Details

sample50.0ms

Algorithm

intervals

Results

33.0ms

441×

body

valid

simplify129.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	70	42
1	252	42
2	1059	42
3	4713	42
4	5001	42

prune5.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.1b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x))
0.1b	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.2b	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b	(sqrt PI)

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

267×	`add-sqr-sqrt`
181×	`associate-l`
147×	`unswap-sqr`
113×	`associate-r`
81×	`pow1`
79×	`add-exp-log` `add-cbrt-cube`
49×	`add-cube-cbrt` `*-un-lft-identity`
48×	`prod-exp` `cbrt-unprod`
33×	`times-frac`
27×	`pow-prod-down`
23×	`*-commutative`
22×	`pow-plus` `pow-prod-up`
19×	`swap-sqr`
18×	`associate-*l/`
8×	`cbrt-undiv` `div-exp`
6×	`associate-/r` `associate-/l`
4×	`pow2` `expm1-log1p-u` `pow3` `pow-sqr` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`frac-2neg` `clear-num` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 311

Calls

4 calls:

19.0ms	(* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x))
53.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
27.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms	(sqrt PI)

series156.0ms

Counts

4 → 10

Calls

4 calls:

33.0ms	(* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x))
71.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
51.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify62.0ms

Algorithm

egg-herbie

Counts

321 → 321

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1218	2645
1	5001	2050

prune998.0ms

Filtered

321 candidates to 184 candidates (57.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	319	2	321
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	319	3	322

Merged error: 0.1b

Counts

322 → 3

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x))
0.1b	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.2b	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b	(sqrt PI)

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

267×	`add-sqr-sqrt`
181×	`associate-l`
147×	`unswap-sqr`
113×	`associate-r`
81×	`pow1`
79×	`add-exp-log` `add-cbrt-cube`
49×	`add-cube-cbrt` `*-un-lft-identity`
48×	`prod-exp` `cbrt-unprod`
33×	`times-frac`
27×	`pow-prod-down`
23×	`*-commutative`
22×	`pow-plus` `pow-prod-up`
19×	`swap-sqr`
18×	`associate-*l/`
8×	`cbrt-undiv` `div-exp`
6×	`associate-/r` `associate-/l`
4×	`pow2` `expm1-log1p-u` `pow3` `pow-sqr` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`frac-2neg` `clear-num` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 311

Calls

4 calls:

16.0ms	(* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x))
56.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
23.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
3.0ms	(sqrt PI)

series155.0ms

Counts

4 → 10

Calls

4 calls:

30.0ms	(* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x))
68.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
56.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify62.0ms

Algorithm

egg-herbie

Counts

321 → 321

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1225	2641
1	5001	2038

prune1.1s

Filtered

321 candidates to 185 candidates (57.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	321	0	321
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	321	3	324

Merged error: 0.1b

Counts

324 → 3

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.2b	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b	(expm1 (log1p (sqrt PI)))
1.0b	(sqrt PI)

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

230×	`add-sqr-sqrt`
135×	`associate-l`
128×	`unswap-sqr`
104×	`associate-r`
70×	`add-exp-log` `add-cbrt-cube`
42×	`prod-exp` `cbrt-unprod`
41×	`add-cube-cbrt` `*-un-lft-identity`
34×	`pow1`
33×	`times-frac`
21×	`pow-prod-down`
18×	`associate-*l/`
16×	`*-commutative`
14×	`swap-sqr`
8×	`cbrt-undiv` `div-exp`
6×	`associate-/r` `associate-/l`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
3×	`sqrt-prod`
2×	`expm1-log1p` `frac-2neg` `clear-num` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `expm1-udef`

Counts

4 → 247

Calls

4 calls:

53.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
26.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms	(expm1 (log1p (sqrt PI)))
2.0ms	(sqrt PI)

series120.0ms

Counts

4 → 8

Calls

4 calls:

70.0ms	(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
50.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms	(expm1 (log1p (sqrt PI)))
0.0ms	(sqrt PI)

simplify54.0ms

Algorithm

egg-herbie

Counts

255 → 255

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1117	2268
1	5002	1795

prune885.0ms

Filtered

255 candidates to 155 candidates (60.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	254	1	255
Fresh	0	0	0
Picked	0	1	1
Done	1	1	2
Total	255	3	258

Merged error: 0.1b

Counts

258 → 3

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b	(expm1 (log1p (* (sqrt (sqrt PI)) (sqrt (sqrt PI)))))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
34×	`associate-r`
31×	`associate-l` `unswap-sqr`
25×	`add-exp-log` `add-cbrt-cube`
22×	`add-cube-cbrt` `*-un-lft-identity`
15×	`pow1` `times-frac`
12×	`prod-exp` `cbrt-unprod`
9×	`associate-*l/`
6×	`swap-sqr` `pow-prod-down` `sqrt-prod` `*-commutative`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/r` `associate-/l`
2×	`rem-sqrt-square` `expm1-log1p` `sqrt-pow1` `pow1/2`
1×	`frac-2neg` `clear-num` `div-inv` `expm1-udef`

Counts

4 → 129

Calls

4 calls:

24.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms	(expm1 (log1p (* (sqrt (sqrt PI)) (sqrt (sqrt PI)))))
2.0ms	(sqrt PI)
2.0ms	(sqrt PI)

series55.0ms

Counts

4 → 6

Calls

4 calls:

55.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms	(expm1 (log1p (* (sqrt (sqrt PI)) (sqrt (sqrt PI)))))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify73.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	469	794
1	2325	674
2	5001	656

prune514.0ms

Filtered

135 candidates to 88 candidates (65.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	135	3	138

Merged error: 0.1b

Counts

138 → 3

regimes154.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	42
1	41	42

end0.0ms

sample1.1s

Algorithm

intervals

Results

912.0ms

13883×

body

valid