Details

analyze270.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

sample64.0ms

Algorithm

intervals

Results

19.0ms	101×	body	2560	nan
16.0ms	76×	body	1280	nan
11.0ms	256×	body	80	valid
5.0ms	42×	body	640	nan
2.0ms	19×	body	320	nan
1.0ms	12×	body	160	nan
0.0ms	10×	body	80	nan

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4760	9
1	4760	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: 32.1b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
0.2b	(log (+ x (sqrt (- (* x x) 1.0))))
29.9b	(sqrt (- (* x x) 1.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

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))

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))

simplify50.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5146	615

prune102.0ms

Filtered

43 candidates to 52 candidates (-20.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	49	3	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	3	53

Merged error: 0.0b

Counts

53 → 3

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.2b	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.4b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`*-un-lft-identity` `sqrt-div`
9×	`associate-r`
8×	`pow1` `add-cube-cbrt`
7×	`associate-l`
6×	`add-exp-log`
5×	`flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
4×	`frac-times` `unswap-sqr`
3×	`log-prod` `flip3--` `pow-prod-down` `flip--`
2×	`log-div` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `difference-of-squares`
1×	`+-commutative` `sqrt-unprod` `rem-log-exp` `prod-exp` `sum-log` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

3 → 67

Calls

3 calls:

3.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
2.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
12.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series33.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
13.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
12.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify44.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5153	1255

prune177.0ms

Filtered

58 candidates to 76 candidates (-31.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	76	3	79

Merged error: 0.0b

Counts

79 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))
0.2b	(+ (log 2) (- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
0.2b	(/ 0.09375 (pow x 4))
0.9b	(/ 0.25 (* x x))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

14.0ms	(+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))
21.0ms	(+ (log 2) (- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
4.0ms	(/ 0.09375 (pow x 4))
5.0ms	(/ 0.25 (* x x))

series29.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))
13.0ms	(+ (log 2) (- (log x) (+ (/ 0.09375 (pow x 4)) (/ 0.25 (* x x)))))
4.0ms	(/ 0.09375 (pow x 4))
3.0ms	(/ 0.25 (* x x))

simplify65.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4931	1421
1	4931	1421

prune192.0ms

Filtered

80 candidates to 122 candidates (-52.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	122	3	125

Merged error: 0b

Counts

125 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 0.09375 (pow x 4))
0.5b	(cbrt (pow (+ (log x) (- (log 2) (+ (/ 0.25 (* x x)) (/ 0.09375 (pow x 4))))) 3))
0.7b	(pow (+ (log x) (- (log 2) (+ (/ 0.25 (* x x)) (/ 0.09375 (pow x 4))))) 3)
0.9b	(/ 0.25 (* x x))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

120×	`*-un-lft-identity`
56×	`distribute-lft-out`
41×	`pow1`
38×	`unpow-prod-down`
36×	`log-pow`
32×	`cbrt-prod` `distribute-lft-out--`
28×	`add-sqr-sqrt` `add-cube-cbrt`
26×	`cube-prod`
24×	`times-frac`
15×	`add-exp-log`
12×	`add-cbrt-cube`
8×	`associate-/r*`
6×	`associate-/l*` `sqr-pow`
5×	`div-exp`
4×	`cube-div` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow`
2×	`cube-mult` `pow-to-exp` `cbrt-div` `frac-2neg` `flip3-+` `unpow3` `pow-exp` `clear-num` `flip-+` `div-inv`
1×	`pow-pow` `pow1/3` `prod-exp` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 154

Calls

4 calls:

4.0ms	(/ 0.09375 (pow x 4))
23.0ms	(cbrt (pow (+ (log x) (- (log 2) (+ (/ 0.25 (* x x)) (/ 0.09375 (pow x 4))))) 3))
24.0ms	(pow (+ (log x) (- (log 2) (+ (/ 0.25 (* x x)) (/ 0.09375 (pow x 4))))) 3)
5.0ms	(/ 0.25 (* x x))

series44.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 0.09375 (pow x 4))
10.0ms	(cbrt (pow (+ (log x) (- (log 2) (+ (/ 0.25 (* x x)) (/ 0.09375 (pow x 4))))) 3))
26.0ms	(pow (+ (log x) (- (log 2) (+ (/ 0.25 (* x x)) (/ 0.09375 (pow x 4))))) 3)
3.0ms	(/ 0.25 (* x x))

simplify68.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4957	3248
1	4957	3248

prune255.0ms

Filtered

78 candidates to 166 candidates (-112.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	166	3	169

Merged error: 0b

Counts

169 → 3

regimes30.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	14
1	56	14

end0.0ms

sample1.8s

Algorithm

intervals

Results

592.0ms	2984×	body	2560	nan
393.0ms	2449×	body	1280	nan
348.0ms	8000×	body	80	valid
160.0ms	1227×	body	640	nan
65.0ms	649×	body	320	nan
21.0ms	311×	body	160	nan
11.0ms	329×	body	80	nan

Details

analyze270.0ms

sample64.0ms

simplify44.0ms

prune3.0ms

localize7.0ms

rewrite17.0ms

series18.0ms

simplify50.0ms

prune102.0ms

localize12.0ms

rewrite19.0ms

series33.0ms

simplify44.0ms

prune177.0ms

localize15.0ms

rewrite48.0ms

series29.0ms

simplify65.0ms

prune192.0ms

localize18.0ms

rewrite63.0ms

series44.0ms

simplify68.0ms

prune255.0ms

regimes30.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.8s

Profiling