Details

sample72.0ms

Algorithm

intervals

Results

33.0ms	63×	body	1280	valid
15.0ms	53×	body	640	valid
7.0ms	22×	body	2560	valid
4.0ms	27×	body	320	valid
3.0ms	74×	body	80	valid
2.0ms	17×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	5
1	10	5

prune2.0ms

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: 52.5b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.4b	(+ x (sqrt (+ (* x x) 1.0)))
5.0b	(log (+ x (sqrt (+ (* x x) 1.0))))
14.2b	(sqrt (+ (* x x) 1.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `log-prod`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow` `hypot-def`

Counts

3 → 52

Calls

3 calls:

6.0ms	(+ x (sqrt (+ (* x x) 1.0)))
6.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))

series287.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(+ x (sqrt (+ (* x x) 1.0)))
181.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
49.0ms	(sqrt (+ (* x x) 1.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	331	423
1	1121	385
2	5002	366

prune155.0ms

Filtered

61 candidates to 55 candidates (90.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	57	4	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	4	62

Merged error: 0b

Counts

62 → 4

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.1b	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
220×	`associate-r`
184×	`add-sqr-sqrt`
140×	`unpow-prod-down` `cube-prod`
126×	`*-un-lft-identity`
120×	`add-cube-cbrt`
80×	`sqrt-prod`
40×	`sqr-pow`
30×	`cube-mult` `unpow3`
25×	`add-exp-log` `unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
7×	`add-cbrt-cube`
6×	`pow1` `pow-to-exp` `pow-exp` `add-log-exp`
5×	`fma-neg` `prod-diff`
4×	`distribute-lft-out`
3×	`associate-r/` `associate-l*`
2×	`expm1-log1p-u` `diff-log` `log-pow` `frac-sub` `cbrt-unprod` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `flip3--` `flip3-+` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `flip--` `flip-+` `div-inv`

Counts

2 → 300

Calls

2 calls:

13.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
55.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series317.0ms

Counts

2 → 6

Calls

2 calls:

167.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
149.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify122.0ms

Algorithm

egg-herbie

Counts

306 → 306

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	888	2291
1	4768	1819
2	5001	1795

prune395.0ms

Filtered

306 candidates to 121 candidates (39.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	306	0	306
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	306	4	310

Merged error: 0b

Counts

310 → 4

localize6.0ms

Local error

Found 2 expressions with local error:

0.4b	(+ x (hypot x (sqrt 1.0)))
5.0b	(log (+ x (hypot x (sqrt 1.0))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity`
4×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod` `add-log-exp`
3×	`pow1` `add-exp-log` `fma-def`
2×	`expm1-log1p-u` `log-div` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `rem-log-exp` `sum-log` `log-pow`

Counts

2 → 34

Calls

2 calls:

3.0ms	(+ x (hypot x (sqrt 1.0)))
3.0ms	(log (+ x (hypot x (sqrt 1.0))))

series442.0ms

Counts

2 → 6

Calls

2 calls:

134.0ms	(+ x (hypot x (sqrt 1.0)))
308.0ms	(log (+ x (hypot x (sqrt 1.0))))

simplify80.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	238	284
1	786	255
2	3259	247
3	5001	245

prune91.0ms

Filtered

40 candidates to 33 candidates (82.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	40	4	44

Merged error: 0b

Counts

44 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 0.0625) (pow x 5))
0.3b	(/ 0.125 (pow x 3))
9.7b	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
19.0b	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite491.0ms

Algorithm

rewrite-expression-head

Rules

2802×	`times-frac`
2496×	`add-sqr-sqrt`
1944×	`*-un-lft-identity`
1522×	`prod-diff`
1510×	`add-cube-cbrt`
965×	`associate--r+`
652×	`unpow-prod-down`
339×	`distribute-rgt-neg-in`
330×	`difference-of-squares`
297×	`distribute-lft-neg-in`
272×	`sqr-pow`
149×	`cube-prod`
134×	`distribute-lft-out--`
104×	`div-inv`
99×	`neg-mul-1`
49×	`cube-mult` `unpow3`
40×	`fma-neg`
19×	`associate-/r*`
15×	`add-exp-log`
13×	`associate-/l*`
12×	`log-prod`
9×	`add-log-exp`
8×	`frac-sub` `add-cbrt-cube`
6×	`div-exp`
5×	`pow1` `log-div`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `sub-neg` `frac-2neg` `div-sub` `pow-exp` `clear-num` `associate--r-`
1×	`distribute-frac-neg` `rem-log-exp` `log-pow`

Counts

4 → 1793

Calls

4 calls:

7.0ms	(/ (- 0.0625) (pow x 5))
5.0ms	(/ 0.125 (pow x 3))
91.0ms	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
166.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series355.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (- 0.0625) (pow x 5))
37.0ms	(/ 0.125 (pow x 3))
197.0ms	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
63.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify442.0ms

Algorithm

egg-herbie

Counts

1805 → 1805

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5002	48078

prune6.2s

Filtered

1805 candidates to 1216 candidates (67.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	1805	0	1805
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	1805	4	1809

Merged error: 0b

Counts

1809 → 4

regimes32.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.8b

bsearch99.0ms

Steps

Iters	Range		Point
10	8.416769919470913e-17	1.2368608357549227	0.0010088757425599948
11	-55383.34621353126	-7.66540900750845e-16	-1.0204783204586885

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	24
1	39	24

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.0s	2303×	body	1280	valid
425.0ms	1511×	body	640	valid
280.0ms	829×	body	2560	valid
124.0ms	766×	body	320	valid
90.0ms	2159×	body	80	valid
42.0ms	432×	body	160	valid