Details

sample429.0ms

Algorithm

intervals

Results

145.0ms	124×	body	10240	exit
99.0ms	111×	body	1280	valid
52.0ms	83×	body	640	valid
32.0ms	44×	body	1280	nan
21.0ms	42×	body	320	valid
19.0ms	31×	body	640	nan
6.0ms	14×	body	320	nan
4.0ms	13×	body	160	valid
4.0ms	14×	body	160	nan
2.0ms	12×	body	80	valid
1.0ms	10×	body	80	nan

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	133	48
1	455	48
2	2797	47
3	5001	47

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 61.9b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (+ (- z 1.0) 7.0) 0.5))
1.0b	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
1.0b	(sqrt (* PI 2.0))
3.8b	(+ (- z 1.0) 1.0)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
19×	`add-log-exp`
15×	`add-cube-cbrt`
12×	`distribute-lft-out`
11×	`associate-+l+` `associate-r`
9×	`add-exp-log` `prod-diff`
7×	`pow1` `unpow-prod-down` `sum-log`
6×	`exp-prod` `add-cbrt-cube`
5×	`fma-def`
4×	`expm1-log1p-u` `associate-+l-` `associate-l` `log1p-expm1-u` `rem-exp-log` `distribute-lft-out--`
3×	`prod-exp` `unswap-sqr`
2×	`sqrt-pow1` `diff-log` `sqrt-prod` `sqr-pow`
1×	`unpow-prod-up` `+-commutative` `pow-to-exp` `sub-neg` `flip3-+` `pow1/2` `exp-diff` `associate-r/` `exp-sum` `pow-prod-down` `pow-exp` `-commutative` `cbrt-unprod` `flip-+` `pow-sub` `difference-of-squares`

Counts

4 → 100

Calls

4 calls:

10.0ms	(exp (+ (+ (- z 1.0) 7.0) 0.5))
19.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms	(sqrt (* PI 2.0))
9.0ms	(+ (- z 1.0) 1.0)

series303.0ms

Counts

4 → 10

Calls

4 calls:

11.0ms	(exp (+ (+ (- z 1.0) 7.0) 0.5))
276.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms	(sqrt (* PI 2.0))
15.0ms	(+ (- z 1.0) 1.0)

simplify66.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	569	751
1	2330	628
2	5001	607

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.3b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- z 0))) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
1.0b	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
1.0b	(sqrt (* PI 2.0))
1.2b	(/ (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- z 0))) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))

rewrite334.0ms

Algorithm

rewrite-expression-head

Rules

224×	`frac-add`
67×	`associate-*r/`
63×	`*-un-lft-identity`
41×	`distribute-lft-out`
37×	`associate-+l-`
35×	`pow-sub`
33×	`associate-/l/`
32×	`frac-times` `flip3-+` `flip-+`
30×	`add-exp-log`
22×	`associate-r`
20×	`add-cbrt-cube`
17×	`prod-exp`
15×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
9×	`pow1`
7×	`unpow-prod-down` `cbrt-unprod`
5×	`div-exp` `associate-l`
4×	`expm1-log1p-u` `times-frac` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `pow-exp` `unswap-sqr`
2×	`sqrt-pow1` `exp-sum` `pow-prod-down` `associate-l/` `sqrt-prod` `-commutative` `sqr-pow`
1×	`unpow-prod-up` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow1/2` `exp-diff` `clear-num` `associate-/r/` `div-inv` `associate-/l*` `distribute-lft-out--`

Counts

4 → 173

Calls

4 calls:

145.0ms	(* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- z 0))) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
19.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms	(sqrt (* PI 2.0))
156.0ms	(/ (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- z 0))) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))

series1.4s

Counts

4 → 10

Calls

4 calls:

520.0ms	(* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- z 0))) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
282.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms	(sqrt (* PI 2.0))
645.0ms	(/ (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- z 0))) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))

simplify175.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 1 (65.0ms)

Iter	Nodes	Cost
0	3199	11202
1	5002	10781

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize78.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (sqrt 2.0) (exp 6.5))
1.0b	(* (log 6.5) (sqrt 2.0))
1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

132×	`add-sqr-sqrt`
104×	`unpow-prod-down`
84×	`times-frac`
68×	`*-un-lft-identity`
62×	`associate-l`
56×	`add-cube-cbrt`
53×	`add-exp-log`
40×	`sqrt-prod`
38×	`unswap-sqr`
26×	`pow-exp`
25×	`prod-exp`
20×	`sqr-pow`
18×	`associate-r`
13×	`div-exp`
12×	`add-cbrt-cube`
8×	`pow-to-exp`
7×	`pow1`
6×	`rec-exp` `1-exp` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `-commutative` `cbrt-unprod` `div-inv`
1×	`cbrt-undiv` `frac-2neg` `pow-prod-down` `clear-num` `log-pow`

Counts

4 → 218

Calls

4 calls:

5.0ms	(/ (sqrt 2.0) (exp 6.5))
6.0ms	(* (log 6.5) (sqrt 2.0))
21.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
15.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/ (sqrt 2.0) (exp 6.5))
0.0ms	(* (log 6.5) (sqrt 2.0))
0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

simplify69.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	572	1976
1	1989	1932
2	5002	1865

prune2.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize86.0ms

Local error

Found 4 expressions with local error:

1.0b	(expm1 (log1p (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))))
1.0b	(* (log 6.5) (sqrt 2.0))
1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

117×	`add-sqr-sqrt`
104×	`unpow-prod-down`
66×	`times-frac`
62×	`associate-l`
53×	`*-un-lft-identity`
52×	`add-exp-log`
41×	`add-cube-cbrt`
38×	`unswap-sqr`
28×	`sqrt-prod`
26×	`pow-exp`
25×	`prod-exp`
20×	`sqr-pow`
18×	`associate-r`
12×	`div-exp`
10×	`add-cbrt-cube`
8×	`pow-to-exp`
7×	`pow1`
6×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `cbrt-unprod`
2×	`div-inv`
1×	`expm1-log1p` `pow-prod-down` `log-pow` `expm1-udef`

Counts

4 → 188

Calls

4 calls:

1.0ms	(expm1 (log1p (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))))
6.0ms	(* (log 6.5) (sqrt 2.0))
15.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
15.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(expm1 (log1p (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))))
0.0ms	(* (log 6.5) (sqrt 2.0))
0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

simplify90.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	372	1475
1	1052	1433
2	3355	1389
3	5001	1375

prune1.9s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes152.0ms

Accuracy

0% (1.2b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 1.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	81	85
1	81	85

end0.0ms

sample12.3s

Algorithm

intervals

Results

4.2s	3760×	body	10240	exit
3.1s	3395×	body	1280	valid
1.6s	2505×	body	640	valid
1.1s	1501×	body	1280	nan
771.0ms	1300×	body	640	nan
548.0ms	1204×	body	320	valid
237.0ms	569×	body	320	nan
187.0ms	629×	body	160	valid
88.0ms	327×	body	160	nan
56.0ms	373×	body	80	valid
33.0ms	266×	body	80	nan