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

sample297.0ms

Algorithm

intervals

Results

78.0ms	107×	body	1280	valid
76.0ms	113×	body	1280	nan
45.0ms	81×	body	640	valid
42.0ms	86×	body	640	nan
15.0ms	42×	body	320	nan
15.0ms	38×	body	320	valid
6.0ms	21×	body	160	valid
3.0ms	13×	body	160	nan
1.0ms	9×	body	80	valid

simplify452.0ms

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: 61.1b

Counts

2 → 1

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 4.0) f)
0.2b	(* (/ PI 4.0) f)
1.0b	(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
5.6b	(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

rewrite36.0ms

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)
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))))

series53.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (/ PI 4.0) f)
8.0ms	(* (/ 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)))))
17.0ms	(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

simplify74.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5270	3034

prune515.0ms

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: 1.6b

Counts

148 → 2

localize15.0ms

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)))))
1.2b	(/ (cosh (* PI (/ f 4.0))) (sinh (* (/ PI 4.0) f)))

rewrite43.0ms

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:

11.0ms	(* PI (/ f 4.0))
6.0ms	(* (/ PI 4.0) f)
14.0ms	(* (/ 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)))

series100.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify79.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4975	3821
1	4975	3821

prune504.0ms

Filtered

157 candidates to 200 candidates (-27.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	193	7	200
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	194	8	202

Merged error: 1.2b

Counts

202 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b	(log (/ (cbrt (cosh (* PI (/ f 4.0)))) (sqrt (sinh (* PI (/ f 4.0))))))
0.8b	(* (/ (cbrt (cosh (* PI (/ f 4.0)))) (sqrt (sinh (* PI (/ f 4.0))))) (cbrt (cosh (* PI (/ f 4.0)))))
1.3b	(/ (cbrt (cosh (* PI (/ f 4.0)))) (sqrt (sinh (* PI (/ f 4.0)))))
1.3b	(/ (cbrt (cosh (* PI (/ f 4.0)))) (sqrt (sinh (* PI (/ f 4.0)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

152×	`times-frac`
140×	`add-sqr-sqrt`
112×	`add-cube-cbrt` `*-un-lft-identity`
90×	`cbrt-prod`
82×	`sqrt-prod`
41×	`log-prod` `associate-l`
16×	`add-exp-log`
12×	`associate-/r` `associate-/l`
10×	`unswap-sqr`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`associate-r`
4×	`sinh-def` `cbrt-div` `cosh-def` `sqrt-div` `div-exp` `associate-/r/` `div-inv` `add-log-exp`
3×	`cbrt-undiv`
2×	`frac-2neg` `rem-log-exp` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`frac-times` `log-div` `associate-r/` `pow-prod-down` `associate-l/` `log-pow` `*-commutative`

Counts

4 → 249

Calls

4 calls:

5.0ms	(log (/ (cbrt (cosh (* PI (/ f 4.0)))) (sqrt (sinh (* PI (/ f 4.0))))))
13.0ms	(* (/ (cbrt (cosh (* PI (/ f 4.0)))) (sqrt (sinh (* PI (/ f 4.0))))) (cbrt (cosh (* PI (/ f 4.0)))))
5.0ms	(/ (cbrt (cosh (* PI (/ f 4.0)))) (sqrt (sinh (* PI (/ f 4.0)))))
6.0ms	(/ (cbrt (cosh (* PI (/ f 4.0)))) (sqrt (sinh (* PI (/ f 4.0)))))

series248.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(log (/ (cbrt (cosh (* PI (/ f 4.0)))) (sqrt (sinh (* PI (/ f 4.0))))))
61.0ms	(* (/ (cbrt (cosh (* PI (/ f 4.0)))) (sqrt (sinh (* PI (/ f 4.0))))) (cbrt (cosh (* PI (/ f 4.0)))))
52.0ms	(/ (cbrt (cosh (* PI (/ f 4.0)))) (sqrt (sinh (* PI (/ f 4.0)))))
57.0ms	(/ (cbrt (cosh (* PI (/ f 4.0)))) (sqrt (sinh (* PI (/ f 4.0)))))

simplify92.0ms

Algorithm

egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4963	6801
1	4963	6801

prune1.8s

Filtered

191 candidates to 261 candidates (-36.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	260	1	261
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	260	9	269

Merged error: 1.2b

Counts

269 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI (/ f 4.0))
0.3b	(* (sqrt (/ 1.0 (/ PI 4.0))) (* (log (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))) (sqrt (* 4.0 (/ 1.0 PI)))))
0.3b	(* (log (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))) (sqrt (* 4.0 (/ 1.0 PI))))
1.2b	(/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

85×	`times-frac`
65×	`add-sqr-sqrt`
58×	`add-cube-cbrt` `*-un-lft-identity`
54×	`associate-l`
45×	`sqrt-prod`
18×	`add-exp-log` `associate-r` `add-cbrt-cube`
14×	`pow1`
8×	`associate-*r/`
6×	`prod-exp` `cbrt-unprod` `div-inv`
5×	`sqrt-div` `pow-prod-down`
4×	`add-log-exp`
3×	`associate-/r` `-commutative` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`frac-times` `sinh-def` `cosh-def` `frac-2neg` `associate-*l/` `clear-num` `log-pow` `associate-/l/`

Counts

4 → 147

Calls

4 calls:

6.0ms	(* PI (/ f 4.0))
17.0ms	(* (sqrt (/ 1.0 (/ PI 4.0))) (* (log (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))) (sqrt (* 4.0 (/ 1.0 PI)))))
7.0ms	(* (log (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))) (sqrt (* 4.0 (/ 1.0 PI))))
4.0ms	(/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))

series164.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* PI (/ f 4.0))
64.0ms	(* (sqrt (/ 1.0 (/ PI 4.0))) (* (log (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))) (sqrt (* 4.0 (/ 1.0 PI)))))
64.0ms	(* (log (/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))) (sqrt (* 4.0 (/ 1.0 PI))))
33.0ms	(/ (cosh (* PI (/ f 4.0))) (sinh (* PI (/ f 4.0))))

simplify63.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4963	3339
1	4963	3339

prune474.0ms

Filtered

130 candidates to 159 candidates (-22.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	157	2	159
Fresh	0	7	7
Picked	0	1	1
Done	1	0	1
Total	158	10	168

Merged error: 1.2b

Counts

168 → 10

regimes80.0ms

Accuracy

0% (0.4b remaining)

Error of 2.1b against oracle of 1.6b and baseline of 2.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	29
1	62	29

end0.0ms

sample8.2s

Algorithm

intervals

Results

2.5s	3470×	body	1280	valid
2.0s	3043×	body	1280	nan
1.2s	2433×	body	640	valid
1.2s	2470×	body	640	nan
458.0ms	1191×	body	320	valid
428.0ms	1221×	body	320	nan
167.0ms	632×	body	160	valid
62.0ms	263×	body	160	nan
36.0ms	274×	body	80	valid
0.0ms	1×	body	80	overflowed

Details

analyze1.1s

sample297.0ms

simplify452.0ms

prune11.0ms

localize28.0ms

rewrite36.0ms

series53.0ms

simplify74.0ms

prune515.0ms

localize15.0ms

rewrite43.0ms

series100.0ms

simplify79.0ms

prune504.0ms

localize26.0ms

rewrite41.0ms

series248.0ms

simplify92.0ms

prune1.8s

localize19.0ms

rewrite41.0ms

series164.0ms

simplify63.0ms

prune474.0ms

regimes80.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample8.2s

Profiling