Details

sample100.0ms

Algorithm

intervals

Results

37.0ms	772×	body	80	nan
10.0ms	183×	body	80	valid
8.0ms	27×	body	640	valid
4.0ms	24×	body	320	valid
3.0ms	4×	body	1280	valid
2.0ms	18×	body	160	valid

simplify68.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.0b	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
0.1b	(* (- x 1.0) (log y))
4.8b	(log (- 1.0 y))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
21×	`log-prod`
20×	`add-cube-cbrt`
11×	`pow1`
10×	`associate-l`
9×	`add-exp-log` `prod-diff` `add-log-exp`
8×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `add-cbrt-cube`
6×	`distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `flip3--` `associate-*l/` `flip--` `log1p-expm1-u`
3×	`fma-neg` `log-pow`
2×	`log-div` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `rem-log-exp` `associate--l+` `sum-log`

Counts

4 → 114

Calls

4 calls:

9.0ms	(* (- z 1.0) (log (- 1.0 y)))
12.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
7.0ms	(* (- x 1.0) (log y))
4.0ms	(log (- 1.0 y))

series302.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (- z 1.0) (log (- 1.0 y)))
157.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
55.0ms	(* (- x 1.0) (log y))
47.0ms	(log (- 1.0 y))

simplify66.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	587	1089
1	2183	902
2	5001	886

prune391.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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))))))) t)
0.0b	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0b	(* (- 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))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt`
80×	`times-frac`
78×	`associate-r`
76×	`*-un-lft-identity`
67×	`add-cube-cbrt`
56×	`unpow-prod-down`
33×	`prod-diff`
31×	`add-exp-log`
24×	`unpow2` `sqr-pow`
20×	`distribute-rgt-in` `distribute-lft-in`
19×	`unswap-sqr`
18×	`pow1`
13×	`associate-l` `add-cbrt-cube`
12×	`log-prod` `prod-exp`
9×	`div-exp` `add-log-exp`
8×	`flip3--` `log-pow` `flip--`
7×	`associate--l+`
6×	`pow-to-exp` `pow-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `frac-times` `associate-*l/` `cbrt-unprod` `log1p-expm1-u` `difference-of-squares`
3×	`sub-neg` `fma-neg` `associate-r/` `pow-prod-down` `-commutative`
2×	`diff-log`
1×	`cbrt-undiv` `sum-log` `div-inv`

Counts

4 → 240

Calls

4 calls:

14.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
20.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
14.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
7.0ms	(* (- x 1.0) (log y))

series425.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
53.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
69.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
56.0ms	(* (- x 1.0) (log y))

simplify66.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1174	3396
1	5002	2459

prune860.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
0.1b	(* (- x 1.0) (log y))
0.1b	(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.4b	(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

105×	`sqrt-prod`
84×	`prod-diff`
81×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
64×	`add-cube-cbrt`
48×	`distribute-rgt-in` `distribute-lft-in`
32×	`frac-times`
29×	`pow1`
22×	`flip3--` `flip--`
20×	`associate-r`
18×	`associate-*l/`
15×	`log-pow`
13×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
11×	`associate-l`
10×	`associate-*r/`
6×	`log-prod` `difference-of-squares`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `distribute-lft-out`
2×	`sub-neg` `sqrt-div` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 224

Calls

4 calls:

4.0ms	(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
7.0ms	(* (- x 1.0) (log y))
14.0ms	(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
30.0ms	(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series548.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
54.0ms	(* (- x 1.0) (log y))
156.0ms	(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
269.0ms	(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify104.0ms

Algorithm

egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1257	9613
1	5002	7108

prune969.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

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)

rewrite29.0ms

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:

8.0ms	(* (- x 1.0) (log (cbrt y)))
14.0ms	(+ (* (* 2 (log (cbrt y))) (- x 1.0)) (* (- x 1.0) (log (cbrt y))))
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series773.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (- x 1.0) (log (cbrt y)))
295.0ms	(+ (* (* 2 (log (cbrt y))) (- x 1.0)) (* (- x 1.0) (log (cbrt y))))
181.0ms	(cbrt y)
178.0ms	(cbrt y)

simplify79.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (68.0ms)

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

prune742.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes448.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	28
1	34	28

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	23975×	body	80	nan
325.0ms	5915×	body	80	valid
228.0ms	726×	body	640	valid
172.0ms	279×	body	1280	valid
131.0ms	702×	body	320	valid
46.0ms	403×	body	160	valid