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

sample312.0ms

Algorithm

intervals

Results

76.0ms	109×	body	1280	valid
41.0ms	79×	body	640	valid
14.0ms	37×	body	320	valid
5.0ms	20×	body	160	valid
1.0ms	11×	body	80	valid

simplify473.0ms

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: 60.6b

Counts

2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 4.0) f)
0.4b	(* (/ 1.0 (/ PI 4.0)) (log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))))
0.7b	(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
57.1b	(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

169×	`times-frac`
157×	`*-un-lft-identity`
133×	`add-sqr-sqrt`
85×	`add-cube-cbrt`
72×	`log-prod`
57×	`associate-l`
36×	`distribute-rgt-in` `distribute-lft-in`
20×	`add-exp-log` `add-cbrt-cube`
19×	`cosh-undef` `distribute-lft-out`
17×	`sinh-undef` `distribute-lft-out--` `difference-of-squares`
9×	`pow1`
8×	`div-inv`
7×	`associate-r` `associate-/r/`
6×	`associate-/r*` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l*` `unswap-sqr`
4×	`flip3--` `flip--`
2×	`pow-prod-down` `associate-l/` `-commutative` `associate-/l/`
1×	`sub-neg` `frac-2neg` `flip3-+` `diff-log` `clear-num` `log-pow` `flip-+`

Counts

4 → 242

Calls

4 calls:

7.0ms	(* (/ PI 4.0) f)
39.0ms	(* (/ 1.0 (/ PI 4.0)) (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)))))
7.0ms	(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

series101.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (/ PI 4.0) f)
57.0ms	(* (/ 1.0 (/ PI 4.0)) (log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ 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))))

simplify95.0ms

Algorithm

egg-herbie

Counts

254 → 254

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5020	9963

prune1.0s

Filtered

175 candidates to 254 candidates (-45.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	249	5	254
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	249	6	255

Merged error: 0.5b

Counts

255 → 6

localize63.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))
1.0b	(cbrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))
1.0b	(cbrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))
2.4b	(log (* (/ (cbrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) 2) (cbrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
10×	`add-exp-log` `cbrt-div`
7×	`pow1` `add-sqr-sqrt` `add-cube-cbrt`
5×	`log-div` `flip3-+` `flip-+`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `rem-log-exp` `distribute-lft-out`
2×	`frac-times` `associate-*r/` `prod-exp` `log-pow`
1×	`log-prod` `div-exp` `pow-prod-down` `associate-*l/`

Counts

4 → 60

Calls

4 calls:

10.0ms	(cbrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))
9.0ms	(cbrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))
12.0ms	(cbrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))
23.0ms	(log (* (/ (cbrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) 2) (cbrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))))

series168.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(cbrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))
34.0ms	(cbrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))
36.0ms	(cbrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))
61.0ms	(log (* (/ (cbrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) 2) (cbrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))))

simplify74.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4942	1652
1	4942	1652

prune491.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	72	6	78

Merged error: 0.5b

Counts

78 → 6

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 4.0) f)
0.3b	(+ (* 1.0 (/ (log 1/2) (/ PI 4.0))) (* 1.0 (/ (log (/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* (/ PI 4.0) f)))) (/ PI 4.0))))
0.3b	(/ (log (/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* (/ PI 4.0) f)))) (/ PI 4.0))
0.7b	(/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* (/ PI 4.0) f)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

119×	`times-frac`
78×	`*-un-lft-identity`
75×	`add-sqr-sqrt`
70×	`add-cube-cbrt`
20×	`pow1`
16×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
14×	`log-pow`
13×	`associate-l`
8×	`div-inv` `associate-/l*`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp` `distribute-lft-out`
3×	`associate-r`
2×	`frac-2neg` `flip3-+` `associate-*r/` `prod-exp` `clear-num` `associate-/r/` `cbrt-unprod` `flip-+` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `sinh-def` `log-div` `div-sub` `pow-prod-down` `associate-l/` `frac-add` `sum-log` `-commutative`

Counts

4 → 164

Calls

4 calls:

6.0ms	(* (/ PI 4.0) f)
12.0ms	(+ (* 1.0 (/ (log 1/2) (/ PI 4.0))) (* 1.0 (/ (log (/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* (/ PI 4.0) f)))) (/ PI 4.0))))
16.0ms	(/ (log (/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* (/ PI 4.0) f)))) (/ PI 4.0))
13.0ms	(/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* (/ PI 4.0) f)))

series174.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (/ PI 4.0) f)
73.0ms	(+ (* 1.0 (/ (log 1/2) (/ PI 4.0))) (* 1.0 (/ (log (/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* (/ PI 4.0) f)))) (/ PI 4.0))))
64.0ms	(/ (log (/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* (/ PI 4.0) f)))) (/ PI 4.0))
34.0ms	(/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* (/ PI 4.0) f)))

simplify75.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5383	5678

prune731.0ms

Filtered

133 candidates to 176 candidates (-32.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	173	3	176
Fresh	1	2	3
Picked	1	0	1
Done	1	1	2
Total	176	6	182

Merged error: 0.5b

Counts

182 → 6

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (log (/ (sqrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) (sinh (* (/ PI 4.0) f)))) (/ PI 4.0))
0.5b	(log (/ (sqrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) (sinh (* (/ PI 4.0) f))))
1.0b	(/ (sqrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) (sinh (* (/ PI 4.0) f)))
1.5b	(log (/ (sqrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) 2))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

160×	`times-frac`
117×	`*-un-lft-identity`
97×	`add-sqr-sqrt` `add-cube-cbrt`
51×	`log-prod`
40×	`sqrt-prod`
20×	`pow1`
17×	`add-exp-log`
16×	`associate-/r*` `log-pow`
11×	`add-cbrt-cube` `associate-/l*`
10×	`distribute-lft-out`
9×	`div-inv`
6×	`div-exp`
4×	`cbrt-undiv` `rem-log-exp` `add-log-exp`
3×	`log-div` `associate-/r/`
2×	`sinh-def` `frac-2neg` `sqrt-div` `clear-num` `associate-/l/`
1×	`flip3-+` `div-sub` `flip-+`

Counts

4 → 204

Calls

4 calls:

17.0ms	(/ (log (/ (sqrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) (sinh (* (/ PI 4.0) f)))) (/ PI 4.0))
12.0ms	(log (/ (sqrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) (sinh (* (/ PI 4.0) f))))
15.0ms	(/ (sqrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) (sinh (* (/ PI 4.0) f)))
11.0ms	(log (/ (sqrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) 2))

series214.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ (log (/ (sqrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) (sinh (* (/ PI 4.0) f)))) (/ PI 4.0))
63.0ms	(log (/ (sqrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) (sinh (* (/ PI 4.0) f))))
38.0ms	(/ (sqrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) (sinh (* (/ PI 4.0) f)))
37.0ms	(log (/ (sqrt (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) 2))

simplify90.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5347	8110

prune1.2s

Filtered

147 candidates to 216 candidates (-46.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	216	6	222

Merged error: 0.5b

Counts

222 → 6

regimes65.0ms

Accuracy

0% (0.4b remaining)

Error of 1.8b against oracle of 1.4b and baseline of 1.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	99	71
1	99	71

end0.0ms

sample8.8s

Algorithm

intervals

Results

2.4s	3412×	body	1280	valid
1.2s	2481×	body	640	valid
444.0ms	1212×	body	320	valid
161.0ms	635×	body	160	valid
33.0ms	260×	body	80	valid

Details

analyze1.1s

sample312.0ms

simplify473.0ms

prune11.0ms

localize29.0ms

rewrite77.0ms

series101.0ms

simplify95.0ms

prune1.0s

localize63.0ms

rewrite56.0ms

series168.0ms

simplify74.0ms

prune491.0ms

localize57.0ms

rewrite54.0ms

series174.0ms

simplify75.0ms

prune731.0ms

localize60.0ms

rewrite65.0ms

series214.0ms

simplify90.0ms

prune1.2s

regimes65.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample8.8s

Profiling