Details

sample1.7s

Algorithm

intervals

Results

671.0ms	142×	body	10240	exit
572.0ms	261×	body	80	valid
205.0ms	52×	body	1280	nan
97.0ms	43×	body	640	nan
55.0ms	18×	body	320	nan
22.0ms	16×	body	160	nan
4.0ms	8×	body	80	nan

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
3	3527
2	616
1	155
0	60

prune96.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize209.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (+ (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- (- 6 z) 1))) (+ (+ (+ (/ -176.6150291621406 (+ (+ 2 (- 1 z)) 1)) 0.9999999999998099) (/ 676.5203681218851 (- 1 z))) (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (+ 2 (- 1 z)))))) (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z)))) (exp (+ (- 7 z) 0.5)))
1.0b	(+ (+ (+ (/ -176.6150291621406 (+ (+ 2 (- 1 z)) 1)) 0.9999999999998099) (/ 676.5203681218851 (- 1 z))) (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (+ 2 (- 1 z)))))
1.0b	(sqrt (* 2 PI))
1.0b	(* PI (sqrt (* 2 PI)))

rewrite3.8m

Algorithm

rewrite-expression-head

Rules

957×	`*-un-lft-identity`
753×	`distribute-lft-out`
564×	`frac-add`
200×	`flip3-+` `flip-+`
134×	`associate-/l/`
132×	`times-frac`
48×	`add-sqr-sqrt`
46×	`add-cube-cbrt`
34×	`exp-sum`
33×	`associate-/l*`
25×	`add-log-exp`
15×	`sum-log`
9×	`pow1`
8×	`add-cbrt-cube`
7×	`add-exp-log`
5×	`fma-def`
4×	`expm1-log1p-u` `associate-/r` `associate-r*` `insert-posit16` `log1p-expm1-u`
3×	`associate-l`
2×	`sqrt-pow1` `pow-prod-down` `sqrt-prod`
1×	`cbrt-undiv` `+-commutative` `associate-+l+` `associate-+r+` `clear-num` `frac-2neg` `pow1/2` `exp-diff` `div-exp` `prod-exp` `associate-/r/` `*-commutative` `associate-+l-` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 399

Calls

4 calls:

3.6m	(/ (+ (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- (- 6 z) 1))) (+ (+ (+ (/ -176.6150291621406 (+ (+ 2 (- 1 z)) 1)) 0.9999999999998099) (/ 676.5203681218851 (- 1 z))) (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (+ 2 (- 1 z)))))) (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z)))) (exp (+ (- 7 z) 0.5)))
7.8s	(+ (+ (+ (/ -176.6150291621406 (+ (+ 2 (- 1 z)) 1)) 0.9999999999998099) (/ 676.5203681218851 (- 1 z))) (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (+ 2 (- 1 z)))))
4.0ms	(sqrt (* 2 PI))
26.0ms	(* PI (sqrt (* 2 PI)))

series402.0ms

Counts

4 → 8

Calls

4 calls:

286.0ms	(/ (+ (+ (+ (/ -0.13857109526572012 (- 6 z)) (/ 12.507343278686905 (- (- 6 z) 1))) (+ (+ (+ (/ -176.6150291621406 (+ (+ 2 (- 1 z)) 1)) 0.9999999999998099) (/ 676.5203681218851 (- 1 z))) (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (+ 2 (- 1 z)))))) (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z)))) (exp (+ (- 7 z) 0.5)))
116.0ms	(+ (+ (+ (/ -176.6150291621406 (+ (+ 2 (- 1 z)) 1)) 0.9999999999998099) (/ 676.5203681218851 (- 1 z))) (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (+ 2 (- 1 z)))))
0.0ms	(sqrt (* 2 PI))
0.0ms	(* PI (sqrt (* 2 PI)))

simplify2.2s

Counts

407 → 407

Iterations

Iter	Nodes
1	2501
0	657

prune15.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize124.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (sqrt PI) (sqrt (* 2 PI)))
1.0b	(sqrt PI)
1.0b	(sqrt PI)
1.0b	(sqrt (* 2 PI))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
15×	`add-sqr-sqrt`
12×	`sqrt-prod`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-pow1`
6×	`add-cbrt-cube` `associate-l` `pow-prod-down` `add-exp-log`
5×	`pow1/2`
4×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `unswap-sqr`
1×	`sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 76

Calls

4 calls:

15.0ms	(* (sqrt PI) (sqrt (* 2 PI)))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
8.0ms	(sqrt (* 2 PI))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(* (sqrt PI) (sqrt (* 2 PI)))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
0.0ms	(sqrt (* 2 PI))

simplify4.8s

Counts

80 → 80

Iterations

Iter	Nodes
7	5805
6	1877
5	1014
4	645
3	418
2	193
1	91
0	55

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize245.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* (- (/ -176.6150291621406 (+ (+ 2 (- 1 z)) 1)) 0.9999999999998099) (- 1 z)) (- (* (/ -1259.1392167224028 (- 2 z)) (/ -1259.1392167224028 (- 2 z))) (* (/ 771.3234287776531 (+ 2 (- 1 z))) (/ 771.3234287776531 (+ 2 (- 1 z))))))
1.0b	(+ (* (+ (* (- (* (/ -176.6150291621406 (+ (+ 2 (- 1 z)) 1)) (/ -176.6150291621406 (+ (+ 2 (- 1 z)) 1))) (* 0.9999999999998099 0.9999999999998099)) (- 1 z)) (* (- (/ -176.6150291621406 (+ (+ 2 (- 1 z)) 1)) 0.9999999999998099) 676.5203681218851)) (- (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (+ 2 (- 1 z))))) (* (* (- (/ -176.6150291621406 (+ (+ 2 (- 1 z)) 1)) 0.9999999999998099) (- 1 z)) (- (* (/ -1259.1392167224028 (- 2 z)) (/ -1259.1392167224028 (- 2 z))) (* (/ 771.3234287776531 (+ 2 (- 1 z))) (/ 771.3234287776531 (+ 2 (- 1 z)))))))
1.0b	(sqrt (* 2 PI))
1.0b	(* PI (sqrt (* 2 PI)))

rewrite3.5s

Algorithm

rewrite-expression-head

Rules

23642×	`frac-times`
17022×	`associate-*l/`
16791×	`flip3--` `flip--`
14873×	`frac-add`
8797×	`associate-*r/`
8189×	`frac-sub`
1645×	`*-un-lft-identity`
1260×	`times-frac`
1017×	`add-sqr-sqrt`
886×	`associate-+l+` `prod-diff`
763×	`add-cube-cbrt`
471×	`flip3-+` `flip-+`
449×	`distribute-rgt-in` `distribute-lft-in`
252×	`distribute-lft-out` `distribute-lft-out--`
168×	`associate-/r/`
127×	`difference-of-squares`
84×	`div-inv`
14×	`pow1`
11×	`add-cbrt-cube` `add-exp-log`
8×	`associate-r`
6×	`associate-+r+` `sub-neg` `add-log-exp`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `associate-l` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
2×	`sqrt-pow1` `*-commutative` `sqrt-prod`
1×	`+-commutative` `sum-log` `fma-def` `pow1/2` `unswap-sqr`

Counts

4 → 9103

Calls

4 calls:

1.3s	(* (* (- (/ -176.6150291621406 (+ (+ 2 (- 1 z)) 1)) 0.9999999999998099) (- 1 z)) (- (* (/ -1259.1392167224028 (- 2 z)) (/ -1259.1392167224028 (- 2 z))) (* (/ 771.3234287776531 (+ 2 (- 1 z))) (/ 771.3234287776531 (+ 2 (- 1 z))))))
932.0ms	(+ (* (+ (* (- (* (/ -176.6150291621406 (+ (+ 2 (- 1 z)) 1)) (/ -176.6150291621406 (+ (+ 2 (- 1 z)) 1))) (* 0.9999999999998099 0.9999999999998099)) (- 1 z)) (* (- (/ -176.6150291621406 (+ (+ 2 (- 1 z)) 1)) 0.9999999999998099) 676.5203681218851)) (- (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (+ 2 (- 1 z))))) (* (* (- (/ -176.6150291621406 (+ (+ 2 (- 1 z)) 1)) 0.9999999999998099) (- 1 z)) (- (* (/ -1259.1392167224028 (- 2 z)) (/ -1259.1392167224028 (- 2 z))) (* (/ 771.3234287776531 (+ 2 (- 1 z))) (/ 771.3234287776531 (+ 2 (- 1 z)))))))
4.0ms	(sqrt (* 2 PI))
13.0ms	(* PI (sqrt (* 2 PI)))

series627.0ms

Counts

4 → 8

Calls

4 calls:

125.0ms	(* (* (- (/ -176.6150291621406 (+ (+ 2 (- 1 z)) 1)) 0.9999999999998099) (- 1 z)) (- (* (/ -1259.1392167224028 (- 2 z)) (/ -1259.1392167224028 (- 2 z))) (* (/ 771.3234287776531 (+ 2 (- 1 z))) (/ 771.3234287776531 (+ 2 (- 1 z))))))
502.0ms	(+ (* (+ (* (- (* (/ -176.6150291621406 (+ (+ 2 (- 1 z)) 1)) (/ -176.6150291621406 (+ (+ 2 (- 1 z)) 1))) (* 0.9999999999998099 0.9999999999998099)) (- 1 z)) (* (- (/ -176.6150291621406 (+ (+ 2 (- 1 z)) 1)) 0.9999999999998099) 676.5203681218851)) (- (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (+ 2 (- 1 z))))) (* (* (- (/ -176.6150291621406 (+ (+ 2 (- 1 z)) 1)) 0.9999999999998099) (- 1 z)) (- (* (/ -1259.1392167224028 (- 2 z)) (/ -1259.1392167224028 (- 2 z))) (* (/ 771.3234287776531 (+ 2 (- 1 z))) (/ 771.3234287776531 (+ 2 (- 1 z)))))))
0.0ms	(sqrt (* 2 PI))
0.0ms	(* PI (sqrt (* 2 PI)))

simplify1.9m

Counts

9111 → 9111

Iterations

Iter	Nodes
1	95705
0	26142

Details

sample1.7s

simplify1.8s

prune96.0ms

localize209.0ms

rewrite3.8m

series402.0ms

simplify2.2s

prune15.6s

localize124.0ms

rewrite26.0ms

series0.0ms

simplify4.8s

prune2.2s

localize245.0ms

rewrite3.5s

series627.0ms

simplify1.9m

prune3.8m