Details

analyze260.0ms (6.1%)

Algorithm

1×

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

sample74.0ms (1.7%)

Algorithm

1×

intervals

Results

35.0ms	79×	body	1280	valid
11.0ms	41×	body	640	valid
9.0ms	28×	body	2560	valid
9.0ms	33×	body	320	valid
3.0ms	67×	body	80	valid
1.0ms	8×	body	160	valid

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	9
1	9	9

prune5.0ms (0.1%)

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: 52.8b

Counts

2 → 1

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.6b	(+ x (sqrt (+ (* x x) 1.0)))
2.0b	(log (+ x (sqrt (+ (* x x) 1.0))))
15.1b	(sqrt (+ (* x x) 1.0))

rewrite16.0ms (0.4%)

Algorithm

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

series16.0ms (0.4%)

Counts

3 → 9

Calls

3 calls:

8.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms	(+ x (sqrt (+ (* x x) 1.0)))
4.0ms	(sqrt (+ (* x x) 1.0))

simplify40.0ms (1%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5075	600

prune122.0ms (2.9%)

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 (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`associate-r`
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`
6×	`add-log-exp`
4×	`prod-exp` `add-cbrt-cube`
3×	`cube-div` `associate-r/` `associate-l*`
2×	`pow1` `diff-log` `pow-exp` `frac-sub` `div-inv` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `flip3-+` `unpow3` `div-exp` `associate--l+` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+`

Counts

2 → 90

Calls

2 calls:

15.0ms	(* 1/6 (pow (/ x (sqrt 1.0)) 3))
14.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (pow (/ x (sqrt 1.0)) 3)))

series27.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

16.0ms	(* 1/6 (pow (/ x (sqrt 1.0)) 3))
11.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (pow (/ x (sqrt 1.0)) 3)))

simplify25.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	4998	1131
1	4998	1131

prune278.0ms (6.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	96	4	100

Merged error: 0.0b

Counts

100 → 4

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/ 0.125 (pow x 3))
0.2b	(/ 0.0625 (pow x 5))
11.9b	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
17.2b	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite83.0ms (2%)

Algorithm

1×	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:

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

series22.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

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))))
4.0ms	(/ 0.0625 (pow x 5))
3.0ms	(/ 0.125 (pow x 3))

simplify55.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5361	2493

prune439.0ms (10.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	171	4	175

Merged error: 0.0b

Counts

175 → 4

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ 0.5 x))
0.0b	(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
0.1b	(/ 0.125 (pow x 3))
10.2b	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite59.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity`
36×	`times-frac`
30×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`add-log-exp`
12×	`unpow-prod-down` `cube-prod` `associate-/r*`
10×	`add-exp-log`
9×	`distribute-lft-out`
6×	`log-prod` `add-cbrt-cube`
5×	`pow1` `sum-log`
4×	`cube-mult` `unpow3` `distribute-lft-out--` `sqr-pow`
3×	`flip3-+` `div-exp` `flip-+` `associate-/l*`
2×	`+-commutative` `log-div` `associate-+r+` `diff-log`
1×	`cbrt-undiv` `pow-to-exp` `associate-+r-` `sub-neg` `frac-2neg` `rem-log-exp` `pow-exp` `associate--l+` `clear-num` `log-pow` `div-inv`

Counts

4 → 113

Calls

4 calls:

22.0ms	(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
21.0ms	(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))
6.0ms	(+ x (/ 0.5 x))
5.0ms	(/ 0.125 (pow x 3))

series21.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

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

simplify46.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5055	1415

prune287.0ms (6.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	125	4	129

Merged error: 0.0b

Counts

129 → 4

regimes86.0ms (2%)

Accuracy

Total 0.2b remaining (76.1%)

Threshold costs 0.2b (76.1%)

bsearch41.0ms (1%)

Steps

Iters	Range		Point
9	0.00015376982843717858	26598.371815489856	0.8962476229902214
9	-157274.44498914763	-0.024100400356733092	-1.0076583790961935

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	117	55
1	117	55

end0.0ms (0%)

sample2.2s (51%)

Algorithm

1×

intervals

Results

1.1s	2328×	body	1280	valid
416.0ms	1492×	body	640	valid
273.0ms	813×	body	2560	valid
138.0ms	797×	body	320	valid
89.0ms	2187×	body	80	valid
39.0ms	383×	body	160	valid

Details

analyze260.0ms (6.1%)

sample74.0ms (1.7%)

simplify3.0ms (0.1%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

rewrite16.0ms (0.4%)

series16.0ms (0.4%)

simplify40.0ms (1%)

prune122.0ms (2.9%)

localize9.0ms (0.2%)

rewrite33.0ms (0.8%)

series27.0ms (0.6%)

simplify25.0ms (0.6%)

prune278.0ms (6.6%)

localize11.0ms (0.3%)

rewrite83.0ms (2%)

series22.0ms (0.5%)

simplify55.0ms (1.3%)

prune439.0ms (10.3%)

localize10.0ms (0.2%)

rewrite59.0ms (1.4%)

series21.0ms (0.5%)

simplify46.0ms (1.1%)

prune287.0ms (6.8%)

regimes86.0ms (2%)

bsearch41.0ms (1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample2.2s (51%)

Profiling