Details

analyze1.7s

Algorithm

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
0%	74.9%	25.1%	2
18.7%	56.2%	25.1%	3
37.5%	37.5%	25.1%	4
42.1%	32.8%	25.1%	5
46.8%	28.1%	25.1%	6
48%	26.9%	25.1%	7
49.2%	25.8%	25.1%	8
49.5%	25.5%	25.1%	9
49.8%	25.2%	25.1%	10
49.8%	25.2%	25.1%	11
49.8%	25.1%	25.1%	12
49.9%	25%	25.1%	13
49.9%	25%	25.1%	14

sample247.0ms

Algorithm

intervals

Results

75.0ms

256×

body

valid

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5022	78

prune19.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 1.2b

Counts

2 → 2

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ PI (sin (* PI z)))
1.0b	(* (exp (- z (+ 7.0 0.5))) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))))))))
1.0b	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
1.0b	(sqrt (* PI 2.0))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

134×	`*-un-lft-identity`
86×	`distribute-lft-out`
20×	`associate-r`
17×	`times-frac`
16×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
9×	`pow1`
8×	`add-cbrt-cube`
7×	`add-exp-log`
6×	`add-log-exp`
4×	`associate-l` `distribute-lft-out--`
3×	`flip3-+` `exp-diff` `associate-/r` `flip-+` `associate-/l`
2×	`frac-times` `sqrt-pow1` `associate-*r/` `pow-prod-down`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `pow1/2` `div-exp` `exp-sum` `associate-l/` `frac-add` `prod-exp` `clear-num` `sum-log` `sqrt-prod` `-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

3.0ms	(/ PI (sin (* PI z)))
187.0ms	(* (exp (- z (+ 7.0 0.5))) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))))))))
28.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
2.0ms	(sqrt (* PI 2.0))

series28.0ms

Counts

4 → 10

Calls

4 calls:

6.0ms	(/ PI (sin (* PI z)))
17.0ms	(* (exp (- z (+ 7.0 0.5))) (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))))))))
4.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
0.0ms	(sqrt (* PI 2.0))

simplify39.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5148	2689

prune507.0ms

Filtered

72 candidates to 108 candidates (-50.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	100	8	108
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	102	8	110

Merged error: 0.0b

Counts

110 → 8

localize61.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ PI (sin (* PI z)))
1.0b	(/ (* (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (exp z)) (exp (+ 7.0 0.5)))
1.0b	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
1.0b	(sqrt (* PI 2.0))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

207×	`frac-add`
70×	`flip3-+` `flip-+`
62×	`associate-*l/` `associate-/l/`
36×	`*-un-lft-identity`
21×	`times-frac`
14×	`add-sqr-sqrt` `add-cube-cbrt`
11×	`add-cbrt-cube`
8×	`add-exp-log`
7×	`pow1` `associate-/r*`
6×	`add-log-exp`
5×	`distribute-lft-out`
4×	`associate-/l*` `distribute-lft-out--`
3×	`cbrt-undiv` `div-exp`
2×	`frac-2neg` `sqrt-pow1` `exp-sum` `clear-num` `div-inv`
1×	`+-commutative` `pow1/2` `pow-prod-down` `prod-exp` `sum-log` `sqrt-prod` `cbrt-unprod`

Counts

4 → 140

Calls

4 calls:

6.0ms	(/ PI (sin (* PI z)))
169.0ms	(/ (* (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (exp z)) (exp (+ 7.0 0.5)))
25.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
2.0ms	(sqrt (* PI 2.0))

series33.0ms

Counts

4 → 10

Calls

4 calls:

6.0ms	(/ PI (sin (* PI z)))
19.0ms	(/ (* (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (exp z)) (exp (+ 7.0 0.5)))
8.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
0.0ms	(sqrt (* PI 2.0))

simplify49.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5486	6839

prune3.3s

Filtered

132 candidates to 150 candidates (-13.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	145	5	150
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	149	9	158

Merged error: 0.0b

Counts

158 → 9

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI (/ 1 (sin (* PI z))))
1.0b	(/ (* (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (exp z)) (exp (+ 7.0 0.5)))
1.0b	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
1.0b	(sqrt (* PI 2.0))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

207×	`frac-add`
70×	`flip3-+` `flip-+`
62×	`associate-*l/` `associate-/l/`
37×	`*-un-lft-identity`
23×	`times-frac`
21×	`add-sqr-sqrt`
15×	`add-exp-log`
14×	`add-cube-cbrt` `add-cbrt-cube`
13×	`associate-r`
9×	`pow1`
6×	`add-log-exp`
5×	`prod-exp` `distribute-lft-out`
4×	`div-exp` `associate-/r*` `distribute-lft-out--`
3×	`cbrt-undiv` `associate-l` `cbrt-unprod` `unswap-sqr`
2×	`sqrt-pow1` `exp-sum` `pow-prod-down` `div-inv`
1×	`+-commutative` `rec-exp` `frac-2neg` `pow1/2` `1-exp` `associate-r/` `clear-num` `sum-log` `sqrt-prod` `un-div-inv` `-commutative` `associate-/l*`

Counts

4 → 149

Calls

4 calls:

7.0ms	(* PI (/ 1 (sin (* PI z))))
130.0ms	(/ (* (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (exp z)) (exp (+ 7.0 0.5)))
30.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
2.0ms	(sqrt (* PI 2.0))

series30.0ms

Counts

4 → 10

Calls

4 calls:

6.0ms	(* PI (/ 1 (sin (* PI z))))
19.0ms	(/ (* (+ (+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ 1.5056327351493116e-07 (- 8.0 z))) 0.9999999999998099))))) (exp z)) (exp (+ 7.0 0.5)))
4.0ms	(+ (/ 771.3234287776531 (- 3.0 z)) (/ -176.6150291621406 (- 4.0 z)))
0.0ms	(sqrt (* PI 2.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5263	6786

prune3.7s

Filtered

133 candidates to 159 candidates (-19.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	159	9	168

Merged error: 0.0b

Counts

168 → 9

localize61.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cbrt PI) (cbrt PI))
1.0b	(cbrt PI)
1.0b	(cbrt PI)
1.0b	(cbrt PI)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

5.0ms	(* (cbrt PI) (cbrt PI))
1.0ms	(cbrt PI)
1.0ms	(cbrt PI)
1.0ms	(cbrt PI)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(* (cbrt PI) (cbrt PI))
0.0ms	(cbrt PI)
0.0ms	(cbrt PI)
0.0ms	(cbrt PI)

simplify53.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4969	648
1	4969	648

prune260.0ms

Filtered

58 candidates to 77 candidates (-32.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	77	9	86

Merged error: 0.0b

Counts

86 → 9

regimes91.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	105	81
1	105	81

end0.0ms

sample7.4s

Algorithm

intervals

Results

2.3s

8000×

body

valid

Details

analyze1.7s

sample247.0ms

simplify34.0ms

prune19.0ms

localize53.0ms

rewrite224.0ms

series28.0ms

simplify39.0ms

prune507.0ms

localize61.0ms

rewrite229.0ms

series33.0ms

simplify49.0ms

prune3.3s

localize58.0ms

rewrite180.0ms

series30.0ms

simplify54.0ms

prune3.7s

localize61.0ms

rewrite11.0ms

series0.0ms

simplify53.0ms

prune260.0ms

regimes91.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample7.4s

Profiling