Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

sample39.0ms (0.2%)

Algorithm

1×

intervals

Results

22.0ms	100×	body	1280	valid
5.0ms	120×	body	80	valid
4.0ms	23×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	5×	body	160	valid

simplify22.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	442	12
1	442	12

prune6.0ms (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: 14.5b

Counts

2 → 1

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
1.9b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`times-frac`
6×	`pow1`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sqrt-prod` `flip--` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 53

Calls

3 calls:

7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
3.0ms	(/ 1.0 (hypot 1.0 x))

series36.0ms (0.2%)

Counts

3 → 9

Calls

3 calls:

18.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
13.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms	(/ 1.0 (hypot 1.0 x))

simplify56.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5548	714

prune148.0ms (0.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	59	3	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	3	63

Merged error: 14.0b

Counts

63 → 3

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ 0.5 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
1.5b	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
19×	`times-frac`
11×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
4×	`pow1`
3×	`diff-log` `distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `div-exp` `clear-num` `frac-sub` `flip--` `div-inv` `difference-of-squares`
1×	`+-commutative` `associate--l-` `flip3-+` `associate--l+` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 86

Calls

4 calls:

10.0ms	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))
3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 0.5 (hypot 1.0 x))

series29.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))
4.0ms	(/ 0.5 (hypot 1.0 x))
4.0ms	(/ 1.0 (hypot 1.0 x))

simplify64.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4939	1071
1	4939	1071

prune315.0ms (1.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	95	6	101

Merged error: 13.8b

Counts

101 → 6

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/ 0.5 (hypot 1.0 x))
0.0b	(log (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x))))
0.1b	(exp (log (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))))
1.5b	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

rewrite37.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`add-cube-cbrt`
14×	`log-prod`
12×	`times-frac`
9×	`distribute-lft-out--` `add-log-exp`
8×	`log-div`
7×	`add-exp-log` `exp-sum`
6×	`pow1` `flip3--` `frac-sub` `add-cbrt-cube` `flip--` `difference-of-squares`
4×	`exp-prod` `exp-diff`
3×	`diff-log` `associate-/r` `associate-/l`
2×	`sub-neg` `log-pow`
1×	`cbrt-undiv` `associate--l-` `frac-2neg` `div-exp` `rem-log-exp` `associate--l+` `clear-num` `div-inv` `rem-exp-log`

Counts

4 → 90

Calls

4 calls:

11.0ms	(exp (log (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))))
10.0ms	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))
9.0ms	(log (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x))))
3.0ms	(/ 0.5 (hypot 1.0 x))

series40.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(log (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x))))
6.0ms	(exp (log (- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))))
6.0ms	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))
4.0ms	(/ 0.5 (hypot 1.0 x))

simplify50.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5043	1326

prune583.0ms (3.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	103	5	108

Merged error: 13.8b

Counts

108 → 5

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (- 1.0 0.5) 3) (pow (/ 0.5 (hypot 1.0 x)) 3)) (+ (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (+ (/ 0.5 (hypot 1.0 x)) (- 1.0 0.5)))))
0.1b	(pow (/ 0.5 (hypot 1.0 x)) 3)
0.1b	(exp (log (/ (- (pow (- 1.0 0.5) 3) (pow (/ 0.5 (hypot 1.0 x)) 3)) (+ (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (+ (/ 0.5 (hypot 1.0 x)) (- 1.0 0.5)))))))
1.4b	(- (pow (- 1.0 0.5) 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

rewrite204.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

471×	`add-sqr-sqrt`
304×	`times-frac`
279×	`*-un-lft-identity`
208×	`frac-add`
192×	`difference-of-squares`
189×	`unpow-prod-down` `log-prod` `cube-prod` `exp-sum`
148×	`associate-/r/`
144×	`flip3--` `flip--`
136×	`frac-times`
104×	`distribute-lft-out--`
103×	`add-cube-cbrt`
100×	`associate-*r/`
81×	`sqr-pow`
52×	`associate-*l/`
37×	`associate-/l*`
34×	`flip3-+` `flip-+`
9×	`add-exp-log` `cube-div` `add-cbrt-cube`
8×	`difference-cubes`
6×	`pow1` `add-log-exp`
4×	`exp-prod` `frac-sub` `div-inv` `associate-/l/`
3×	`pow-unpow` `associate-/r*`
2×	`cbrt-undiv` `div-exp` `pow-exp` `rem-cube-cbrt`
1×	`cube-mult` `pow-to-exp` `sub-neg` `log-div` `pow-pow` `frac-2neg` `exp-diff` `diff-log` `unpow3` `div-sub` `clear-num` `log-pow` `rem-exp-log`

Counts

4 → 537

Calls

4 calls:

60.0ms	(exp (log (/ (- (pow (- 1.0 0.5) 3) (pow (/ 0.5 (hypot 1.0 x)) 3)) (+ (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (+ (/ 0.5 (hypot 1.0 x)) (- 1.0 0.5)))))))
54.0ms	(/ (- (pow (- 1.0 0.5) 3) (pow (/ 0.5 (hypot 1.0 x)) 3)) (+ (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (+ (/ 0.5 (hypot 1.0 x)) (- 1.0 0.5)))))
29.0ms	(- (pow (- 1.0 0.5) 3) (pow (/ 0.5 (hypot 1.0 x)) 3))
5.0ms	(pow (/ 0.5 (hypot 1.0 x)) 3)

series141.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(exp (log (/ (- (pow (- 1.0 0.5) 3) (pow (/ 0.5 (hypot 1.0 x)) 3)) (+ (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (+ (/ 0.5 (hypot 1.0 x)) (- 1.0 0.5)))))))
56.0ms	(/ (- (pow (- 1.0 0.5) 3) (pow (/ 0.5 (hypot 1.0 x)) 3)) (+ (* (- 1.0 0.5) (- 1.0 0.5)) (* (/ 0.5 (hypot 1.0 x)) (+ (/ 0.5 (hypot 1.0 x)) (- 1.0 0.5)))))
15.0ms	(- (pow (- 1.0 0.5) 3) (pow (/ 0.5 (hypot 1.0 x)) 3))
9.0ms	(pow (/ 0.5 (hypot 1.0 x)) 3)

simplify194.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

549 → 549

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5906	33884

prune12.7s (78.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	546	3	549
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	549	5	554

Merged error: 13.7b

Counts

554 → 5

regimes367.0ms (2.3%)

Accuracy

Total 0.3b remaining (1.7%)

Threshold costs 0.3b (1.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	106	62
1	106	62

end0.0ms (0%)

sample1.1s (6.7%)

Algorithm

1×

intervals

Results

642.0ms	2812×	body	1280	valid
169.0ms	4056×	body	80	valid
116.0ms	650×	body	640	valid
39.0ms	311×	body	320	valid
14.0ms	171×	body	160	valid

Details

analyze1.0ms (0%)

sample39.0ms (0.2%)

simplify22.0ms (0.1%)

prune6.0ms (0%)

localize8.0ms (0.1%)

rewrite14.0ms (0.1%)

series36.0ms (0.2%)

simplify56.0ms (0.3%)

prune148.0ms (0.9%)

localize16.0ms (0.1%)

rewrite21.0ms (0.1%)

series29.0ms (0.2%)

simplify64.0ms (0.4%)

prune315.0ms (1.9%)

localize19.0ms (0.1%)

rewrite37.0ms (0.2%)

series40.0ms (0.2%)

simplify50.0ms (0.3%)

prune583.0ms (3.6%)

localize26.0ms (0.2%)

rewrite204.0ms (1.3%)

series141.0ms (0.9%)

simplify194.0ms (1.2%)

prune12.7s (78.3%)

regimes367.0ms (2.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.1s (6.7%)

Profiling