Details

sample117.0ms

Algorithm

intervals

Results

48.0ms	764×	body	80	nan
14.0ms	198×	body	80	valid
7.0ms	18×	body	640	valid
6.0ms	8×	body	1280	valid
4.0ms	17×	body	320	valid
2.0ms	16×	body	160	valid

simplify71.0ms

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

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: 7.1b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.1b	(* (- x 1.0) (log y))
5.7b	(log (- 1.0 y))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

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

series278.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
46.0ms	(* (- z 1.0) (log (- 1.0 y)))
55.0ms	(* (- x 1.0) (log y))
47.0ms	(log (- 1.0 y))

simplify77.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	682	971
1	2728	901
2	5001	884

prune377.0ms

Filtered

130 candidates to 100 candidates (76.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	124	6	130
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	125	6	131

Merged error: 0.1b

Counts

131 → 6

localize20.0ms

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)))))))
0.1b	(* (- x 1.0) (log y))

rewrite71.0ms

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:

22.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
13.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
15.0ms	(+ (* (- x 1.0) (log y)) (* (- 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))

series324.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
66.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
151.0ms	(+ (* (- 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))

simplify73.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1523	4441
1	5002	3593

prune944.0ms

Filtered

292 candidates to 186 candidates (63.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	287	5	292
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	290	8	298

Merged error: 0.1b

Counts

298 → 8

localize32.0ms

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)

rewrite11.0ms

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)

series766.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(* (cbrt y) (cbrt y))
208.0ms	(cbrt y)
191.0ms	(cbrt y)
177.0ms	(cbrt y)

simplify93.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (82.0ms)

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

prune449.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	93	8	101

Merged error: 0.1b

Counts

101 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- 1.0 y))
0.1b	(* (- x 1.0) (log y))
5.8b	(log (sqrt (- 1.0 y)))
5.8b	(log (sqrt (- 1.0 y)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

4.0ms	(sqrt (- 1.0 y))
7.0ms	(* (- x 1.0) (log y))
4.0ms	(log (sqrt (- 1.0 y)))
4.0ms	(log (sqrt (- 1.0 y)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (- 1.0 y))
58.0ms	(* (- x 1.0) (log y))
82.0ms	(log (sqrt (- 1.0 y)))
83.0ms	(log (sqrt (- 1.0 y)))

simplify36.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	345	624
1	1074	568
2	5002	539

prune307.0ms

Filtered

108 candidates to 79 candidates (73.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	108	8	116

Merged error: 0.1b

Counts

116 → 8

regimes366.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	15
1	28	15

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.6s	24440×	body	80	nan
423.0ms	5893×	body	80	valid
292.0ms	776×	body	640	valid
195.0ms	276×	body	1280	valid
152.0ms	643×	body	320	valid
65.0ms	443×	body	160	valid