Details

sample423.0ms

Algorithm

intervals

Results

147.0ms	142×	body	10240	exit
96.0ms	109×	body	1280	valid
45.0ms	70×	body	640	valid
42.0ms	66×	body	1280	nan
15.0ms	36×	body	320	valid
13.0ms	26×	body	640	nan
8.0ms	30×	body	160	valid
6.0ms	17×	body	320	nan
2.0ms	9×	body	160	nan
2.0ms	13×	body	80	valid
1.0ms	11×	body	80	nan

simplify75.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (15.0ms)

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

prune27.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 60.3b

localize49.0ms

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))
7.6b	(+ (- z 1.0) 1.0)

rewrite599.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
20×	`add-log-exp`
17×	`add-cube-cbrt` `distribute-lft-out`
16×	`exp-prod`
11×	`associate-+l+` `associate-r`
9×	`add-exp-log` `prod-diff`
7×	`pow1` `unpow-prod-down` `sum-log`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `add-cbrt-cube`
5×	`fma-def` `rem-exp-log` `distribute-lft-out--`
4×	`expm1-log1p-u` `associate-l` `neg-log` `log1p-expm1-u`
3×	`prod-exp` `unswap-sqr`
2×	`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` `difference-of-squares`

Counts

4 → 112

Calls

4 calls:

267.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
310.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms	(sqrt (* PI 2.0))
16.0ms	(+ (- z 1.0) 1.0)

series312.0ms

Counts

4 → 10

Calls

4 calls:

17.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
281.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms	(sqrt (* PI 2.0))
13.0ms	(+ (- z 1.0) 1.0)

simplify73.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	595	821
1	2411	692
2	5001	670

prune990.0ms

Filtered

122 candidates to 89 candidates (73.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.2b

localize46.0ms

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))
1.0b	(* (* (* (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))))

rewrite10.0m

Algorithm: rewrite-expression-head