Details

sample120.0ms

Algorithm

intervals

Results

46.0ms	820×	body	80	nan
19.0ms	304×	body	80	valid
0.0ms	1×	body	320	valid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	39	10
1	111	8
2	464	8
3	1654	8
4	5001	8

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
0.0b	(+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i))
0.1b	(* (- b 0.5) (log c))
0.3b	(* x (log y))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

38×	`add-log-exp`
25×	`sum-log`
23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
18×	`log-prod`
16×	`add-cube-cbrt`
10×	`pow1`
9×	`distribute-rgt-in` `distribute-lft-in`
8×	`add-exp-log` `fma-def` `associate-r` `associate-l` `add-cbrt-cube`
6×	`associate-+r+` `associate-*l/`
4×	`expm1-log1p-u` `flip3-+` `frac-add` `flip-+` `log1p-expm1-u`
3×	`flip3--` `flip--` `distribute-lft-out`
2×	`+-commutative` `associate-+l+` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-lft-out--` `difference-of-squares`

Counts

4 → 111

Calls

4 calls:

300.0ms	(+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
1.2s	(+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i))
11.0ms	(* (- b 0.5) (log c))
4.0ms	(* x (log y))

series836.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c)))
508.0ms	(+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i))
57.0ms	(* (- b 0.5) (log c))
40.0ms	(* x (log y))

simplify71.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	678	1061
1	2790	964
2	5003	931

prune496.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x (log (cbrt y)))
0.3b	(+ (* x (* 2 (log (cbrt y)))) (* x (log (cbrt y))))
0.6b	(cbrt y)
0.6b	(cbrt y)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

48×	`log-prod`
36×	`distribute-rgt-in` `distribute-lft-in`
30×	`cbrt-prod`
26×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `associate-+l+` `*-un-lft-identity`
12×	`associate-+r+`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow1/3` `associate-l`
2×	`log-pow`
1×	`+-commutative` `fma-def` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 111

Calls

4 calls:

5.0ms	(* x (log (cbrt y)))
13.0ms	(+ (* x (* 2 (log (cbrt y)))) (* x (log (cbrt y))))
0.0ms	(cbrt y)
1.0ms	(cbrt y)

series538.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* x (log (cbrt y)))
99.0ms	(+ (* x (* 2 (log (cbrt y)))) (* x (log (cbrt y))))
172.0ms	(cbrt y)
176.0ms	(cbrt y)

simplify57.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	384	753
1	1636	640
2	5001	570

prune710.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x (* 2 (log (cbrt y))))
0.3b	(+ (* x (* 2 (log (cbrt y)))) (* x (log (pow (/ 1 y) -1/3))))
0.6b	(cbrt y)
4.9b	(pow (/ 1 y) -1/3)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

82×	`log-prod`
65×	`distribute-rgt-in` `distribute-lft-in`
46×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
39×	`unpow-prod-down`
34×	`associate-+r+`
27×	`cbrt-prod` `times-frac`
24×	`associate-+l+`
14×	`add-exp-log`
11×	`pow1`
9×	`add-cbrt-cube`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u`
3×	`pow-unpow` `pow-pow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `div-inv` `sqr-pow`
2×	`div-exp`
1×	`+-commutative` `pow-to-exp` `rec-exp` `pow-flip` `fma-def` `flip3-+` `pow1/3` `1-exp` `associate-r` `sum-log` `*-commutative` `flip-+` `distribute-lft-out` `inv-pow`

Counts

4 → 164

Calls

4 calls:

10.0ms	(* x (* 2 (log (cbrt y))))
20.0ms	(+ (* x (* 2 (log (cbrt y)))) (* x (log (pow (/ 1 y) -1/3))))
0.0ms	(cbrt y)
4.0ms	(pow (/ 1 y) -1/3)

series648.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* x (* 2 (log (cbrt y))))
186.0ms	(+ (* x (* 2 (log (cbrt y)))) (* x (log (pow (/ 1 y) -1/3))))
179.0ms	(cbrt y)
182.0ms	(pow (/ 1 y) -1/3)

simplify85.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	780	1312
1	2661	1156
2	5001	1100

prune987.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma x (* 2 (log (cbrt y))) (* x (log (pow (/ 1 y) -1/3))))
0.3b	(* x (log (pow (/ 1 y) -1/3)))
0.6b	(cbrt y)
4.9b	(pow (/ 1 y) -1/3)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

39×	`unpow-prod-down`
34×	`log-prod`
33×	`add-sqr-sqrt`
31×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
17×	`distribute-rgt-in` `distribute-lft-in`
11×	`add-exp-log`
8×	`pow1`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `associate-r` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow-unpow` `pow-pow` `associate-l` `div-inv` `sqr-pow`
2×	`div-exp`
1×	`pow-to-exp` `rec-exp` `pow-flip` `pow1/3` `1-exp` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `fma-udef` `inv-pow` `unswap-sqr`

Counts

4 → 112

Calls

4 calls:

0.0ms	(fma x (* 2 (log (cbrt y))) (* x (log (pow (/ 1 y) -1/3))))
13.0ms	(* x (log (pow (/ 1 y) -1/3)))
0.0ms	(cbrt y)
4.0ms	(pow (/ 1 y) -1/3)

series633.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(fma x (* 2 (log (cbrt y))) (* x (log (pow (/ 1 y) -1/3))))
82.0ms	(* x (log (pow (/ 1 y) -1/3)))
184.0ms	(cbrt y)
179.0ms	(pow (/ 1 y) -1/3)

simplify57.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	434	840
1	1787	732
2	5001	644

prune567.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes745.0ms

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	40	17
1	40	17

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.5s	27897×	body	80	nan
607.0ms	9211×	body	80	valid
1.0ms	2×	body	640	valid
0.0ms	1×	body	320	valid