Details

sample413.0ms

Algorithm

intervals

Results

137.0ms	137×	body	10240	exit
88.0ms	104×	body	1280	valid
49.0ms	82×	body	640	valid
29.0ms	46×	body	1280	nan
26.0ms	46×	body	640	nan
18.0ms	42×	body	320	valid
6.0ms	18×	body	320	nan
5.0ms	19×	body	160	valid
3.0ms	11×	body	160	nan
2.0ms	12×	body	80	valid
1.0ms	10×	body	80	nan

simplify72.0ms

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: 61.7b

localize47.0ms

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))) (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))
6.1b	(+ (- z 1.0) 1.0)

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cube-cbrt` `associate-r`
11×	`associate-+l+` `add-cbrt-cube`
10×	`prod-exp`
9×	`pow1` `prod-diff` `add-log-exp`
7×	`unpow-prod-down` `distribute-lft-out`
6×	`associate-*r/`
5×	`associate-+l-` `fma-def` `associate-l`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `pow-sub`
3×	`exp-neg` `distribute-lft-out--` `unswap-sqr`
2×	`neg-sub0` `frac-times` `pow-to-exp` `sqrt-pow1` `exp-diff` `pow-prod-down` `pow-exp` `sum-log` `sqrt-prod` `*-commutative` `sqr-pow`
1×	`unpow-prod-up` `+-commutative` `sub-neg` `distribute-neg-in` `flip3-+` `pow1/2` `diff-log` `exp-sum` `associate-*l/` `un-div-inv` `flip-+` `difference-of-squares`

Counts

4 → 107

Calls

4 calls:

1.1s	(* (* (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))))
304.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms	(sqrt (* PI 2.0))
15.0ms	(+ (- z 1.0) 1.0)

series662.0ms

Counts

4 → 10

Calls

4 calls:

378.0ms	(* (* (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))))
274.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms	(sqrt (* PI 2.0))
9.0ms	(+ (- z 1.0) 1.0)

simplify108.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	775	1254
1	3561	1056
2	5001	1041

prune973.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.9b

localize51.0ms

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))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5))))
0.7b	(* (* (* (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 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))

rewrite9.9m

Algorithm

rewrite-expression-head

Calls

2 calls:

322.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms	(sqrt (* PI 2.0))