Details

analyze1.1s

Algorithm

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

sample256.0ms

Algorithm

intervals

Results

69.0ms	102×	body	1280	valid
60.0ms	93×	body	1280	nan
44.0ms	88×	body	640	valid
29.0ms	65×	body	640	nan
16.0ms	45×	body	320	valid
13.0ms	40×	body	320	nan
6.0ms	18×	body	160	valid
2.0ms	9×	body	160	nan
0.0ms	3×	body	80	valid

simplify458.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5009	37

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 63.2b

Counts

2 → 1

localize17.0ms

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)))))
4.9b	(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

rewrite49.0ms

Algorithm

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:

6.0ms	(* (/ PI 4.0) f)
6.0ms	(* (/ PI 4.0) f)
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))))

series47.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (/ PI 4.0) f)
3.0ms	(* (/ PI 4.0) f)
23.0ms	(/ (+ (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))))

simplify70.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5270	3034

prune523.0ms

Filtered

117 candidates to 147 candidates (-25.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	147	1	148

Merged error: 1.7b

Counts

148 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI (/ f 4.0))
0.3b	(* (/ PI 4.0) f)
0.4b	(* (/ 1.0 (/ PI 4.0)) (log (/ (cosh (* PI (/ f 4.0))) (sinh (* (/ PI 4.0) f)))))
1.5b	(/ (cosh (* PI (/ f 4.0))) (sinh (* (/ PI 4.0) f)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

116×	`times-frac`
97×	`add-sqr-sqrt`
78×	`add-cube-cbrt` `*-un-lft-identity`
60×	`associate-l`
28×	`log-prod`
25×	`add-exp-log` `add-cbrt-cube`
20×	`associate-r`
14×	`distribute-rgt-in` `distribute-lft-in`
11×	`pow1`
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-/r` `-commutative` `associate-/l*`
2×	`associate-*l/`
1×	`cosh-def` `frac-2neg` `associate-*r/` `clear-num` `log-pow` `associate-/l/`

Counts

4 → 188

Calls

4 calls:

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

series98.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* PI (/ f 4.0))
3.0ms	(* (/ PI 4.0) f)
57.0ms	(* (/ 1.0 (/ PI 4.0)) (log (/ (cosh (* PI (/ f 4.0))) (sinh (* (/ PI 4.0) f)))))
35.0ms	(/ (cosh (* PI (/ f 4.0))) (sinh (* (/ PI 4.0) f)))

simplify80.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4975	3821
1	4975	3821

prune489.0ms

Filtered

157 candidates to 200 candidates (-27.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	193	7	200
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	194	7	201

Merged error: 1.2b

Counts

201 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (log (/ (sqrt (cosh (* PI (/ f 4.0)))) (sinh (* PI (/ f 4.0))))) (/ PI 4.0))
1.0b	(log (/ (sqrt (cosh (* PI (/ f 4.0)))) (sinh (* PI (/ f 4.0)))))
1.5b	(/ (sqrt (cosh (* PI (/ f 4.0)))) (sinh (* PI (/ f 4.0))))
2.6b	(log (sqrt (cosh (* PI (/ f 4.0)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

133×	`times-frac`
83×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
29×	`log-prod`
24×	`sqrt-prod`
21×	`pow1`
18×	`log-pow`
16×	`associate-/r*`
15×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`associate-/l*`
8×	`div-inv`
5×	`div-exp`
4×	`cbrt-undiv` `add-log-exp`
3×	`log-div` `rem-log-exp` `associate-/r/`
2×	`sinh-def` `cosh-def` `frac-2neg` `sqrt-div` `clear-num`
1×	`sqrt-pow1` `pow1/2` `div-sub` `associate-/l/`

Counts

4 → 178

Calls

4 calls:

9.0ms	(/ (log (/ (sqrt (cosh (* PI (/ f 4.0)))) (sinh (* PI (/ f 4.0))))) (/ PI 4.0))
4.0ms	(log (/ (sqrt (cosh (* PI (/ f 4.0)))) (sinh (* PI (/ f 4.0)))))
5.0ms	(/ (sqrt (cosh (* PI (/ f 4.0)))) (sinh (* PI (/ f 4.0))))
4.0ms	(log (sqrt (cosh (* PI (/ f 4.0)))))

series188.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (log (/ (sqrt (cosh (* PI (/ f 4.0)))) (sinh (* PI (/ f 4.0))))) (/ PI 4.0))
55.0ms	(log (/ (sqrt (cosh (* PI (/ f 4.0)))) (sinh (* PI (/ f 4.0)))))
37.0ms	(/ (sqrt (cosh (* PI (/ f 4.0)))) (sinh (* PI (/ f 4.0))))
28.0ms	(log (sqrt (cosh (* PI (/ f 4.0)))))

simplify71.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5700	4957

prune697.0ms

Filtered

136 candidates to 190 candidates (-39.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	190	7	197

Merged error: 1.2b

Counts

197 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))) (sqrt (* 4.0 (/ 1.0 PI))))
0.3b	(* PI (/ f 4.0))
0.3b	(* PI (/ f 4.0))
1.5b	(/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
30×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
29×	`times-frac`
18×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`associate-l`
5×	`prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`associate-*r/` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/r` `-commutative` `div-inv` `associate-/l*`
1×	`sinh-def` `cosh-def` `frac-2neg` `sqrt-div` `clear-num` `sqrt-prod` `associate-/r/` `log-pow` `associate-/l/`

Counts

4 → 114

Calls

4 calls:

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

series100.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (log (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))) (sqrt (* 4.0 (/ 1.0 PI))))
3.0ms	(* PI (/ f 4.0))
3.0ms	(* PI (/ f 4.0))
32.0ms	(/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))

simplify56.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4974	1703
1	4974	1703

prune309.0ms

Filtered

95 candidates to 126 candidates (-32.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	126	7	133

Merged error: 1.2b

Counts

133 → 7

regimes62.0ms

Accuracy

0% (0.4b remaining)

Error of 2.0b against oracle of 1.6b and baseline of 2.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	86	37
1	86	37

end0.0ms

sample7.7s

Algorithm

intervals

Results

2.3s	3397×	body	1280	valid
1.8s	2930×	body	1280	nan
1.2s	2534×	body	640	valid
1.1s	2407×	body	640	nan
432.0ms	1207×	body	320	valid
389.0ms	1193×	body	320	nan
156.0ms	620×	body	160	valid
62.0ms	281×	body	160	nan
30.0ms	242×	body	80	valid
0.0ms	1×	body	80	overflowed

Details

analyze1.1s

sample256.0ms

simplify458.0ms

prune10.0ms

localize17.0ms

rewrite49.0ms

series47.0ms

simplify70.0ms

prune523.0ms

localize17.0ms

rewrite40.0ms

series98.0ms

simplify80.0ms

prune489.0ms

localize18.0ms

rewrite29.0ms

series188.0ms

simplify71.0ms

prune697.0ms

localize17.0ms

rewrite27.0ms

series100.0ms

simplify56.0ms

prune309.0ms

regimes62.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample7.7s

Profiling