Details

analyze1.1s (6.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	75%	25%	3
0%	62.5%	37.5%	4
0%	56.2%	43.8%	5
3.1%	46.9%	50%	6
3.1%	45.3%	51.6%	7
3.1%	44.5%	52.4%	8
3.5%	44.1%	52.4%	9
3.7%	43.9%	52.4%	10
3.8%	43.8%	52.4%	11
3.8%	43.8%	52.4%	12
3.8%	43.8%	52.4%	13
3.8%	43.7%	52.4%	14

sample275.0ms (1.6%)

Algorithm

1×

intervals

Results

81.0ms	116×	body	1280	valid
63.0ms	96×	body	1280	nan
41.0ms	83×	body	640	valid
39.0ms	85×	body	640	nan
15.0ms	45×	body	320	nan
12.0ms	34×	body	320	valid
4.0ms	18×	body	160	valid
2.0ms	7×	body	160	nan
1.0ms	5×	body	80	valid

simplify456.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5009	37

prune9.0ms (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: 62.3b

Counts

2 → 1

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(* (/ PI 4.0) f)
0.3b	(* (/ PI 4.0) f)
1.2b	(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
4.8b	(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

rewrite36.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`*-un-lft-identity`
57×	`add-sqr-sqrt`
50×	`times-frac`
33×	`add-cube-cbrt`
26×	`associate-l`
16×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
7×	`sinh-undef` `cosh-undef` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
6×	`associate-r` `associate-/r*` `add-log-exp`
5×	`associate-/l*`
4×	`prod-exp` `cbrt-unprod` `unswap-sqr`
3×	`cbrt-undiv` `div-exp` `div-inv`
2×	`flip3--` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `flip3-+` `diff-log` `clear-num` `flip-+`

Counts

4 → 135

Calls

4 calls:

10.0ms	(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
7.0ms	(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))
6.0ms	(* (/ PI 4.0) f)
6.0ms	(* (/ PI 4.0) f)

series56.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
18.0ms	(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))
3.0ms	(* (/ PI 4.0) f)
3.0ms	(* (/ PI 4.0) f)

simplify66.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5270	3034

prune583.0ms (3.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	3	148

Merged error: 2.0b

Counts

148 → 3

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(* (/ PI 4.0) f)
0.3b	(* (/ PI 4.0) f)
0.4b	(* (/ 1.0 (/ PI 4.0)) (log (/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f)))))
1.4b	(/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f)))

rewrite43.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`times-frac`
97×	`add-sqr-sqrt`
78×	`add-cube-cbrt` `*-un-lft-identity`
70×	`associate-l`
28×	`log-prod`
25×	`add-exp-log` `add-cbrt-cube`
14×	`distribute-rgt-in` `distribute-lft-in`
11×	`pow1`
10×	`associate-r`
9×	`div-inv`
7×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`cbrt-undiv` `div-exp`
4×	`associate-/r/` `add-log-exp`
3×	`sinh-def` `pow-prod-down` `associate-l/` `associate-/r` `-commutative` `associate-/l`
1×	`cosh-def` `frac-2neg` `clear-num` `log-pow` `associate-/l/`

Counts

4 → 188

Calls

4 calls:

15.0ms	(* (/ 1.0 (/ PI 4.0)) (log (/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f)))))
7.0ms	(/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f)))
6.0ms	(* (/ PI 4.0) f)
6.0ms	(* (/ PI 4.0) f)

series107.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (/ 1.0 (/ PI 4.0)) (log (/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f)))))
34.0ms	(/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f)))
3.0ms	(* (/ PI 4.0) f)
3.0ms	(* (/ PI 4.0) f)

simplify60.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5002	3817

prune646.0ms (3.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	193	7	200
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	196	7	203

Merged error: 1.5b

Counts

203 → 7

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(* (/ PI 4.0) f)
0.3b	(* (log (/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f)))) (sqrt (/ 1.0 (/ PI 4.0))))
0.3b	(* (sqrt (/ 1.0 (/ PI 4.0))) (* (log (/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f)))) (sqrt (/ 1.0 (/ PI 4.0)))))
1.4b	(/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f)))

rewrite57.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

154×	`times-frac`
109×	`add-sqr-sqrt`
93×	`add-cube-cbrt` `*-un-lft-identity`
91×	`sqrt-prod`
64×	`associate-l`
51×	`associate-r`
18×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
10×	`div-inv`
6×	`prod-exp` `cbrt-unprod` `unswap-sqr`
5×	`sqrt-div` `pow-prod-down`
4×	`associate-*r/` `add-log-exp`
3×	`associate-/r` `associate-/r/` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `associate-*l/`
1×	`frac-times` `sinh-def` `cosh-def` `frac-2neg` `clear-num` `log-pow` `associate-/l/`

Counts

4 → 193

Calls

4 calls:

20.0ms	(* (sqrt (/ 1.0 (/ PI 4.0))) (* (log (/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f)))) (sqrt (/ 1.0 (/ PI 4.0)))))
16.0ms	(* (log (/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f)))) (sqrt (/ 1.0 (/ PI 4.0))))
6.0ms	(* (/ PI 4.0) f)
4.0ms	(/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f)))

series176.0ms (1%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (sqrt (/ 1.0 (/ PI 4.0))) (* (log (/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f)))) (sqrt (/ 1.0 (/ PI 4.0)))))
66.0ms	(* (log (/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f)))) (sqrt (/ 1.0 (/ PI 4.0))))
35.0ms	(/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f)))
4.0ms	(* (/ PI 4.0) f)

simplify77.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4967	4422
1	4967	4422

prune823.0ms (4.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	203	2	205
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	206	6	212

Merged error: 1.5b

Counts

212 → 6

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (/ 1.0 (/ PI 4.0))) (* (log (/ (/ (cosh (* (/ PI 4.0) f)) (sqrt (sinh (* (/ PI 4.0) f)))) (sqrt (sinh (* (/ PI 4.0) f))))) (sqrt (/ 1.0 (/ PI 4.0)))))
1.3b	(log (/ (/ (cosh (* (/ PI 4.0) f)) (sqrt (sinh (* (/ PI 4.0) f)))) (sqrt (sinh (* (/ PI 4.0) f)))))
1.3b	(/ (cosh (* (/ PI 4.0) f)) (sqrt (sinh (* (/ PI 4.0) f))))
1.6b	(/ (/ (cosh (* (/ PI 4.0) f)) (sqrt (sinh (* (/ PI 4.0) f)))) (sqrt (sinh (* (/ PI 4.0) f))))

rewrite86.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

594×	`times-frac`
319×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
314×	`sqrt-prod`
143×	`log-prod`
47×	`associate-l`
26×	`associate-/l*`
22×	`add-exp-log`
20×	`sqrt-div` `div-inv`
17×	`associate-/r/`
16×	`sinh-def` `add-cbrt-cube`
12×	`associate-/r*`
10×	`pow1`
7×	`div-exp`
4×	`cbrt-undiv` `add-log-exp`
3×	`associate-*r/` `rem-log-exp` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `log-div` `cosh-def` `associate-r` `associate-l/` `log-pow` `-commutative`

Counts

4 → 444

Calls

4 calls:

21.0ms	(* (sqrt (/ 1.0 (/ PI 4.0))) (* (log (/ (/ (cosh (* (/ PI 4.0) f)) (sqrt (sinh (* (/ PI 4.0) f)))) (sqrt (sinh (* (/ PI 4.0) f))))) (sqrt (/ 1.0 (/ PI 4.0)))))
14.0ms	(log (/ (/ (cosh (* (/ PI 4.0) f)) (sqrt (sinh (* (/ PI 4.0) f)))) (sqrt (sinh (* (/ PI 4.0) f)))))
13.0ms	(/ (/ (cosh (* (/ PI 4.0) f)) (sqrt (sinh (* (/ PI 4.0) f)))) (sqrt (sinh (* (/ PI 4.0) f))))
5.0ms	(/ (cosh (* (/ PI 4.0) f)) (sqrt (sinh (* (/ PI 4.0) f))))

series193.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (sqrt (/ 1.0 (/ PI 4.0))) (* (log (/ (/ (cosh (* (/ PI 4.0) f)) (sqrt (sinh (* (/ PI 4.0) f)))) (sqrt (sinh (* (/ PI 4.0) f))))) (sqrt (/ 1.0 (/ PI 4.0)))))
51.0ms	(log (/ (/ (cosh (* (/ PI 4.0) f)) (sqrt (sinh (* (/ PI 4.0) f)))) (sqrt (sinh (* (/ PI 4.0) f)))))
39.0ms	(/ (cosh (* (/ PI 4.0) f)) (sqrt (sinh (* (/ PI 4.0) f))))
32.0ms	(/ (/ (cosh (* (/ PI 4.0) f)) (sqrt (sinh (* (/ PI 4.0) f)))) (sqrt (sinh (* (/ PI 4.0) f))))

simplify126.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

456 → 456

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4970	15664
1	4970	15664

prune3.8s (22.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	453	3	456
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	454	8	462

Merged error: 1.5b

Counts

462 → 8

regimes135.0ms (0.8%)

Accuracy

Total 0.5b remaining (25.4%)

Threshold costs 0.5b (25.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	30
1	47	30

end0.0ms (0%)

sample7.8s (46.4%)

Algorithm

1×

intervals

Results

2.4s	3529×	body	1280	valid
1.8s	2946×	body	1280	nan
1.2s	2385×	body	640	valid
1.1s	2443×	body	640	nan
431.0ms	1201×	body	320	valid
404.0ms	1227×	body	320	nan
161.0ms	640×	body	160	valid
56.0ms	231×	body	160	nan
31.0ms	245×	body	80	valid
1.0ms	5×	body	80	overflowed

Details

analyze1.1s (6.7%)

sample275.0ms (1.6%)

simplify456.0ms (2.7%)

prune9.0ms (0.1%)

localize18.0ms (0.1%)

rewrite36.0ms (0.2%)

series56.0ms (0.3%)

simplify66.0ms (0.4%)

prune583.0ms (3.5%)

localize13.0ms (0.1%)

rewrite43.0ms (0.3%)

series107.0ms (0.6%)

simplify60.0ms (0.4%)

prune646.0ms (3.8%)

localize18.0ms (0.1%)

rewrite57.0ms (0.3%)

series176.0ms (1%)

simplify77.0ms (0.5%)

prune823.0ms (4.9%)

localize18.0ms (0.1%)

rewrite86.0ms (0.5%)

series193.0ms (1.1%)

simplify126.0ms (0.7%)

prune3.8s (22.6%)

regimes135.0ms (0.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample7.8s (46.4%)

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