Details

sample2.3s

Algorithm

intervals

Results

80.0ms	676×	body	80	overflowed
71.0ms	99×	body	1280	valid
38.0ms	79×	body	640	valid
17.0ms	47×	body	320	valid
5.0ms	20×	body	160	valid
1.0ms	11×	body	80	valid
1.0ms	8×	body	80	nan

simplify322.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

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

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 60.9b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ PI 4.0) f)
0.3b	(* (/ PI 4.0) f)
2.2b	(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
6.2b	(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

rewrite33.0ms

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)
9.0ms	(/ (+ (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))))

series55.0ms

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

simplify52.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (36.0ms)

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

prune408.0ms

Filtered

135 candidates to 99 candidates (26.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	4	136

Merged error: 2.9b

Counts

136 → 4

localize35.0ms

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)
2.2b	(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))))))

rewrite51.0ms

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:

25.0ms	(* (/ 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)
14.0ms	(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))))))

series128.0ms

Counts

4 → 8

Calls

4 calls:

73.0ms	(* (/ 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)
55.0ms	(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))))))

simplify82.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1519	5738
1	5001	5408

prune939.0ms

Filtered

180 candidates to 124 candidates (31.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	170	10	180
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	171	13	184

Merged error: 2.4b

Counts

184 → 13

localize36.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow PI 3)
1.0b	(pow PI 5)
2.2b	(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))))))
3.1b	(log (sqrt (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))))

rewrite27.0ms

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)
15.0ms	(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))))))

series72.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(pow PI 3)
0.0ms	(pow PI 5)
45.0ms	(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))))))
26.0ms	(log (sqrt (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))))

simplify103.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	775	2273
1	3534	2109
2	5002	2086

prune547.0ms

Filtered

106 candidates to 68 candidates (35.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	106	13	119

Merged error: 2.4b

Counts

119 → 13

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (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)
2.2b	(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))))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
26×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`times-frac`
18×	`log-prod`
11×	`add-exp-log`
7×	`pow1` `add-cbrt-cube` `distribute-lft-out`
6×	`unpow-prod-down` `pow-unpow`
4×	`associate-/r/` `associate-/l*` `add-log-exp`
3×	`flip3-+` `cube-prod` `associate-/r*` `flip-+`
2×	`pow-to-exp` `pow-pow` `div-exp` `rem-log-exp` `pow-exp` `div-inv` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `cube-mult` `log-div` `frac-2neg` `unpow3` `clear-num` `log-pow` `rem-cube-cbrt`

Counts

4 → 104

Calls

4 calls:

15.0ms	(/ (+ (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)
14.0ms	(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))))))

series80.0ms

Counts

4 → 8

Calls

4 calls:

28.0ms	(/ (+ (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)
51.0ms	(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))))))

simplify140.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	981	2808
1	4847	2642
2	5001	2642

prune552.0ms

Filtered

112 candidates to 78 candidates (30.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	113	12	125

Merged error: 2.4b

Counts

125 → 12

regimes228.0ms

Accuracy

0% (0.7b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample8.8s

Algorithm

intervals

Results

2.3s	22433×	body	80	overflowed
2.3s	3401×	body	1280	valid
1.1s	2404×	body	640	valid
431.0ms	1222×	body	320	valid
172.0ms	705×	body	160	valid
56.0ms	460×	body	80	nan
34.0ms	268×	body	80	valid

Details

sample2.3s

simplify322.0ms

prune5.0ms

localize18.0ms

rewrite33.0ms

series55.0ms

simplify52.0ms

prune408.0ms

localize35.0ms

rewrite51.0ms

series128.0ms

simplify82.0ms

prune939.0ms

localize36.0ms

rewrite27.0ms

series72.0ms

simplify103.0ms

prune547.0ms

localize33.0ms

rewrite37.0ms

series80.0ms

simplify140.0ms

prune552.0ms

regimes228.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample8.8s

Profiling