Details

analyze260.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

sample76.0ms

Algorithm

intervals

Results

35.0ms	77×	body	1280	valid
12.0ms	49×	body	640	valid
9.0ms	27×	body	2560	valid
6.0ms	67×	body	80	valid
5.0ms	30×	body	320	valid
1.0ms	6×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	9
1	9	9

prune3.0ms

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: 54.8b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.6b	(+ x (sqrt (+ (* x x) 1.0)))
2.3b	(log (+ x (sqrt (+ (* x x) 1.0))))
16.3b	(sqrt (+ (* x x) 1.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`add-exp-log` `log-prod`
3×	`flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow`

Counts

3 → 42

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))

series17.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ x (sqrt (+ (* x x) 1.0)))
9.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
3.0ms	(sqrt (+ (* x x) 1.0))

simplify39.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5075	600

prune109.0ms

Filtered

42 candidates to 51 candidates (-21.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	4	52

Merged error: 0.0b

Counts

52 → 4

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

50×	`associate-l`
49×	`add-sqr-sqrt`
40×	`times-frac`
30×	`add-cube-cbrt` `*-un-lft-identity`
25×	`unpow-prod-down` `cube-prod`
20×	`sqrt-prod`
10×	`add-exp-log`
8×	`unswap-sqr`
4×	`prod-exp` `add-cbrt-cube` `add-log-exp`
3×	`associate-r`
2×	`pow1` `cube-div` `associate-*l/` `pow-exp` `div-inv` `sqr-pow`
1×	`+-commutative` `cube-mult` `pow-to-exp` `flip3-+` `unpow3` `div-exp` `frac-add` `sum-log` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 87

Calls

2 calls:

9.0ms	(+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) -1/6))
16.0ms	(* (pow (/ x (sqrt 1.0)) 3) -1/6)

series41.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) -1/6))
14.0ms	(* (pow (/ x (sqrt 1.0)) 3) -1/6)

simplify44.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5452	1007

prune170.0ms

Filtered

51 candidates to 93 candidates (-82.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	91	6	97

Merged error: 0.0b

Counts

97 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 0.0625 (pow x 5))
0.3b	(/ 0.125 (pow x 3))
11.2b	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
18.8b	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
71×	`times-frac`
68×	`*-un-lft-identity`
46×	`add-cube-cbrt`
26×	`unpow-prod-down`
19×	`associate-/r*`
15×	`add-exp-log`
14×	`cube-prod`
11×	`log-prod`
10×	`difference-of-squares` `sqr-pow`
9×	`add-log-exp`
8×	`add-cbrt-cube`
6×	`div-exp` `frac-sub` `associate-/l*` `distribute-lft-out--`
5×	`pow1` `log-div`
4×	`cube-mult` `unpow3` `distribute-lft-out`
2×	`cbrt-undiv` `pow-to-exp` `flip3--` `frac-2neg` `flip3-+` `diff-log` `frac-add` `pow-exp` `clear-num` `flip--` `flip-+` `div-inv`
1×	`sub-neg` `rem-log-exp` `sum-log` `log-pow` `associate--r+`

Counts

4 → 159

Calls

4 calls:

4.0ms	(/ 0.0625 (pow x 5))
5.0ms	(/ 0.125 (pow x 3))
35.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
36.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series22.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 0.0625 (pow x 5))
3.0ms	(/ 0.125 (pow x 3))
9.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
5.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify55.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5361	2493

prune504.0ms

Filtered

110 candidates to 171 candidates (-55.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	170	7	177

Merged error: 0.0b

Counts

177 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

11.2b	(log (* (* (cbrt (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))) (cbrt (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))) (cbrt (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))))
18.8b	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))
18.8b	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))
18.8b	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite268.0ms

Algorithm

rewrite-expression-head

Rules

540×	`cbrt-div`
333×	`frac-sub`
325×	`frac-times`
215×	`log-div`
111×	`flip3--` `flip3-+` `frac-add` `flip--` `flip-+`
65×	`associate-*l/`
43×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
35×	`associate-*r/`
24×	`pow1`
21×	`times-frac`
19×	`add-log-exp`
15×	`log-pow` `difference-of-squares`
10×	`add-exp-log`
9×	`pow1/3` `pow-prod-up` `distribute-lft-out--`
6×	`pow-plus` `diff-log` `distribute-lft-out`
5×	`pow-prod-down`
4×	`add-cube-cbrt` `add-cbrt-cube`
3×	`sub-neg` `unpow-prod-down` `cube-prod` `rem-log-exp` `prod-exp` `sum-log` `pow-sqr` `associate--r+` `sqr-pow`
2×	`pow2`
1×	`log-prod` `pow3`

Counts

4 → 313

Calls

4 calls:

128.0ms	(log (* (* (cbrt (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))) (cbrt (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))) (cbrt (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))))
34.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))
37.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))
35.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series32.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(log (* (* (cbrt (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))) (cbrt (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))) (cbrt (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))))
5.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))
5.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))
5.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify195.0ms

Algorithm

egg-herbie

Counts

325 → 325

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5025	27627

prune1.2s

Filtered

132 candidates to 325 candidates (-146.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	325	0	325
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	325	7	332

Merged error: 0.0b

Counts

332 → 7

regimes63.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 31.8b

bsearch30.0ms

Steps

Iters	Range		Point
10	0.00019317580626152485	2508181633839.384	0.9499057402908623
9	-23142.42908923746	-0.00041155687183893296	-1.0165679408165877

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	103	58
1	103	58

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	2361×	body	1280	valid
437.0ms	1549×	body	640	valid
265.0ms	803×	body	2560	valid
124.0ms	743×	body	320	valid
88.0ms	2119×	body	80	valid
42.0ms	425×	body	160	valid

Details

analyze260.0ms

sample76.0ms

simplify3.0ms

prune3.0ms

localize6.0ms

rewrite17.0ms

series17.0ms

simplify39.0ms

prune109.0ms

localize9.0ms

rewrite28.0ms

series41.0ms

simplify44.0ms

prune170.0ms

localize12.0ms

rewrite86.0ms

series22.0ms

simplify55.0ms

prune504.0ms

localize19.0ms

rewrite268.0ms

series32.0ms

simplify195.0ms

prune1.2s

regimes63.0ms

bsearch30.0ms

simplify2.0ms

end0.0ms

sample2.2s

Profiling