Details

sample136.0ms

Algorithm

intervals

Results

60.0ms	744×	body	80	nan
17.0ms	191×	body	80	valid
13.0ms	29×	body	640	valid
8.0ms	9×	body	1280	valid
5.0ms	15×	body	320	valid
2.0ms	13×	body	160	valid

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	9
1	57	8
2	136	8
3	312	8
4	709	8
5	1629	8
6	3564	8
7	5001	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
0.1b	(* (- x 1.0) (log y))
4.3b	(log (- 1.0 y))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 83

Calls

3 calls:

14.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
11.0ms	(* (- x 1.0) (log y))
4.0ms	(log (- 1.0 y))

series223.0ms

Counts

3 → 9

Calls

3 calls:

122.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
58.0ms	(* (- x 1.0) (log y))
43.0ms	(log (- 1.0 y))

simplify59.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	606	705
1	2351	656
2	5001	650

prune323.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0b	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.1b	(* (- x 1.0) (log y))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
48×	`prod-diff`
43×	`add-cube-cbrt`
40×	`distribute-rgt-in` `distribute-lft-in`
34×	`associate-+r+`
27×	`flip3--` `flip--`
24×	`log-prod` `associate-*l/`
21×	`pow1`
16×	`frac-add`
14×	`log-pow`
12×	`frac-times` `associate--l+`
10×	`associate-r` `associate-l`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-+l+` `associate-*r/`
5×	`add-log-exp`
4×	`sub-neg` `distribute-lft-out--`
3×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+`

Counts

3 → 168

Calls

3 calls:

41.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
18.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
12.0ms	(* (- x 1.0) (log y))

series281.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
155.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
58.0ms	(* (- x 1.0) (log y))

simplify57.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1020	3793
1	5001	2864

prune697.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 1.0) (log (cbrt y)))
0.3b	(+ (* (* 2 (log (cbrt y))) (- x 1.0)) (* (- x 1.0) (log (cbrt y))))
0.6b	(cbrt y)
0.6b	(cbrt y)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

12.0ms	(* (- x 1.0) (log (cbrt y)))
17.0ms	(+ (* (* 2 (log (cbrt y))) (- x 1.0)) (* (- x 1.0) (log (cbrt y))))
0.0ms	(cbrt y)
1.0ms	(cbrt y)

series784.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* (- x 1.0) (log (cbrt y)))
297.0ms	(+ (* (* 2 (log (cbrt y))) (- x 1.0)) (* (- x 1.0) (log (cbrt y))))
182.0ms	(cbrt y)
176.0ms	(cbrt y)

simplify78.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	542	1129
1	2640	925
2	5002	878

prune767.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- x 1.0) 1/3)
0.3b	(* (* (- x 1.0) 1/3) (log y))
0.3b	(+ (* (* 2 (log (cbrt y))) (- x 1.0)) (* (* (- x 1.0) 1/3) (log y)))
0.6b	(cbrt y)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

10.0ms	(* (- x 1.0) 1/3)
16.0ms	(* (* (- x 1.0) 1/3) (log y))
17.0ms	(+ (* (* 2 (log (cbrt y))) (- x 1.0)) (* (* (- x 1.0) 1/3) (log y)))
1.0ms	(cbrt y)

series803.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (- x 1.0) 1/3)
66.0ms	(* (* (- x 1.0) 1/3) (log y))
469.0ms	(+ (* (* 2 (log (cbrt y))) (- x 1.0)) (* (* (- x 1.0) 1/3) (log y)))
180.0ms	(cbrt y)

simplify92.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	666	1091
1	3166	885
2	5002	843

prune715.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes268.0ms

Accuracy

0% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	15
1	28	15

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.9s	24078×	body	80	nan
533.0ms	5863×	body	80	valid
353.0ms	779×	body	640	valid
218.0ms	277×	body	1280	valid
202.0ms	691×	body	320	valid
79.0ms	421×	body	160	valid