Details

analyze1.2s

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

sample291.0ms

Algorithm

intervals

Results

86.0ms	116×	body	1280	valid
78.0ms	109×	body	1280	nan
41.0ms	79×	body	640	valid
34.0ms	67×	body	640	nan
14.0ms	38×	body	320	nan
13.0ms	34×	body	320	valid
5.0ms	17×	body	160	valid
1.0ms	6×	body	160	nan
1.0ms	10×	body	80	valid

simplify448.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

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: 61.4b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ PI 4.0) f)
0.3b	(log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))))
0.8b	(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
5.4b	(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

87×	`*-un-lft-identity`
70×	`times-frac`
66×	`add-sqr-sqrt`
37×	`add-cube-cbrt`
36×	`log-prod`
14×	`add-exp-log`
13×	`cosh-undef` `associate-l` `distribute-lft-out`
12×	`sinh-undef` `distribute-lft-out--` `difference-of-squares`
11×	`add-cbrt-cube`
7×	`pow1`
6×	`associate-/r*` `add-log-exp`
5×	`associate-/l*`
4×	`associate-/r/`
3×	`flip3--` `div-exp` `associate-r` `flip--` `div-inv`
2×	`cbrt-undiv` `rem-log-exp` `prod-exp` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`sub-neg` `log-div` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `associate-l/` `clear-num` `log-pow` `-commutative` `flip-+`

Counts

4 → 150

Calls

4 calls:

6.0ms	(* (/ PI 4.0) f)
9.0ms	(log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ 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)))))
6.0ms	(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

series94.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (/ PI 4.0) f)
43.0ms	(log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ 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)))))
25.0ms	(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

simplify92.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4923	4834
1	4923	4834

prune657.0ms

Filtered

123 candidates to 162 candidates (-31.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	154	8	162
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	155	8	163

Merged error: 1.6b

Counts

163 → 8

localize15.0ms

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

115×	`times-frac`
91×	`add-sqr-sqrt`
77×	`add-cube-cbrt` `*-un-lft-identity`
57×	`associate-l`
42×	`log-prod`
23×	`add-exp-log`
20×	`add-cbrt-cube`
14×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow1`
9×	`div-inv`
7×	`associate-r`
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` `associate-l/` `log-pow` `-commutative`
1×	`log-div` `cosh-def` `frac-2neg` `clear-num` `associate-/l/`

Counts

4 → 181

Calls

4 calls:

6.0ms	(* (/ PI 4.0) f)
3.0ms	(log (/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f))))
14.0ms	(* (/ 1.0 (/ PI 4.0)) (log (/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f)))))
4.0ms	(/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f)))

series144.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (/ PI 4.0) f)
49.0ms	(log (/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f))))
61.0ms	(* (/ 1.0 (/ PI 4.0)) (log (/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f)))))
31.0ms	(/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f)))

simplify50.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5094	4243

prune550.0ms

Filtered

150 candidates to 193 candidates (-28.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	182	11	193
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	188	13	201

Merged error: 1.2b

Counts

201 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

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

series86.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (/ PI 4.0) f)
3.0ms	(* (/ PI 4.0) f)
50.0ms	(log (/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f))))
29.0ms	(/ (cosh (* (/ PI 4.0) f)) (sinh (* (/ PI 4.0) f)))

simplify57.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5020	1699

prune403.0ms

Filtered

100 candidates to 130 candidates (-30.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	126	4	130
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	130	13	143

Merged error: 1.2b

Counts

143 → 13

localize26.0ms

Local error

Found 4 expressions with local error:

0.8b	(log (* (* (/ (cbrt (cosh (* (/ PI 4.0) f))) (sqrt (sinh (* (/ PI 4.0) f)))) (cbrt (cosh (* (/ PI 4.0) f)))) (/ (cbrt (cosh (* (/ PI 4.0) f))) (sqrt (sinh (* (/ PI 4.0) f))))))
1.0b	(/ (cbrt (cosh (* (/ PI 4.0) f))) (sqrt (sinh (* (/ PI 4.0) f))))
1.0b	(/ (cbrt (cosh (* (/ PI 4.0) f))) (sqrt (sinh (* (/ PI 4.0) f))))
1.2b	(* (* (/ (cbrt (cosh (* (/ PI 4.0) f))) (sqrt (sinh (* (/ PI 4.0) f)))) (cbrt (cosh (* (/ PI 4.0) f)))) (/ (cbrt (cosh (* (/ PI 4.0) f))) (sqrt (sinh (* (/ PI 4.0) f)))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
85×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
60×	`cbrt-prod` `sqrt-prod`
51×	`add-exp-log`
41×	`associate-r`
20×	`prod-exp`
18×	`add-cbrt-cube`
15×	`pow1`
12×	`div-exp` `associate-/r` `associate-/l`
10×	`frac-times` `cbrt-div` `cosh-def` `associate-*l/` `cbrt-unprod`
7×	`cbrt-undiv` `log-div` `rem-log-exp`
6×	`associate-*r/` `pow-prod-down`
4×	`add-log-exp`
3×	`sinh-def` `sqrt-div` `associate-/r/` `log-pow` `div-inv`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`log-prod` `associate-l` `*-commutative`

Counts

4 → 220

Calls

4 calls:

14.0ms	(log (* (* (/ (cbrt (cosh (* (/ PI 4.0) f))) (sqrt (sinh (* (/ PI 4.0) f)))) (cbrt (cosh (* (/ PI 4.0) f)))) (/ (cbrt (cosh (* (/ PI 4.0) f))) (sqrt (sinh (* (/ PI 4.0) f))))))
6.0ms	(/ (cbrt (cosh (* (/ PI 4.0) f))) (sqrt (sinh (* (/ PI 4.0) f))))
6.0ms	(/ (cbrt (cosh (* (/ PI 4.0) f))) (sqrt (sinh (* (/ PI 4.0) f))))
19.0ms	(* (* (/ (cbrt (cosh (* (/ PI 4.0) f))) (sqrt (sinh (* (/ PI 4.0) f)))) (cbrt (cosh (* (/ PI 4.0) f)))) (/ (cbrt (cosh (* (/ PI 4.0) f))) (sqrt (sinh (* (/ PI 4.0) f)))))

series189.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(log (* (* (/ (cbrt (cosh (* (/ PI 4.0) f))) (sqrt (sinh (* (/ PI 4.0) f)))) (cbrt (cosh (* (/ PI 4.0) f)))) (/ (cbrt (cosh (* (/ PI 4.0) f))) (sqrt (sinh (* (/ PI 4.0) f))))))
52.0ms	(/ (cbrt (cosh (* (/ PI 4.0) f))) (sqrt (sinh (* (/ PI 4.0) f))))
55.0ms	(/ (cbrt (cosh (* (/ PI 4.0) f))) (sqrt (sinh (* (/ PI 4.0) f))))
31.0ms	(* (* (/ (cbrt (cosh (* (/ PI 4.0) f))) (sqrt (sinh (* (/ PI 4.0) f)))) (cbrt (cosh (* (/ PI 4.0) f)))) (/ (cbrt (cosh (* (/ PI 4.0) f))) (sqrt (sinh (* (/ PI 4.0) f)))))

simplify91.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5277	5887

prune1.1s

Filtered

158 candidates to 232 candidates (-46.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	231	1	232
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	232	13	245

Merged error: 1.2b

Counts

245 → 13

regimes186.0ms

Accuracy

0% (0.5b remaining)

Error of 1.9b against oracle of 1.4b and baseline of 1.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	55
1	67	55

end0.0ms

sample8.3s

Algorithm

intervals

Results

2.5s	3458×	body	1280	valid
2.0s	2981×	body	1280	nan
1.3s	2447×	body	640	valid
1.1s	2302×	body	640	nan
482.0ms	1235×	body	320	valid
432.0ms	1190×	body	320	nan
171.0ms	636×	body	160	valid
61.0ms	251×	body	160	nan
31.0ms	224×	body	80	valid
0.0ms	1×	body	80	overflowed

Details

analyze1.2s

sample291.0ms

simplify448.0ms

prune11.0ms

localize18.0ms

rewrite38.0ms

series94.0ms

simplify92.0ms

prune657.0ms

localize15.0ms

rewrite35.0ms

series144.0ms

simplify50.0ms

prune550.0ms

localize18.0ms

rewrite23.0ms

series86.0ms

simplify57.0ms

prune403.0ms

localize26.0ms

rewrite57.0ms

series189.0ms

simplify91.0ms

prune1.1s

regimes186.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample8.3s

Profiling