Details

sample1.9s

Algorithm

intervals

Results

726.0ms	98×	body	1280	valid
506.0ms	127×	body	10240	exit
164.0ms	83×	body	640	valid
138.0ms	54×	body	1280	nan
123.0ms	56×	body	640	nan
104.0ms	18×	body	320	nan
60.0ms	42×	body	320	valid
20.0ms	21×	body	160	valid
7.0ms	7×	body	160	nan
6.0ms	13×	body	80	valid
2.0ms	5×	body	80	nan

simplify225.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

224.0ms

(* (* (* (sqrt (* PI 2)) (pow (+ (+ (- z 1) 7) 0.5) (+ (- z 1) 0.5))) (exp (- (+ (+ (- z 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- z 1) 1))) (/ -1259.1392167224028 (+ (- z 1) 2))) (/ 771.3234287776531 (+ (- z 1) 3))) (/ -176.6150291621406 (+ (- z 1) 4))) (/ 12.507343278686905 (+ (- z 1) 5))) (/ -0.13857109526572012 (+ (- z 1) 6))) (/ 9.984369578019572e-06 (+ (- z 1) 7))) (/ 1.5056327351493116e-07 (+ (- z 1) 8))))

prune43.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize141.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (* PI 2))
1.0b	(sqrt (* PI 2))
1.0b	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
1.0b	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))

rewrite941.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
22×	`associate-l`
20×	`add-sqr-sqrt`
14×	`unpow-prod-down` `add-exp-log`
10×	`pow1` `add-cube-cbrt` `distribute-lft-out`
8×	`add-cbrt-cube` `associate-r`
6×	`prod-exp` `unswap-sqr`
4×	`expm1-log1p-u` `sqrt-pow1` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `unpow-prod-up` `pow1/2` `pow-prod-down` `associate-l/` `pow-exp` `-commutative` `associate-+l-` `cbrt-unprod` `distribute-lft-out--` `pow-sub`

Counts

4 → 96

Calls

4 calls:

Slowest

472.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
454.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
7.0ms	(sqrt (* PI 2))
6.0ms	(sqrt (* PI 2))

series842.0ms

Counts

4 → 8

Calls

4 calls:

Slowest

451.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
391.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))
0.0ms	(sqrt (* PI 2))

simplify14.9s

Counts

64 → 104

Calls

64 calls:

Slowest

855.0ms	(+ (* (+ (/ 12.507343278686905 (+ z 4)) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (+ (/ 676.5203681218851 z) (+ 0.9999999999998099 (/ -1259.1392167224028 (- z -1))))) (/ -176.6150291621406 (+ z 3))) (/ -0.13857109526572012 (- z -5)))) (* (* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (- (+ (+ 7 (- z 1)) 0.5))))) (* (+ (/ 9.984369578019572e-06 (+ 7 (- z 1))) (/ 1.5056327351493116e-07 (+ z 7))) (* (* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (- (+ (+ 7 (- z 1)) 0.5))))))
768.0ms	(+ (* (+ (/ 12.507343278686905 (+ z 4)) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (+ (/ 676.5203681218851 z) (+ 0.9999999999998099 (/ -1259.1392167224028 (- z -1))))) (/ -176.6150291621406 (+ z 3))) (/ -0.13857109526572012 (- z -5)))) (* (* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (- (+ (+ 7 (- z 1)) 0.5))))) (* (+ (/ 9.984369578019572e-06 (+ 7 (- z 1))) (/ 1.5056327351493116e-07 (+ z 7))) (* (* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (- (+ (+ 7 (- z 1)) 0.5))))))
480.0ms	(+ (* (log (+ (+ 7 (- z 1)) 0.5)) (+ (- z 1) 0.5)) (log (sqrt (* PI 2))))
477.0ms	(pow (+ (+ 7 (- z 1)) 0.5) (- z 1))
474.0ms	(pow (+ (+ 7 (- z 1)) 0.5) (- z 1))

prune4.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize168.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (* PI 2))
1.0b	(sqrt (* PI 2))
1.0b	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
1.0b	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))

rewrite781.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
22×	`associate-l`
20×	`add-sqr-sqrt`
14×	`unpow-prod-down` `add-exp-log`
10×	`pow1` `add-cube-cbrt` `distribute-lft-out`
8×	`add-cbrt-cube` `associate-r`
6×	`prod-exp` `unswap-sqr`
4×	`expm1-log1p-u` `sqrt-pow1` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `unpow-prod-up` `pow1/2` `pow-prod-down` `associate-l/` `pow-exp` `-commutative` `associate-+l-` `cbrt-unprod` `distribute-lft-out--` `pow-sub`

Counts

4 → 96

Calls

4 calls:

Slowest

391.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
380.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
4.0ms	(sqrt (* PI 2))
4.0ms	(sqrt (* PI 2))

series730.0ms

Counts

4 → 8

Calls

4 calls:

Slowest

377.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
353.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
0.0ms	(sqrt (* PI 2))
0.0ms	(sqrt (* PI 2))

simplify14.6s

Counts

64 → 104

Calls

64 calls:

Slowest

852.0ms	(+ (* (+ (/ 12.507343278686905 (+ z 4)) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (+ (/ 676.5203681218851 z) (+ 0.9999999999998099 (/ -1259.1392167224028 (- z -1))))) (/ -176.6150291621406 (+ z 3))) (/ -0.13857109526572012 (- z -5)))) (* (* 1 (* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))) (exp (- (+ (+ 7 (- z 1)) 0.5))))) (* (+ (/ 9.984369578019572e-06 (+ 7 (- z 1))) (/ 1.5056327351493116e-07 (+ z 7))) (* (* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (- (+ (+ 7 (- z 1)) 0.5))))))
800.0ms	(+ (* (+ (/ 12.507343278686905 (+ z 4)) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (+ (/ 676.5203681218851 z) (+ 0.9999999999998099 (/ -1259.1392167224028 (- z -1))))) (/ -176.6150291621406 (+ z 3))) (/ -0.13857109526572012 (- z -5)))) (* (* 1 (* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))) (exp (- (+ (+ 7 (- z 1)) 0.5))))) (* (+ (/ 9.984369578019572e-06 (+ 7 (- z 1))) (/ 1.5056327351493116e-07 (+ z 7))) (* (* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (- (+ (+ 7 (- z 1)) 0.5))))))
634.0ms	(pow (sqrt (+ (+ 7 (- z 1)) 0.5)) (+ (- z 1) 0.5))
485.0ms	(pow (+ (+ 7 (- z 1)) 0.5) (- z 1))
442.0ms	(* (pow (+ (+ 7 (- z 1)) 0.5) (/ (+ (- z 1) 0.5) 2)) (sqrt (sqrt (* PI 2))))

prune4.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize164.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (* PI 2))
1.0b	(/ (sqrt (* PI 2)) (/ (exp (- (+ z 0.5) -6)) (pow (- (+ z 0.5) -6) (+ 0.5 (- z 1)))))
0.9b	(/ (exp (- (+ z 0.5) -6)) (pow (- (+ z 0.5) -6) (+ 0.5 (- z 1))))
0.9b	(+ (/ -0.13857109526572012 (- z -5)) (+ (/ 1.5056327351493116e-07 (+ 7 z)) (/ 9.984369578019572e-06 (+ z 6))))

rewrite547.0ms

Algorithm

rewrite-expression-head

Rules

2039×	`times-frac`
1994×	`*-un-lft-identity`
1200×	`add-sqr-sqrt`
1005×	`exp-sum`
976×	`add-cube-cbrt`
804×	`prod-diff`
654×	`unpow-prod-down`
337×	`distribute-lft-out`
225×	`distribute-lft-out--`
214×	`associate-/r*`
205×	`sqrt-prod`
112×	`difference-of-squares`
109×	`unpow-prod-up` `sqr-pow`
67×	`sub-neg` `associate--l+`
22×	`associate-/l*`
21×	`fma-def`
13×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`div-exp`
9×	`associate-/r/` `add-log-exp`
8×	`div-inv`
7×	`pow1`
6×	`associate-+r-` `pow-sub`
4×	`expm1-log1p-u` `cbrt-undiv` `frac-add` `insert-posit16` `log1p-expm1-u`
3×	`sum-log`
2×	`pow-to-exp` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `pow-exp` `flip-+`
1×	`+-commutative` `associate-+r+` `flip3--` `pow1/2` `exp-diff` `pow-prod-down` `flip--` `associate-/l/`

Counts

4 → 1349

Calls

4 calls:

Slowest

170.0ms	(/ (sqrt (* PI 2)) (/ (exp (- (+ z 0.5) -6)) (pow (- (+ z 0.5) -6) (+ 0.5 (- z 1)))))
155.0ms	(/ (exp (- (+ z 0.5) -6)) (pow (- (+ z 0.5) -6) (+ 0.5 (- z 1))))
143.0ms	(+ (/ -0.13857109526572012 (- z -5)) (+ (/ 1.5056327351493116e-07 (+ 7 z)) (/ 9.984369578019572e-06 (+ z 6))))
6.0ms	(sqrt (* PI 2))

series870.0ms

Counts

4 → 10

Calls

4 calls:

Slowest

537.0ms	(/ (sqrt (* PI 2)) (/ (exp (- (+ z 0.5) -6)) (pow (- (+ z 0.5) -6) (+ 0.5 (- z 1)))))
220.0ms	(/ (exp (- (+ z 0.5) -6)) (pow (- (+ z 0.5) -6) (+ 0.5 (- z 1))))
113.0ms	(+ (/ -0.13857109526572012 (- z -5)) (+ (/ 1.5056327351493116e-07 (+ 7 z)) (/ 9.984369578019572e-06 (+ z 6))))
0.0ms	(sqrt (* PI 2))