Details

analyze1.1s (8.6%)

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

sample265.0ms (2%)

Algorithm

1×

intervals

Results

69.0ms	90×	body	1280	valid
60.0ms	95×	body	1280	nan
49.0ms	98×	body	640	valid
29.0ms	63×	body	640	nan
16.0ms	47×	body	320	nan
15.0ms	39×	body	320	valid
6.0ms	23×	body	160	valid
3.0ms	11×	body	160	nan
1.0ms	6×	body	80	valid

simplify447.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5009	37

prune11.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 61.8b

Counts

2 → 1

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(* (/ PI 4.0) f)
0.3b	(* (/ PI 4.0) f)
1.5b	(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
5.9b	(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

rewrite36.0ms (0.3%)

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:

11.0ms	(/ (+ (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)

series47.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
17.0ms	(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))
3.0ms	(* (/ PI 4.0) f)
3.0ms	(* (/ PI 4.0) f)

simplify76.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5270	3034

prune685.0ms (5.2%)

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: 2.6b

Counts

148 → 3

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(* PI (/ f 4.0))
0.4b	(* (/ 1.0 (/ PI 4.0)) (log (/ (cosh (* PI (/ f 4.0))) (sinh (* (/ PI 4.0) f)))))
0.5b	(log (/ (cosh (* PI (/ f 4.0))) (sinh (* (/ PI 4.0) f))))
1.7b	(/ (cosh (* PI (/ f 4.0))) (sinh (* (/ PI 4.0) f)))

rewrite40.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

115×	`times-frac`
91×	`add-sqr-sqrt`
77×	`add-cube-cbrt` `*-un-lft-identity`
47×	`associate-l`
42×	`log-prod`
23×	`add-exp-log`
20×	`add-cbrt-cube`
17×	`associate-r`
14×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow1`
9×	`div-inv`
6×	`div-exp`
5×	`cbrt-undiv` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
4×	`sinh-def` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`rem-log-exp` `pow-prod-down` `log-pow` `*-commutative`
1×	`log-div` `cosh-def` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/l/`

Counts

4 → 181

Calls

4 calls:

18.0ms	(* (/ 1.0 (/ PI 4.0)) (log (/ (cosh (* PI (/ f 4.0))) (sinh (* (/ PI 4.0) f)))))
7.0ms	(* PI (/ f 4.0))
5.0ms	(/ (cosh (* PI (/ f 4.0))) (sinh (* (/ PI 4.0) f)))
3.0ms	(log (/ (cosh (* PI (/ f 4.0))) (sinh (* (/ PI 4.0) f))))

series145.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (/ 1.0 (/ PI 4.0)) (log (/ (cosh (* PI (/ f 4.0))) (sinh (* (/ PI 4.0) f)))))
53.0ms	(log (/ (cosh (* PI (/ f 4.0))) (sinh (* (/ PI 4.0) f))))
31.0ms	(/ (cosh (* PI (/ f 4.0))) (sinh (* (/ PI 4.0) f)))
3.0ms	(* PI (/ f 4.0))

simplify51.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5086	4249

prune702.0ms (5.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	181	12	193
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	184	12	196

Merged error: 1.9b

Counts

196 → 12

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(* (neg (log (sqrt (sinh (* PI (/ f 4.0)))))) (* 4.0 (/ 1.0 PI)))
1.4b	(/ (cosh (* PI (/ f 4.0))) (sqrt (sinh (* PI (/ f 4.0)))))
1.5b	(log (sqrt (sinh (* PI (/ f 4.0)))))
1.5b	(log (/ (cosh (* PI (/ f 4.0))) (sqrt (sinh (* PI (/ f 4.0))))))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`times-frac`
29×	`log-prod`
24×	`sqrt-prod`
19×	`add-exp-log`
16×	`pow1` `associate-l`
15×	`add-cbrt-cube`
10×	`log-pow`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-/r*`
5×	`prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`sinh-def` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `rem-log-exp` `pow-prod-down` `associate-/l*`
2×	`cbrt-undiv` `log-div` `associate-*r/` `associate-/r/` `div-inv`
1×	`distribute-lft-neg-out` `neg-mul-1` `cosh-def` `frac-2neg` `associate-r` `clear-num` `*-commutative` `associate-/l/`

Counts

4 → 128

Calls

4 calls:

8.0ms	(* (neg (log (sqrt (sinh (* PI (/ f 4.0)))))) (* 4.0 (/ 1.0 PI)))
5.0ms	(/ (cosh (* PI (/ f 4.0))) (sqrt (sinh (* PI (/ f 4.0)))))
4.0ms	(log (/ (cosh (* PI (/ f 4.0))) (sqrt (sinh (* PI (/ f 4.0))))))
2.0ms	(log (sqrt (sinh (* PI (/ f 4.0)))))

series145.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

56.0ms	(log (/ (cosh (* PI (/ f 4.0))) (sqrt (sinh (* PI (/ f 4.0))))))
34.0ms	(* (neg (log (sqrt (sinh (* PI (/ f 4.0)))))) (* 4.0 (/ 1.0 PI)))
29.0ms	(/ (cosh (* PI (/ f 4.0))) (sqrt (sinh (* PI (/ f 4.0)))))
26.0ms	(log (sqrt (sinh (* PI (/ f 4.0)))))

simplify62.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4970	2814
1	4970	2814

prune696.0ms (5.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	141	11	152

Merged error: 1.9b

Counts

152 → 11

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(* PI (/ f 4.0))
0.3b	(/ (* (log (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))) 1.0) (/ PI 4.0))
0.5b	(log (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0)))))
1.7b	(/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`times-frac`
46×	`add-sqr-sqrt`
41×	`add-cube-cbrt` `*-un-lft-identity`
26×	`add-exp-log`
23×	`add-cbrt-cube`
16×	`associate-/r*`
14×	`log-prod`
13×	`associate-r`
9×	`div-exp`
8×	`cbrt-undiv`
7×	`pow1`
6×	`div-inv`
4×	`prod-exp` `cbrt-unprod` `associate-/l*` `add-log-exp`
3×	`associate-l` `associate-/r/`
2×	`sinh-def` `frac-2neg` `rem-log-exp` `clear-num` `unswap-sqr`
1×	`log-div` `cosh-def` `associate-r/` `pow-prod-down` `log-pow` `-commutative` `associate-/l/`

Counts

4 → 132

Calls

4 calls:

8.0ms	(* PI (/ f 4.0))
6.0ms	(/ (* (log (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))) 1.0) (/ PI 4.0))
4.0ms	(/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))
3.0ms	(log (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0)))))

series137.0ms (1%)

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (* (log (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))) 1.0) (/ PI 4.0))
49.0ms	(log (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0)))))
29.0ms	(/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))
3.0ms	(* PI (/ f 4.0))

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4966	2644
1	4966	2644

prune388.0ms (2.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	145	10	155

Merged error: 1.9b

Counts

155 → 10

regimes78.0ms (0.6%)

Accuracy

Total 0.4b remaining (24.7%)

Threshold costs 0.4b (24.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	29
1	62	29

end0.0ms (0%)

sample7.8s (59.5%)

Algorithm

1×

intervals

Results

2.3s	3383×	body	1280	valid
1.8s	2851×	body	1280	nan
1.2s	2438×	body	640	valid
1.1s	2369×	body	640	nan
459.0ms	1241×	body	320	valid
429.0ms	1246×	body	320	nan
175.0ms	673×	body	160	valid
51.0ms	212×	body	160	nan
35.0ms	265×	body	80	valid

Details

analyze1.1s (8.6%)

sample265.0ms (2%)

simplify447.0ms (3.4%)

prune11.0ms (0.1%)

localize26.0ms (0.2%)

rewrite36.0ms (0.3%)

series47.0ms (0.4%)

simplify76.0ms (0.6%)

prune685.0ms (5.2%)

localize16.0ms (0.1%)

rewrite40.0ms (0.3%)

series145.0ms (1.1%)

simplify51.0ms (0.4%)

prune702.0ms (5.3%)

localize24.0ms (0.2%)

rewrite24.0ms (0.2%)

series145.0ms (1.1%)

simplify62.0ms (0.5%)

prune696.0ms (5.3%)

localize14.0ms (0.1%)

rewrite26.0ms (0.2%)

series137.0ms (1%)

simplify68.0ms (0.5%)

prune388.0ms (2.9%)

regimes78.0ms (0.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample7.8s (59.5%)

Profiling