Details

sample97.0ms

Algorithm

intervals

Results

37.0ms	844×	body	80	nan
9.0ms	31×	body	640	valid
9.0ms	184×	body	80	valid
6.0ms	11×	body	1280	valid
2.0ms	15×	body	320	valid
2.0ms	17×	body	160	valid

simplify26.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	22	7
1	38	6
2	53	6
3	61	6
4	78	6
5	110	6
6	175	6
7	284	6
8	363	6
9	392	6
10	476	6
11	476	6

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 9.3b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(* z (log (- 1.0 y)))
0.2b	(* x (log y))
6.7b	(log (- 1.0 y))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
21×	`log-prod`
18×	`*-un-lft-identity`
12×	`add-cube-cbrt`
10×	`pow1`
8×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `associate-r`
7×	`add-cbrt-cube`
6×	`associate-l`
3×	`expm1-log1p-u` `log-pow` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`log-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`flip3--` `rem-log-exp` `flip--`

Counts

3 → 76

Calls

3 calls:

6.0ms	(* z (log (- 1.0 y)))
4.0ms	(* x (log y))
4.0ms	(log (- 1.0 y))

series147.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(* z (log (- 1.0 y)))
36.0ms	(* x (log y))
45.0ms	(log (- 1.0 y))

simplify39.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	353	439
1	1262	387
2	5001	373

prune429.0ms

Filtered

85 candidates to 57 candidates (67.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	77	8	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	8	86

Merged error: 0.1b

Counts

86 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

118×	`add-sqr-sqrt`
81×	`*-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`
24×	`pow1` `log-prod` `unpow2` `sqr-pow`
19×	`unswap-sqr`
14×	`log-pow`
13×	`add-cbrt-cube`
12×	`prod-exp` `associate--l+`
9×	`div-exp` `associate-l`
6×	`pow-to-exp` `associate-+l+` `pow-exp` `add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `cbrt-unprod` `log1p-expm1-u`
3×	`associate-r/` `pow-prod-down` `-commutative`
2×	`distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `flip3--` `fma-def` `flip3-+` `sum-log` `flip--` `flip-+` `div-inv` `difference-of-squares`

Counts

4 → 252

Calls

4 calls:

11.0ms	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
20.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
10.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
4.0ms	(* x (log y))

series307.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
51.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
99.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
37.0ms	(* x (log y))

simplify127.0ms

Algorithm

egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	1032	3139
1	4195	2176
2	5001	2168

prune843.0ms

Filtered

264 candidates to 156 candidates (59.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	258	6	264
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	263	9	272

Merged error: 0.0b

Counts

272 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt y) (cbrt y))
0.7b	(cbrt y)
0.7b	(cbrt y)
0.7b	(cbrt y)

rewrite12.0ms

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:

6.0ms	(* (cbrt y) (cbrt y))
1.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series737.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(* (cbrt y) (cbrt y))
174.0ms	(cbrt y)
176.0ms	(cbrt y)
184.0ms	(cbrt y)

simplify91.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (85.0ms)

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

prune495.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	93	9	102

Merged error: 0.0b

Counts

102 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* x (log (pow (pow y 2/3) 1))) (fma (log (cbrt y)) x (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.2b	(* x (log (pow (pow y 2/3) 1)))
0.7b	(cbrt y)
5.9b	(pow y 2/3)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

44×	`log-prod`
43×	`unpow-prod-down`
23×	`add-sqr-sqrt`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
21×	`add-cube-cbrt` `*-un-lft-identity`
9×	`sqr-pow`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`cbrt-prod` `pow-unpow` `associate-l`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `pow-pow` `fma-def` `flip3-+` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `log-pow` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `unswap-sqr`

Counts

4 → 112

Calls

4 calls:

8.0ms	(+ (* x (log (pow (pow y 2/3) 1))) (fma (log (cbrt y)) x (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
7.0ms	(* x (log (pow (pow y 2/3) 1)))
1.0ms	(cbrt y)
2.0ms	(pow y 2/3)

series675.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(+ (* x (log (pow (pow y 2/3) 1))) (fma (log (cbrt y)) x (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
82.0ms	(* x (log (pow (pow y 2/3) 1)))
180.0ms	(cbrt y)
185.0ms	(pow y 2/3)

simplify64.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	478	1144
1	1820	995
2	5001	939

prune586.0ms

Filtered

124 candidates to 92 candidates (74.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	126	7	133

Merged error: 0.0b

Counts

133 → 7

regimes171.0ms

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	32	17
1	32	17

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.1s	24041×	body	80	nan
273.0ms	5540×	body	80	valid
263.0ms	894×	body	640	valid
227.0ms	389×	body	1280	valid
129.0ms	759×	body	320	valid
48.0ms	447×	body	160	valid