Details

sample144.0ms

Algorithm

intervals

Results

67.0ms	819×	body	80	nan
18.0ms	195×	body	80	valid
10.0ms	21×	body	640	valid
7.0ms	8×	body	1280	valid
5.0ms	16×	body	320	valid
3.0ms	17×	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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.5b

localize12.0ms

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)
0.2b	(* (- x 1.0) (log y))
5.6b	(log (- 1.0 y))

rewrite73.0ms

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:

15.0ms	(* (- z 1.0) (log (- 1.0 y)))
40.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
11.0ms	(* (- x 1.0) (log y))
3.0ms	(log (- 1.0 y))

series299.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (- z 1.0) (log (- 1.0 y)))
156.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
58.0ms	(* (- x 1.0) (log y))
43.0ms	(log (- 1.0 y))

simplify59.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (48.0ms)

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

prune372.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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))))))
0.0b	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.2b	(* (- x 1.0) (log y))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-sqr-sqrt`
85×	`*-un-lft-identity`
80×	`times-frac`
78×	`add-cube-cbrt` `associate-r`
56×	`unpow-prod-down`
48×	`prod-diff`
40×	`distribute-rgt-in` `distribute-lft-in`
34×	`associate-+r+`
31×	`add-exp-log`
27×	`flip3--` `flip--`
24×	`pow1` `log-prod` `associate-*l/` `unpow2` `sqr-pow`
19×	`unswap-sqr`
16×	`frac-add`
14×	`log-pow`
13×	`associate-l` `add-cbrt-cube`
12×	`frac-times` `prod-exp` `associate--l+`
9×	`div-exp`
7×	`associate-*r/`
6×	`pow-to-exp` `associate-+l+` `pow-exp` `add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--`
3×	`pow-prod-down` `*-commutative` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+` `div-inv`

Counts

4 → 280

Calls

4 calls:

25.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
38.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
19.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
11.0ms	(* (- x 1.0) (log y))

series322.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
67.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
150.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
54.0ms	(* (- x 1.0) (log y))

simplify74.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1523	4441
1	5002	3593

prune1.1s

Pruning

7 alts after pruning (7 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	(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.2b	(* (- x 1.0) (log y))
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)))))))

rewrite160.0ms

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:

3.0ms	(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
46.0ms	(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
11.0ms	(* (- x 1.0) (log y))
89.0ms	(* (* (- 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)))))))

series572.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
162.0ms	(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
62.0ms	(* (- x 1.0) (log y))
285.0ms	(* (* (- 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)))))))

simplify101.0ms

Algorithm

egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1257	9614
1	5002	7109

prune939.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt y) (cbrt y))
0.7b	(cbrt y)
0.7b	(cbrt y)
0.7b	(cbrt y)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

5.0ms	(* (cbrt y) (cbrt y))
0.0ms	(cbrt y)
0.0ms	(cbrt y)
1.0ms	(cbrt y)

series737.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(* (cbrt y) (cbrt y))
175.0ms	(cbrt y)
181.0ms	(cbrt y)
178.0ms	(cbrt y)

simplify85.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (80.0ms)

Iter	Nodes	Cost
0	119	308
1	477	281
2	2972	258
3	5001	255

prune473.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes254.0ms

Accuracy

0% (0.3b 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	42	23
1	42	23

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.9s	24353×	body	80	nan
525.0ms	5853×	body	80	valid
359.0ms	817×	body	640	valid
191.0ms	245×	body	1280	valid
189.0ms	660×	body	320	valid
86.0ms	464×	body	160	valid