Details

sample425.0ms

Algorithm

intervals

Results

132.0ms	137×	body	10240	exit
109.0ms	115×	body	1280	valid
48.0ms	78×	body	640	valid
36.0ms	52×	body	1280	nan
23.0ms	41×	body	640	nan
16.0ms	38×	body	320	valid
6.0ms	15×	body	320	nan
5.0ms	20×	body	160	valid
3.0ms	10×	body	160	nan
2.0ms	13×	body	80	valid
1.0ms	12×	body	80	nan

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	133	48
1	453	48
2	2766	47
3	5002	47

prune31.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 62.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(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))
5.8b	(+ (- z 1.0) 1.0)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
20×	`add-log-exp`
17×	`distribute-lft-out`
16×	`exp-prod`
15×	`add-sqr-sqrt`
11×	`associate-r`
10×	`add-cube-cbrt`
9×	`add-exp-log`
7×	`pow1` `unpow-prod-down` `sum-log`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `add-cbrt-cube`
5×	`rem-exp-log`
4×	`associate-l` `neg-log` `distribute-lft-out--`
3×	`prod-exp` `unswap-sqr`
2×	`associate-+l-` `associate-+l+` `sqrt-pow1` `diff-log` `sqrt-prod` `sqr-pow`
1×	`unpow-prod-up` `+-commutative` `neg-sub0` `exp-neg` `pow-to-exp` `neg-mul-1` `sub-neg` `distribute-neg-in` `flip3-+` `pow1/2` `exp-diff` `associate-r/` `exp-sum` `pow-prod-down` `pow-exp` `-commutative` `cbrt-unprod` `flip-+` `pow-sub`

Counts

4 → 90

Calls

4 calls:

11.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
21.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms	(sqrt (* PI 2.0))
7.0ms	(+ (- z 1.0) 1.0)

series315.0ms

Counts

4 → 10

Calls

4 calls:

23.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
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))
10.0ms	(+ (- z 1.0) 1.0)

simplify57.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	552	708
1	2026	642
2	5001	637

prune774.0ms

Filtered

100 candidates to 68 candidates (68.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
0.9b	(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -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))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

392×	`frac-add`
130×	`frac-times`
102×	`associate-*r/`
82×	`*-un-lft-identity`
56×	`flip3-+` `flip-+`
52×	`exp-neg` `associate-+l-` `pow-sub`
51×	`distribute-lft-out`
35×	`neg-sub0` `exp-diff`
23×	`associate-*l/`
22×	`associate-r`
21×	`add-exp-log`
17×	`un-div-inv`
16×	`add-sqr-sqrt` `exp-prod`
15×	`prod-exp` `add-cbrt-cube` `add-log-exp`
12×	`pow1`
11×	`add-cube-cbrt`
7×	`unpow-prod-down` `cbrt-unprod`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
5×	`associate-l` `sum-log` `rem-exp-log`
4×	`pow-prod-down` `neg-log`
3×	`distribute-lft-out--` `unswap-sqr`
2×	`pow-to-exp` `sqrt-pow1` `pow-exp` `sqrt-prod` `*-commutative` `sqr-pow`
1×	`unpow-prod-up` `distribute-rgt-in` `neg-mul-1` `distribute-neg-in` `distribute-lft-in` `pow1/2` `diff-log` `exp-sum`

Counts

4 → 223

Calls

4 calls:

15.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
146.0ms	(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -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))))
22.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms	(sqrt (* PI 2.0))

series943.0ms

Counts

4 → 10

Calls

4 calls:

17.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
637.0ms	(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -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))))
288.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms	(sqrt (* PI 2.0))

simplify294.0ms

Algorithm

egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 1 (63.0ms)

Iter	Nodes	Cost
0	3749	23934
1	5001	23816

prune1.8s

Filtered

233 candidates to 140 candidates (60.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

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))
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))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

216×	`add-sqr-sqrt`
208×	`unpow-prod-down`
132×	`times-frac`
116×	`associate-l`
96×	`add-exp-log` `*-un-lft-identity`
72×	`add-cube-cbrt` `unswap-sqr`
52×	`pow-exp`
48×	`prod-exp` `sqrt-prod`
40×	`sqr-pow`
24×	`div-exp` `associate-r`
16×	`pow-to-exp`
12×	`rec-exp` `1-exp` `add-cbrt-cube`
4×	`pow1` `*-commutative` `cbrt-unprod` `div-inv` `add-log-exp`

Counts

4 → 296

Calls

4 calls:

15.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
19.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
14.0ms	(* (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	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
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))
0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

simplify75.0ms

Algorithm

egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	429	2848
1	1483	2748
2	5001	2600

prune2.5s

Filtered

300 candidates to 177 candidates (59.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(sqrt PI)
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))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

114×	`add-sqr-sqrt`
104×	`unpow-prod-down`
66×	`times-frac`
58×	`associate-l`
52×	`*-un-lft-identity`
50×	`add-exp-log`
40×	`add-cube-cbrt`
36×	`unswap-sqr`
30×	`sqrt-prod`
26×	`pow-exp`
24×	`prod-exp`
20×	`sqr-pow`
12×	`div-exp` `associate-r`
8×	`pow-to-exp` `add-cbrt-cube`
6×	`pow1` `rec-exp` `1-exp`
4×	`add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 174

Calls

4 calls:

1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
14.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
14.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
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))

simplify51.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	406	1556
1	1274	1528
2	5002	1480

prune1.3s

Filtered

178 candidates to 109 candidates (61.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes99.0ms

Accuracy

0% (1.0b remaining)

Error of 1.1b against oracle of 0.1b and baseline of 1.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	66
1	77	66

end0.0ms

sample11.8s

Algorithm

intervals

Results

4.0s	3896×	body	10240	exit
3.1s	3446×	body	1280	valid
1.6s	2481×	body	640	valid
1.0s	1466×	body	1280	nan
690.0ms	1235×	body	640	nan
539.0ms	1203×	body	320	valid
262.0ms	649×	body	320	nan
168.0ms	596×	body	160	valid
81.0ms	316×	body	160	nan
54.0ms	375×	body	80	valid
32.0ms	272×	body	80	nan