Details

analyze1.1s

Algorithm: search

sample282.0ms

Algorithm

intervals

Results

84.0ms	109×	body	1280	valid
62.0ms	95×	body	1280	nan
43.0ms	83×	body	640	valid
38.0ms	81×	body	640	nan
16.0ms	44×	body	320	valid
13.0ms	38×	body	320	nan
4.0ms	15×	body	160	valid
4.0ms	16×	body	160	nan
1.0ms	5×	body	80	valid

simplify440.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	22
1	97	22
2	223	22
3	561	22
4	1215	22
5	2815	22
6	5002	22

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 62.4b

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)
1.7b	(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
4.2b	(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
53×	`add-sqr-sqrt`
40×	`times-frac`
31×	`add-cube-cbrt`
26×	`associate-l`
16×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`associate-r` `distribute-lft-out` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
5×	`associate-/r*`
4×	`prod-exp` `cbrt-unprod` `associate-/l*` `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 → 123

Calls

4 calls:

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

series56.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (/ PI 4.0) f)
3.0ms	(* (/ PI 4.0) f)
32.0ms	(/ (+ (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))))

simplify51.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	439	1718
1	1513	1596
2	5001	1570

prune426.0ms

Filtered

99 candidates to 135 candidates (-36.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	2	136

Merged error: 2.2b

Counts

136 → 2

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1.0 (/ PI 4.0)) (log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (+ (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))) (* 0.5 (* f PI)))))))
1.0b	(pow PI 3)
1.0b	(pow PI 5)
1.7b	(log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (+ (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))) (* 0.5 (* f PI))))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

105×	`times-frac`
87×	`*-un-lft-identity`
78×	`add-sqr-sqrt`
69×	`add-cube-cbrt`
54×	`log-prod`
44×	`associate-l`
18×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in`
14×	`add-cbrt-cube`
10×	`pow1`
9×	`distribute-lft-out`
7×	`associate-/r/` `div-inv`
6×	`unpow-prod-down` `pow-unpow`
4×	`div-exp` `associate-r` `add-log-exp`
3×	`cbrt-undiv` `flip3-+` `cube-prod` `prod-exp` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `rem-log-exp` `pow-exp` `log-pow` `sqr-pow`
1×	`cube-mult` `log-div` `unpow3` `pow-prod-down` `associate-l/` `-commutative` `rem-cube-cbrt`

Counts

4 → 172

Calls

4 calls:

31.0ms	(* (/ 1.0 (/ PI 4.0)) (log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (+ (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))) (* 0.5 (* f PI)))))))
2.0ms	(pow PI 3)
2.0ms	(pow PI 5)
15.0ms	(log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (+ (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))) (* 0.5 (* f PI))))))

series132.0ms

Counts

4 → 8

Calls

4 calls:

79.0ms	(* (/ 1.0 (/ PI 4.0)) (log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (+ (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))) (* 0.5 (* f PI)))))))
0.0ms	(pow PI 3)
0.0ms	(pow PI 5)
53.0ms	(log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (+ (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))) (* 0.5 (* f PI))))))

simplify80.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1519	5738
1	5001	5408

prune979.0ms

Filtered

124 candidates to 180 candidates (-45.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	174	6	180
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	175	7	182

Merged error: 1.7b

Counts

182 → 7

localize37.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow PI 3)
1.0b	(pow PI 5)
1.5b	(log (/ (sqrt (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))) (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (+ (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))) (* 0.5 (* f PI))))))
2.4b	(log (sqrt (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

34×	`log-prod`
33×	`*-un-lft-identity`
25×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`times-frac`
16×	`sqrt-prod`
10×	`add-exp-log`
9×	`pow1`
6×	`unpow-prod-down` `pow-unpow`
5×	`add-cbrt-cube`
4×	`log-pow` `distribute-lft-out` `add-log-exp`
3×	`log-div` `cube-prod` `rem-log-exp`
2×	`pow-to-exp` `pow-pow` `flip3-+` `sqrt-div` `pow-exp` `associate-/r/` `flip-+` `sqr-pow`
1×	`cube-mult` `sqrt-pow1` `pow1/2` `unpow3` `div-exp` `div-inv` `rem-cube-cbrt`

Counts

4 → 98

Calls

4 calls:

2.0ms	(pow PI 3)
2.0ms	(pow PI 5)
16.0ms	(log (/ (sqrt (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))) (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (+ (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))) (* 0.5 (* f PI))))))
5.0ms	(log (sqrt (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))))

series76.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(pow PI 3)
0.0ms	(pow PI 5)
48.0ms	(log (/ (sqrt (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))) (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (+ (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))) (* 0.5 (* f PI))))))
27.0ms	(log (sqrt (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))))

simplify104.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	775	2269
1	3534	2109
2	5002	2086

prune556.0ms

Filtered

68 candidates to 106 candidates (-55.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	106	7	113

Merged error: 1.7b

Counts

113 → 7

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (log f) PI)
1.0b	(pow PI 3)
1.0b	(pow PI 3)
2.0b	(log (/ 4.0 PI))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
13×	`log-prod`
11×	`pow1` `add-exp-log`
8×	`add-cbrt-cube`
6×	`unpow-prod-down` `pow-unpow` `cube-prod`
5×	`log-pow`
4×	`associate-/l*` `add-log-exp`
3×	`associate-/r*`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `div-exp` `rem-log-exp` `pow-exp` `div-inv` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `log-div` `frac-2neg` `clear-num`

Counts

4 → 101

Calls

4 calls:

6.0ms	(/ (log f) PI)
2.0ms	(pow PI 3)
2.0ms	(pow PI 3)
3.0ms	(log (/ 4.0 PI))

series14.0ms

Counts

4 → 6

Calls

4 calls:

14.0ms	(/ (log f) PI)
0.0ms	(pow PI 3)
0.0ms	(pow PI 3)
0.0ms	(log (/ 4.0 PI))

simplify43.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	319	432
1	1478	407
2	5001	396

prune265.0ms

Filtered

63 candidates to 107 candidates (-69.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	107	7	114

Merged error: 1.7b

Counts

114 → 7

regimes80.0ms

Accuracy

0% (0.7b remaining)

Error of 2.2b against oracle of 1.5b and baseline of 2.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	38
1	67	38
2	67	38

end0.0ms

analyze888.0ms

Algorithm: search

sample7.9s

Algorithm

intervals

Results

2.4s	3407×	body	1280	valid
1.8s	2934×	body	1280	nan
1.2s	2415×	body	640	valid
1.2s	2475×	body	640	nan
472.0ms	1290×	body	320	valid
398.0ms	1157×	body	320	nan
165.0ms	636×	body	160	valid
66.0ms	277×	body	160	nan
33.0ms	252×	body	80	valid
0.0ms	1×	body	80	overflowed

Details

analyze1.1s

sample282.0ms

simplify440.0ms

prune6.0ms

localize17.0ms

rewrite36.0ms

series56.0ms

simplify51.0ms

prune426.0ms

localize32.0ms

rewrite59.0ms

series132.0ms

simplify80.0ms

prune979.0ms

localize37.0ms

rewrite29.0ms

series76.0ms

simplify104.0ms

prune556.0ms

localize30.0ms

rewrite16.0ms

series14.0ms

simplify43.0ms

prune265.0ms

regimes80.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze888.0ms

sample7.9s

Profiling