Details

sample518.0ms

Algorithm

intervals

Results

262.0ms	111×	body	1280	valid
54.0ms	498×	body	80	overflowed
53.0ms	86×	body	1280	nan
38.0ms	81×	body	640	nan
38.0ms	77×	body	640	valid
14.0ms	37×	body	320	valid
12.0ms	37×	body	320	nan
6.0ms	23×	body	160	valid
6.0ms	26×	body	160	nan
5.0ms	25×	body	80	nan
1.0ms	8×	body	80	valid

simplify458.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5009	37

prune11.0ms

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: 60.9b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 4.0) f)
0.2b	(* (/ PI 4.0) f)
0.5b	(/ (+ (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))))

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 → 136

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)
3.0ms	(* (/ PI 4.0) f)
29.0ms	(/ (+ (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

148 → 148

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5270	3042

prune497.0ms

Filtered

117 candidates to 148 candidates (-26.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	144	4	148
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	4	149

Merged error: 1.4b

Counts

149 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 4.0) f)
0.2b	(* PI (/ f 4.0))
0.4b	(* (/ 1.0 (/ PI 4.0)) (log (/ (cosh (* PI (/ f 4.0))) (sinh (* (/ PI 4.0) f)))))
0.7b	(/ (cosh (* PI (/ f 4.0))) (sinh (* (/ PI 4.0) f)))

rewrite42.0ms

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 4.0) f)
7.0ms	(* PI (/ f 4.0))
16.0ms	(* (/ 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)))

series101.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (/ PI 4.0) f)
3.0ms	(* PI (/ f 4.0))
59.0ms	(* (/ 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)))

simplify79.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4975	3821
1	4975	3821

prune501.0ms

Filtered

157 candidates to 200 candidates (-27.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	191	9	200
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	195	9	204

Merged error: 1.0b

Counts

204 → 9

localize19.0ms

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))
0.5b	(log (/ (sqrt (cosh (* PI (/ f 4.0)))) (sinh (* PI (/ f 4.0)))))
0.7b	(/ (sqrt (cosh (* PI (/ f 4.0)))) (sinh (* PI (/ f 4.0))))
4.9b	(log (sqrt (cosh (* PI (/ f 4.0)))))

rewrite28.0ms

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:

10.0ms	(/ (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))))
2.0ms	(log (sqrt (cosh (* PI (/ f 4.0)))))

series195.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (log (/ (sqrt (cosh (* PI (/ f 4.0)))) (sinh (* PI (/ f 4.0))))) (/ PI 4.0))
58.0ms	(log (/ (sqrt (cosh (* PI (/ f 4.0)))) (sinh (* PI (/ f 4.0)))))
39.0ms	(/ (sqrt (cosh (* PI (/ f 4.0)))) (sinh (* PI (/ f 4.0))))
29.0ms	(log (sqrt (cosh (* PI (/ f 4.0)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5700	4957

prune688.0ms

Filtered

136 candidates to 190 candidates (-39.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	190	9	199

Merged error: 1.0b

Counts

199 → 9

localize20.0ms

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)))))
0.7b	(/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))
0.7b	(/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))

rewrite20.0ms

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

series188.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(cbrt (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0)))))
64.0ms	(cbrt (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0)))))
30.0ms	(/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))
30.0ms	(/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))

simplify58.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5228	2578

prune489.0ms

Filtered

98 candidates to 116 candidates (-18.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	3	4	7
Picked	1	0	1
Done	1	0	1
Total	119	6	125

Merged error: 1.0b

Counts

125 → 6

regimes56.0ms

Accuracy

0% (0.3b remaining)

Error of 2.0b against oracle of 1.7b and baseline of 2.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	107	47
1	107	47

end0.0ms

sample9.8s

Algorithm

intervals

Results

2.4s	3442×	body	1280	valid
1.8s	2943×	body	1280	nan
1.6s	15248×	body	80	overflowed
1.2s	2475×	body	640	valid
1.1s	2354×	body	640	nan
431.0ms	1199×	body	320	valid
414.0ms	1239×	body	320	nan
162.0ms	644×	body	160	valid
143.0ms	618×	body	160	nan
93.0ms	793×	body	80	nan
30.0ms	240×	body	80	valid

Details

sample518.0ms

simplify458.0ms

prune11.0ms

localize17.0ms

rewrite37.0ms

series54.0ms

simplify71.0ms

prune497.0ms

localize17.0ms

rewrite42.0ms

series101.0ms

simplify79.0ms

prune501.0ms

localize19.0ms

rewrite28.0ms

series195.0ms

simplify68.0ms

prune688.0ms

localize20.0ms

rewrite20.0ms

series188.0ms

simplify58.0ms

prune489.0ms

regimes56.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample9.8s

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