Details

sample411.0ms

Algorithm

intervals

Results

126.0ms	108×	body	10240	exit
95.0ms	103×	body	1280	valid
60.0ms	89×	body	640	valid
31.0ms	46×	body	1280	nan
21.0ms	40×	body	640	nan
17.0ms	37×	body	320	valid
9.0ms	24×	body	320	nan
5.0ms	19×	body	160	valid
3.0ms	11×	body	160	nan
2.0ms	11×	body	80	valid
1.0ms	11×	body	80	nan

simplify72.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

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: 61.8b

localize53.0ms

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))
5.9b	(+ (- z 1.0) 1.0)

rewrite495.0ms

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:

154.0ms	(exp (+ (+ (- z 1.0) 7.0) 0.5))
320.0ms	(* (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)

series306.0ms

Counts

4 → 10

Calls

4 calls:

11.0ms	(exp (+ (+ (- z 1.0) 7.0) 0.5))
285.0ms	(* (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)

simplify69.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (59.0ms)

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

prune932.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.2b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (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))
1.0b	(/ (* (* (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)))

rewrite10.0m

Algorithm: rewrite-expression-head