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

sample238.0ms

Algorithm

intervals

Results

70.0ms	96×	body	1280	valid
45.0ms	75×	body	1280	nan
42.0ms	87×	body	640	valid
33.0ms	74×	body	640	nan
15.0ms	43×	body	320	valid
10.0ms	31×	body	320	nan
5.0ms	21×	body	160	valid
2.0ms	7×	body	160	nan
1.0ms	9×	body	80	valid

simplify436.0ms

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: 61.4b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 4.0) f)
0.2b	(* (/ PI 4.0) f)
1.3b	(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
5.7b	(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

rewrite37.0ms

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)
7.0ms	(* (/ PI 4.0) f)
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))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (/ PI 4.0) f)
9.0ms	(* (/ PI 4.0) f)
24.0ms	(/ (+ (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))))

simplify71.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5270	3034

prune494.0ms

Filtered

117 candidates to 147 candidates (-25.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	146	2	148

Merged error: 1.7b

Counts

148 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI (/ f 4.0))
0.2b	(* (/ 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)))

rewrite44.0ms

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:

7.0ms	(* 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)
61.0ms	(* (/ 1.0 (/ PI 4.0)) (log (/ (cosh (* PI (/ f 4.0))) (sinh (* (/ PI 4.0) f)))))
31.0ms	(/ (cosh (* PI (/ f 4.0))) (sinh (* (/ PI 4.0) f)))

simplify78.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4975	3821
1	4975	3821

prune483.0ms

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	1	0	1
Picked	1	0	1
Done	0	0	0
Total	195	7	202

Merged error: 1.2b

Counts

202 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
52×	`add-sqr-sqrt`
42×	`add-cube-cbrt` `*-un-lft-identity`
28×	`add-exp-log` `add-cbrt-cube`
26×	`associate-r`
16×	`associate-/r*`
9×	`cbrt-undiv` `div-exp`
8×	`pow1`
6×	`associate-l` `prod-exp` `cbrt-unprod` `div-inv`
4×	`associate-/l*` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `associate-/r/` `-commutative`
1×	`sinh-def` `cosh-def` `associate-/l/`

Counts

4 → 139

Calls

4 calls:

7.0ms	(* PI (/ f 4.0))
7.0ms	(* 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))))

series96.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* PI (/ f 4.0))
3.0ms	(* PI (/ f 4.0))
58.0ms	(/ (* (log (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))) 1.0) (/ PI 4.0))
32.0ms	(/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))

simplify37.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4982	2226
1	4982	2226

prune296.0ms

Filtered

114 candidates to 151 candidates (-32.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	151	7	158

Merged error: 1.2b

Counts

158 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0)))))
0.5b	(cbrt (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0)))))
1.5b	(/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))
1.5b	(/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
28×	`cbrt-prod`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
4×	`pow1` `sinh-def` `associate-/r/` `div-inv` `add-log-exp`
2×	`cbrt-undiv` `cbrt-div` `cosh-def` `frac-2neg` `pow1/3` `div-exp` `clear-num` `associate-/l/`

Counts

4 → 104

Calls

4 calls:

3.0ms	(cbrt (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0)))))
3.0ms	(cbrt (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0)))))
4.0ms	(/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))
4.0ms	(/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))

series184.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(cbrt (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0)))))
61.0ms	(cbrt (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0)))))
32.0ms	(/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))
30.0ms	(/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))

simplify61.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5228	2578

prune485.0ms

Filtered

98 candidates to 116 candidates (-18.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	117	6	123

Merged error: 1.2b

Counts

123 → 6

regimes51.0ms

Accuracy

0% (0.3b remaining)

Error of 1.9b against oracle of 1.6b and baseline of 1.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	107	47
1	107	47

end0.0ms

sample7.5s

Algorithm

intervals

Results

2.3s	3413×	body	1280	valid
1.7s	2828×	body	1280	nan
1.1s	2458×	body	640	valid
1.1s	2482×	body	640	nan
432.0ms	1224×	body	320	valid
412.0ms	1266×	body	320	nan
151.0ms	627×	body	160	valid
55.0ms	247×	body	160	nan
34.0ms	278×	body	80	valid

Details

analyze1.1s

sample238.0ms

simplify436.0ms

prune10.0ms

localize26.0ms

rewrite37.0ms

series54.0ms

simplify71.0ms

prune494.0ms

localize13.0ms

rewrite44.0ms

series98.0ms

simplify78.0ms

prune483.0ms

localize13.0ms

rewrite29.0ms

series96.0ms

simplify37.0ms

prune296.0ms

localize21.0ms

rewrite18.0ms

series184.0ms

simplify61.0ms

prune485.0ms

regimes51.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample7.5s

Profiling