Details

sample827.0ms

Algorithm

intervals

Results

244.0ms	113×	body	10240	exit
215.0ms	115×	body	1280	valid
93.0ms	47×	body	1280	nan
73.0ms	67×	body	640	valid
69.0ms	41×	body	640	nan
26.0ms	38×	body	320	valid
12.0ms	24×	body	160	valid
12.0ms	18×	body	320	nan
4.0ms	15×	body	80	valid
3.0ms	7×	body	160	nan
2.0ms	10×	body	80	nan

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 3 (729.0ms)

Iter	Nodes	Cost
0	55	94
1	133	94
2	449	92
3	2874	89
done	5001	89

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.9b

localize84.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
1.0b	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
1.0b	(sqrt (* PI 2.0))
1.4b	(* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (+ (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (+ (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (+ (/ 676.5203681218851 z) 0.9999999999998099))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))

rewrite3.2m

Algorithm

rewrite-expression-head

Rules

916×	`frac-add`
336×	`flip3-+` `flip-+`
198×	`*-un-lft-identity`
152×	`distribute-lft-out`
116×	`frac-times` `associate-*r/`
37×	`associate-r`
27×	`add-exp-log`
20×	`associate-l` `add-cbrt-cube`
19×	`add-sqr-sqrt`
14×	`prod-exp`
12×	`add-cube-cbrt`
9×	`pow1`
8×	`times-frac` `div-exp`
7×	`unpow-prod-down`
6×	`associate-+l-` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `exp-sum` `associate-*l/` `pow-exp`
2×	`sqrt-pow1` `exp-diff` `pow-prod-down` `sqrt-prod` `associate-/r/` `*-commutative` `div-inv` `pow-sub` `sqr-pow`
1×	`unpow-prod-up` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow1/2` `clear-num` `associate-/l/` `associate-/l*` `distribute-lft-out--`

Counts

4 → 372

Calls

4 calls:

600.0ms	(/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
630.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
4.0ms	(sqrt (* PI 2.0))
3.2m	(* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (+ (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (+ (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (+ (/ 676.5203681218851 z) 0.9999999999998099))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))

series1.3s

Counts

4 → 10

Calls

4 calls:

389.0ms	(/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
256.0ms	(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
0.0ms	(sqrt (* PI 2.0))
612.0ms	(* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (+ (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (+ (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (+ (/ 676.5203681218851 z) 0.9999999999998099))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))

simplify649.0ms

Counts

382 → 382

Iterations

Useful iterations: done (546.0ms)

Iter	Nodes	Cost
0	1429	98383
done	5001	90484

prune6.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize91.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (sqrt 2.0) (exp 6.5))
1.0b	(* (log 6.5) (sqrt 2.0))
1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

132×	`add-sqr-sqrt`
104×	`unpow-prod-down`
84×	`times-frac`
68×	`*-un-lft-identity`
62×	`associate-l`
56×	`add-cube-cbrt`
53×	`add-exp-log`
40×	`sqrt-prod`
38×	`unswap-sqr`
26×	`pow-exp`
25×	`prod-exp`
20×	`sqr-pow`
18×	`associate-r`
13×	`div-exp`
12×	`add-cbrt-cube`
8×	`pow-to-exp`
7×	`pow1`
6×	`rec-exp` `1-exp` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `-commutative` `cbrt-unprod` `div-inv`
1×	`cbrt-undiv` `frac-2neg` `pow-prod-down` `clear-num` `log-pow`

Counts

4 → 218

Calls

4 calls:

9.0ms	(/ (sqrt 2.0) (exp 6.5))
11.0ms	(* (log 6.5) (sqrt 2.0))
50.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
54.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/ (sqrt 2.0) (exp 6.5))
0.0ms	(* (log 6.5) (sqrt 2.0))
0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

simplify874.0ms

Counts

222 → 222

Iterations

Useful iterations: done (867.0ms)

Iter	Nodes	Cost
0	278	3530
1	593	3336
2	2187	3227
done	5001	3169

prune2.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize89.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(* (log 6.5) (sqrt 2.0))
1.0b	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
1.2b	(/ (* (sqrt PI) (pow (log 6.5) 2)) (/ (exp 6.5) (* z (sqrt 2.0))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`add-exp-log`
52×	`unpow-prod-down`
46×	`times-frac`
35×	`*-un-lft-identity`
33×	`associate-l`
29×	`add-cube-cbrt` `add-cbrt-cube`
26×	`div-exp` `prod-exp`
20×	`unswap-sqr`
19×	`sqrt-prod`
16×	`pow-exp`
12×	`associate-r`
10×	`cbrt-undiv` `sqr-pow`
8×	`pow1`
7×	`pow-to-exp` `associate-/r*` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`*-commutative`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `associate-/r/` `log-pow` `associate-/l*`

Counts

4 → 162

Calls

4 calls:

1.0ms	(sqrt PI)
11.0ms	(* (log 6.5) (sqrt 2.0))
51.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
24.0ms	(/ (* (sqrt PI) (pow (log 6.5) 2)) (/ (exp 6.5) (* z (sqrt 2.0))))

series418.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(sqrt PI)
0.0ms	(* (log 6.5) (sqrt 2.0))
0.0ms	(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
418.0ms	(/ (* (sqrt PI) (pow (log 6.5) 2)) (/ (exp 6.5) (* z (sqrt 2.0))))

simplify1.2s

Counts

168 → 168

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	324	2824
1	789	2635
2	3785	2464
done	5000	2441

prune1.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize93.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(* (log 6.5) (sqrt 2.0))
1.0b	(fma 0.5 (- (log (pow 6.5 1.0))) (log (sqrt PI)))
1.2b	(/ (* (sqrt PI) (pow (log 6.5) 2)) (/ (exp 6.5) (* z (sqrt 2.0))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-exp-log`
27×	`add-cbrt-cube`
20×	`div-exp`
17×	`add-sqr-sqrt`
14×	`prod-exp`
13×	`times-frac`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`cbrt-undiv`
8×	`pow1`
7×	`associate-/r*` `sqrt-prod`
6×	`associate-r` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-exp` `div-inv`
2×	`unswap-sqr`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `associate-/r/` `log-pow` `-commutative` `fma-udef` `associate-/l`

Counts

4 → 96

Calls

4 calls:

1.0ms	(sqrt PI)
11.0ms	(* (log 6.5) (sqrt 2.0))
0.0ms	(fma 0.5 (- (log (pow 6.5 1.0))) (log (sqrt PI)))
31.0ms	(/ (* (sqrt PI) (pow (log 6.5) 2)) (/ (exp 6.5) (* z (sqrt 2.0))))

series414.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(sqrt PI)
0.0ms	(* (log 6.5) (sqrt 2.0))
0.0ms	(fma 0.5 (- (log (pow 6.5 1.0))) (log (sqrt PI)))
414.0ms	(/ (* (sqrt PI) (pow (log 6.5) 2)) (/ (exp 6.5) (* z (sqrt 2.0))))

simplify1.0s

Counts

102 → 102

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	210	1804
1	540	1682
2	2889	1521
done	5001	1500

prune1.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes140.0ms

Accuracy

0% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 1.1b

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	61	126
1	81	126
done	81	126

end0.0ms

sample22.4s

Algorithm

intervals

Results

8.1s	3826×	body	10240	exit
6.3s	3439×	body	1280	valid
2.8s	2490×	body	640	valid
1.8s	1500×	body	1280	nan
1.1s	1221×	body	320	valid
1.1s	1249×	body	640	nan
354.0ms	592×	body	320	nan
211.0ms	608×	body	160	valid
135.0ms	321×	body	160	nan
59.0ms	317×	body	80	valid
41.0ms	272×	body	80	nan