt y)) (+ y 0.5))
0.2b	(- (fma (- (+ y 0.5)) (* 2 (log (cbrt y))) x) (* (log (cbrt y)) (+ y 0.5)))
0.6b	(cbrt y)
0.6b	(cbrt y)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-cube-cbrt`
7×	`pow1`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube` `add-log-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`fma-neg` `pow1/3` `prod-diff`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/` `log-pow` `associate--r+`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `fma-udef` `distribute-lft-out` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

10.0ms	(* (log (cbrt y)) (+ y 0.5))
3.0ms	(- (fma (- (+ y 0.5)) (* 2 (log (cbrt y))) x) (* (log (cbrt y)) (+ y 0.5)))
0.0ms	(cbrt y)
1.0ms	(cbrt y)

series939.0ms

Counts

4 → 12

Calls

4 calls:

443.0ms	(* (log (cbrt y)) (+ y 0.5))
137.0ms	(- (fma (- (+ y 0.5)) (* 2 (log (cbrt y))) x) (* (log (cbrt y)) (+ y 0.5)))
174.0ms	(cbrt y)
184.0ms	(cbrt y)

simplify50.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	334	658
1	1322	596
2	5002	567

prune328.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (log y) (+ y 0.5))
0.2b	(- (fma (- (+ y 0.5)) (* 2 (log (cbrt y))) x) (* 1/3 (* (log y) (+ y 0.5))))
0.3b	(* 1/3 (* (log y) (+ y 0.5)))
0.6b	(cbrt y)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1` `add-sqr-sqrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt`
9×	`distribute-rgt-in` `distribute-lft-in`
7×	`associate-l`
6×	`associate-*r/` `add-log-exp`
5×	`associate-r`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `associate--r+`
3×	`cbrt-prod` `fma-neg` `prod-diff`
2×	`flip3-+` `*-commutative` `flip-+`
1×	`sub-neg` `flip3--` `pow1/3` `diff-log` `associate--l+` `log-pow` `flip--` `fma-udef` `distribute-lft-out` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

14.0ms	(* (log y) (+ y 0.5))
3.0ms	(- (fma (- (+ y 0.5)) (* 2 (log (cbrt y))) x) (* 1/3 (* (log y) (+ y 0.5))))
12.0ms	(* 1/3 (* (log y) (+ y 0.5)))
1.0ms	(cbrt y)

series804.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(* (log y) (+ y 0.5))
125.0ms	(- (fma (- (+ y 0.5)) (* 2 (log (cbrt y))) x) (* 1/3 (* (log y) (+ y 0.5))))
260.0ms	(* 1/3 (* (log y) (+ y 0.5)))
175.0ms	(cbrt y)

simplify71.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	517	805
1	2100	708
2	5003	684

prune364.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes91.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	6
1	16	6
2	16	6

end0.0ms

sample818.0ms

Algorithm

intervals

Results

273.0ms	8035×	body	80	valid
218.0ms	8042×	body	80	nan
0.0ms	2×	body	640	valid
0.0ms	1×	body	1280	valid