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

sample276.0ms

Algorithm

intervals

Results

74.0ms	106×	body	1280	valid
63.0ms	98×	body	1280	nan
43.0ms	76×	body	640	valid
38.0ms	81×	body	640	nan
15.0ms	42×	body	320	valid
14.0ms	42×	body	320	nan
6.0ms	21×	body	160	valid
3.0ms	12×	body	160	nan
2.0ms	11×	body	80	valid

simplify447.0ms

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: 60.6b

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)
1.0b	(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
5.7b	(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

rewrite54.0ms

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)
30.0ms	(/ (+ (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))))

series47.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (/ PI 4.0) f)
3.0ms	(* (/ 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)))))
18.0ms	(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

simplify75.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5270	3034

prune521.0ms

Filtered

117 candidates to 147 candidates (-25.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	145	3	148

Merged error: 1.8b

Counts

148 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI (/ f 4.0))
0.4b	(* (/ 1.0 (/ PI 4.0)) (log (* 1/2 (/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* PI (/ f 4.0)))))))
1.2b	(/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* PI (/ f 4.0))))
1.3b	(log (* 1/2 (/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* PI (/ f 4.0))))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

91×	`times-frac`
71×	`add-sqr-sqrt`
65×	`*-un-lft-identity`
57×	`add-cube-cbrt`
47×	`associate-l`
26×	`add-exp-log`
20×	`add-cbrt-cube`
18×	`associate-r`
14×	`pow1`
7×	`prod-exp`
6×	`div-exp` `div-inv`
5×	`cbrt-undiv` `cbrt-unprod` `unswap-sqr`
4×	`pow-prod-down` `log-pow` `distribute-lft-out` `associate-/l*` `add-log-exp`
3×	`log-prod` `rem-log-exp` `associate-/r*`
2×	`associate-r/` `associate-/r/` `-commutative` `associate-/l/`
1×	`distribute-rgt-in` `sinh-def` `log-div` `frac-2neg` `distribute-lft-in` `flip3-+` `associate-*l/` `clear-num` `flip-+`

Counts

4 → 150

Calls

4 calls:

6.0ms	(* PI (/ f 4.0))
25.0ms	(* (/ 1.0 (/ PI 4.0)) (log (* 1/2 (/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* PI (/ f 4.0)))))))
12.0ms	(/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* PI (/ f 4.0))))
12.0ms	(log (* 1/2 (/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* PI (/ f 4.0))))))

series163.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* PI (/ f 4.0))
65.0ms	(* (/ 1.0 (/ PI 4.0)) (log (* 1/2 (/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* PI (/ f 4.0)))))))
34.0ms	(/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* PI (/ f 4.0))))
61.0ms	(log (* 1/2 (/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* PI (/ f 4.0))))))

simplify48.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5607	4080

prune592.0ms

Filtered

129 candidates to 162 candidates (-25.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	153	9	162
Fresh	0	1	1
Picked	1	0	1
Done	1	0	1
Total	155	10	165

Merged error: 1.3b

Counts

165 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI (/ f 4.0))
0.3b	(/ (* (log (* 1/2 (/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* PI (/ f 4.0)))))) 1.0) (/ PI 4.0))
1.2b	(/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* PI (/ f 4.0))))
1.3b	(log (* 1/2 (/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* PI (/ f 4.0))))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

53×	`times-frac`
43×	`*-un-lft-identity`
40×	`add-sqr-sqrt`
35×	`add-cube-cbrt`
29×	`add-exp-log`
23×	`add-cbrt-cube`
16×	`associate-/r*`
13×	`associate-r`
9×	`pow1` `div-exp`
8×	`cbrt-undiv`
6×	`prod-exp`
5×	`div-inv` `associate-/l*`
4×	`cbrt-unprod` `distribute-lft-out` `add-log-exp`
3×	`rem-log-exp` `associate-l`
2×	`frac-2neg` `associate-*r/` `pow-prod-down` `clear-num` `associate-/r/` `log-pow` `associate-/l/` `unswap-sqr`
1×	`sinh-def` `log-div` `log-prod` `flip3-+` `*-commutative` `flip-+`

Counts

4 → 126

Calls

4 calls:

6.0ms	(* PI (/ f 4.0))
17.0ms	(/ (* (log (* 1/2 (/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* PI (/ f 4.0)))))) 1.0) (/ PI 4.0))
12.0ms	(/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* PI (/ f 4.0))))
12.0ms	(log (* 1/2 (/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* PI (/ f 4.0))))))

series157.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* PI (/ f 4.0))
64.0ms	(/ (* (log (* 1/2 (/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* PI (/ f 4.0)))))) 1.0) (/ PI 4.0))
33.0ms	(/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* PI (/ f 4.0))))
57.0ms	(log (* 1/2 (/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (sinh (* PI (/ f 4.0))))))

simplify67.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4979	3301
1	4979	3301

prune428.0ms

Filtered

103 candidates to 138 candidates (-34.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	138	10	148

Merged error: 1.3b

Counts

148 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) (log (sinh (* PI (/ f 4.0)))))
1.0b	(log (sinh (* PI (/ f 4.0))))
1.0b	(log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))
1.5b	(+ (log 1/2) (- (log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) (log (sinh (* PI (/ f 4.0))))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
23×	`pow1`
21×	`log-prod`
19×	`log-pow`
13×	`distribute-lft-out`
12×	`add-sqr-sqrt` `distribute-lft-out--`
10×	`add-cube-cbrt`
8×	`associate--l+`
7×	`log-div`
6×	`add-exp-log` `associate-+r+`
5×	`add-log-exp`
4×	`add-cbrt-cube`
3×	`sinh-def` `associate-+l+` `flip3-+` `flip-+` `associate--r+`
2×	`associate--l-` `sub-neg` `diff-log` `rem-log-exp` `sum-log` `associate--r-`
1×	`+-commutative` `associate-+r-` `flip3--` `flip--` `difference-of-squares`

Counts

4 → 86

Calls

4 calls:

15.0ms	(- (log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) (log (sinh (* PI (/ f 4.0)))))
2.0ms	(log (sinh (* PI (/ f 4.0))))
9.0ms	(log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))
16.0ms	(+ (log 1/2) (- (log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) (log (sinh (* PI (/ f 4.0))))))

series165.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) (log (sinh (* PI (/ f 4.0)))))
26.0ms	(log (sinh (* PI (/ f 4.0))))
27.0ms	(log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))
59.0ms	(+ (log 1/2) (- (log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) (log (sinh (* PI (/ f 4.0))))))

simplify43.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4981	2450
1	4981	2450

prune314.0ms

Filtered

71 candidates to 98 candidates (-38.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	97	11	108

Merged error: 1.3b

Counts

108 → 11

regimes101.0ms

Accuracy

0% (0.4b remaining)

Error of 2.0b against oracle of 1.5b and baseline of 2.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	75	39
1	75	39

end0.0ms

sample7.8s

Algorithm

intervals

Results

2.4s	3398×	body	1280	valid
1.7s	2824×	body	1280	nan
1.2s	2443×	body	640	valid
1.1s	2384×	body	640	nan
462.0ms	1268×	body	320	valid
423.0ms	1258×	body	320	nan
170.0ms	649×	body	160	valid
59.0ms	249×	body	160	nan
32.0ms	242×	body	80	valid
0.0ms	2×	body	80	overflowed

Details

analyze1.1s

sample276.0ms

simplify447.0ms

prune11.0ms

localize17.0ms

rewrite54.0ms

series47.0ms

simplify75.0ms

prune521.0ms

localize22.0ms

rewrite62.0ms

series163.0ms

simplify48.0ms

prune592.0ms

localize23.0ms

rewrite51.0ms

series157.0ms

simplify67.0ms

prune428.0ms

localize25.0ms

rewrite44.0ms

series165.0ms

simplify43.0ms

prune314.0ms

regimes101.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample7.8s

Profiling