Details

analyze276.0ms

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

sample78.0ms

Algorithm

intervals

Results

38.0ms	76×	body	1280	valid
16.0ms	59×	body	640	valid
10.0ms	28×	body	2560	valid
3.0ms	19×	body	320	valid
3.0ms	64×	body	80	valid
1.0ms	10×	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: 53.4b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.6b	(+ x (sqrt (+ (* x x) 1.0)))
1.7b	(log (+ x (sqrt (+ (* x x) 1.0))))
15.4b	(sqrt (+ (* x x) 1.0))

rewrite20.0ms

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

series18.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ x (sqrt (+ (* x x) 1.0)))
9.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))

simplify41.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5075	600

prune121.0ms

Filtered

42 candidates to 51 candidates (-21.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	46	5	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	5	52

Merged error: 0.0b

Counts

52 → 5

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 75

Calls

1 calls:

14.0ms

(* (pow (/ x (sqrt 1.0)) 3) -1/6)

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

(* (pow (/ x (sqrt 1.0)) 3) -1/6)

simplify41.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4973	758
1	4973	758

prune136.0ms

Filtered

40 candidates to 78 candidates (-95.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	78	5	83

Merged error: 0.0b

Counts

83 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 0.125 (pow x 3))
0.3b	(/ 0.0625 (pow x 5))
11.9b	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
20.4b	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite90.0ms

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:

5.0ms	(/ 0.125 (pow x 3))
4.0ms	(/ 0.0625 (pow x 5))
34.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
40.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series27.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 0.125 (pow x 3))
4.0ms	(/ 0.0625 (pow x 5))
13.0ms	(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))))

simplify59.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5361	2493

prune316.0ms

Filtered

110 candidates to 171 candidates (-55.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	171	5	176

Merged error: 0.0b

Counts

176 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow x 4) (* 0.5 0.5))
0.4b	(/ 0.125 (pow x 4))
0.7b	(/ 0.25 (* x x))
9.4b	(+ (/ 0.125 (pow x 4)) (- (log (/ -1 x)) (+ (/ 0.25 (* x x)) (/ 0.0078125 (* (pow x 4) (* 0.5 0.5))))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity`
33×	`add-sqr-sqrt` `times-frac`
31×	`add-cube-cbrt`
27×	`add-exp-log`
16×	`unpow-prod-down` `add-cbrt-cube`
14×	`associate-+r+`
13×	`log-prod` `associate--l+`
11×	`add-log-exp`
10×	`prod-exp`
8×	`associate-/r*`
7×	`associate-l` `distribute-lft-out`
6×	`pow1` `associate-/l*` `sqr-pow`
5×	`div-exp`
4×	`sum-log` `cbrt-unprod` `distribute-lft-out--`
3×	`cbrt-undiv` `pow-to-exp` `pow-exp` `div-inv` `unswap-sqr`
2×	`frac-2neg` `diff-log` `frac-add` `clear-num` `log-pow`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3--` `flip3-+` `associate-r` `*-commutative` `flip--` `flip-+`

Counts

4 → 128

Calls

4 calls:

7.0ms	(* (pow x 4) (* 0.5 0.5))
4.0ms	(/ 0.125 (pow x 4))
6.0ms	(/ 0.25 (* x x))
29.0ms	(+ (/ 0.125 (pow x 4)) (- (log (/ -1 x)) (+ (/ 0.25 (* x x)) (/ 0.0078125 (* (pow x 4) (* 0.5 0.5))))))

series18.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (pow x 4) (* 0.5 0.5))
4.0ms	(/ 0.125 (pow x 4))
3.0ms	(/ 0.25 (* x x))
8.0ms	(+ (/ 0.125 (pow x 4)) (- (log (/ -1 x)) (+ (/ 0.25 (* x x)) (/ 0.0078125 (* (pow x 4) (* 0.5 0.5))))))

simplify32.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5012	1804

prune303.0ms

Filtered

92 candidates to 140 candidates (-52.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	140	5	145

Merged error: 0.0b

Counts

145 → 5

regimes49.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.9b

bsearch31.0ms

Steps

Iters	Range		Point
10	7.063849918137196e-08	1234859807.5445511	0.8842132773950566
8	-114.9517686598657	-0.020051319480660194	-1.0264810884786884

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	94	55
1	94	55

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.1s	2400×	body	1280	valid
452.0ms	1577×	body	640	valid
271.0ms	792×	body	2560	valid
131.0ms	760×	body	320	valid
94.0ms	2056×	body	80	valid
43.0ms	415×	body	160	valid

Details

analyze276.0ms

sample78.0ms

simplify3.0ms

prune3.0ms

localize7.0ms

rewrite20.0ms

series18.0ms

simplify41.0ms

prune121.0ms

localize9.0ms

rewrite18.0ms

series19.0ms

simplify41.0ms

prune136.0ms

localize13.0ms

rewrite90.0ms

series27.0ms

simplify59.0ms

prune316.0ms

localize19.0ms

rewrite52.0ms

series18.0ms

simplify32.0ms

prune303.0ms

regimes49.0ms

bsearch31.0ms

simplify2.0ms

end0.0ms

sample2.3s

Profiling