Details

sample828.0ms

Algorithm

intervals

Results

286.0ms	121×	body	10240	exit
238.0ms	114×	body	1280	valid
68.0ms	73×	body	640	valid
65.0ms	60×	body	1280	nan
37.0ms	44×	body	640	nan
25.0ms	41×	body	320	valid
15.0ms	21×	body	320	nan
7.0ms	18×	body	160	valid
5.0ms	11×	body	160	nan
2.0ms	12×	body	80	nan
2.0ms	11×	body	80	valid

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5022
3	2253
2	443
1	133
0	55

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.2b

localize178.0ms

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))
5.7b	(+ (- z 1.0) 1.0)

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
20×	`add-log-exp`
17×	`add-cube-cbrt` `distribute-lft-out`
16×	`exp-prod`
11×	`associate-+l+` `associate-r`
9×	`prod-diff` `add-exp-log`
7×	`pow1` `sum-log` `unpow-prod-down`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `add-cbrt-cube`
5×	`fma-def` `distribute-lft-out--` `rem-exp-log`
4×	`expm1-log1p-u` `associate-l` `neg-log` `log1p-expm1-u`
3×	`prod-exp` `unswap-sqr`
2×	`sqrt-pow1` `diff-log` `associate-+l-` `sqrt-prod` `sqr-pow`
1×	`neg-sub0` `exp-neg` `pow-to-exp` `unpow-prod-up` `+-commutative` `distribute-neg-in` `neg-mul-1` `sub-neg` `flip3-+` `pow1/2` `exp-diff` `exp-sum` `pow-prod-down` `pow-exp` `associate-r/` `-commutative` `cbrt-unprod` `flip-+` `pow-sub` `difference-of-squares`

Counts

4 → 112

Calls

4 calls:

711.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
741.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
6.0ms	(sqrt (* PI 2.0))
48.0ms	(+ (- z 1.0) 1.0)

series422.0ms

Counts

4 → 10

Calls

4 calls:

18.0ms	(exp (- (+ (+ (- z 1.0) 7.0) 0.5)))
392.0ms	(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms	(sqrt (* PI 2.0))
12.0ms	(+ (- z 1.0) 1.0)

simplify2.6s

Counts

122 → 122

Iterations

Iter	Nodes
done	5001
2	2127
1	612
0	252

prune1.8s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.3b

localize202.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) (/ -0.13857109526572012 (+ 6.0 (- z 1.0))))
1.0b	(/ (pow (+ 0.5 (+ 7.0 (- z 1.0))) (+ 0.5 (- z 1.0))) (exp (+ 0.5 (+ 7.0 (- z 1.0)))))
1.0b	(sqrt (* 2.0 PI))
1.2b	(* (+ (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)) (+ (+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) (/ -0.13857109526572012 (+ 6.0 (- z 1.0)))) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -176.6150291621406 (+ 4.0 (- z 1.0)))) (+ (/ 771.3234287776531 (+ 3.0 (- z 1.0))) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 676.5203681218851 z) 0.9999999999998099)))))) (* (/ (pow (+ 0.5 (+ 7.0 (- z 1.0))) (+ 0.5 (- z 1.0))) (exp (+ 0.5 (+ 7.0 (- z 1.0))))) (sqrt (* 2.0 PI))))

rewrite1.2m

Algorithm

rewrite-expression-head

Rules

537×	`frac-add`
265×	`*-un-lft-identity`
147×	`distribute-lft-out`
142×	`flip3-+` `flip-+`
129×	`associate-*l/`
77×	`times-frac`
64×	`frac-times`
36×	`add-sqr-sqrt` `add-cube-cbrt`
30×	`unpow-prod-down`
22×	`associate-l`
21×	`fma-def`
19×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`distribute-lft-out--`
12×	`pow1` `exp-sum`
11×	`associate-/l*`
9×	`prod-exp`
6×	`div-exp` `add-log-exp`
5×	`unpow-prod-up` `cbrt-unprod` `sqr-pow`
4×	`expm1-log1p-u` `associate-/r*` `pow-prod-down` `log1p-expm1-u`
3×	`associate-+r-` `associate-/r/`
2×	`pow-to-exp` `cbrt-undiv` `sqrt-pow1` `pow-exp` `div-inv`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `pow1/2` `exp-diff` `associate-r` `associate-r/` `-commutative` `sqrt-prod` `pow-sub` `associate-/l/`

Counts

4 → 307

Calls

4 calls:

206.0ms	(+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) (/ -0.13857109526572012 (+ 6.0 (- z 1.0))))
551.0ms	(/ (pow (+ 0.5 (+ 7.0 (- z 1.0))) (+ 0.5 (- z 1.0))) (exp (+ 0.5 (+ 7.0 (- z 1.0)))))
7.0ms	(sqrt (* 2.0 PI))
1.2m	(* (+ (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)) (+ (+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) (/ -0.13857109526572012 (+ 6.0 (- z 1.0)))) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -176.6150291621406 (+ 4.0 (- z 1.0)))) (+ (/ 771.3234287776531 (+ 3.0 (- z 1.0))) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 676.5203681218851 z) 0.9999999999998099)))))) (* (/ (pow (+ 0.5 (+ 7.0 (- z 1.0))) (+ 0.5 (- z 1.0))) (exp (+ 0.5 (+ 7.0 (- z 1.0))))) (sqrt (* 2.0 PI))))

series1.3s

Counts

4 → 10

Calls

4 calls:

125.0ms	(+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) (/ -0.13857109526572012 (+ 6.0 (- z 1.0))))
250.0ms	(/ (pow (+ 0.5 (+ 7.0 (- z 1.0))) (+ 0.5 (- z 1.0))) (exp (+ 0.5 (+ 7.0 (- z 1.0)))))
0.0ms	(sqrt (* 2.0 PI))
967.0ms	(* (+ (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)) (+ (+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) (/ -0.13857109526572012 (+ 6.0 (- z 1.0)))) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -176.6150291621406 (+ 4.0 (- z 1.0)))) (+ (/ 771.3234287776531 (+ 3.0 (- z 1.0))) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 676.5203681218851 z) 0.9999999999998099)))))) (* (/ (pow (+ 0.5 (+ 7.0 (- z 1.0))) (+ 0.5 (- z 1.0))) (exp (+ 0.5 (+ 7.0 (- z 1.0))))) (sqrt (* 2.0 PI))))

simplify14.3s

Counts

317 → 317

Iterations

Iter	Nodes
done	5000
1	4797
0	1229

prune7.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize166.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) (/ -0.13857109526572012 (+ 6.0 (- z 1.0))))
1.0b	(/ (pow (+ 0.5 (+ 7.0 (- z 1.0))) (+ 0.5 (- z 1.0))) (exp (+ 0.5 (+ 7.0 (- z 1.0)))))
1.0b	(sqrt (* 2.0 PI))
1.3b	(* (+ (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)) (+ (+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) (/ -0.13857109526572012 (+ 6.0 (- z 1.0)))) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -176.6150291621406 (+ 4.0 (- z 1.0)))) (+ (/ 771.3234287776531 (+ 3.0 (- z 1.0))) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 676.5203681218851 z) 0.9999999999998099)))))) (/ (pow (+ 0.5 (+ 7.0 (- z 1.0))) (+ 0.5 (- z 1.0))) (exp (+ 0.5 (+ 7.0 (- z 1.0))))))

rewrite1.1m

Algorithm

rewrite-expression-head

Rules

537×	`frac-add`
321×	`*-un-lft-identity`
167×	`distribute-lft-out`
142×	`flip3-+` `flip-+`
124×	`times-frac`
66×	`add-sqr-sqrt`
64×	`frac-times` `associate-*l/`
56×	`add-cube-cbrt`
55×	`unpow-prod-down`
49×	`associate-r`
23×	`exp-sum`
22×	`associate-l`
21×	`fma-def`
18×	`distribute-lft-out--`
13×	`add-exp-log`
11×	`add-cbrt-cube` `associate-/l*`
10×	`sqr-pow`
9×	`pow1` `unpow-prod-up`
6×	`div-exp` `add-log-exp`
5×	`associate-+r-`
4×	`expm1-log1p-u` `associate-/r*` `prod-exp` `associate-/r/` `log1p-expm1-u` `unswap-sqr`
3×	`div-inv`
2×	`pow-to-exp` `cbrt-undiv` `sqrt-pow1` `exp-diff` `pow-prod-down` `pow-exp` `cbrt-unprod`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `pow1/2` `associate-r/` `-commutative` `sqrt-prod` `pow-sub` `associate-/l/`

Counts

4 → 356

Calls

4 calls:

128.0ms	(+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) (/ -0.13857109526572012 (+ 6.0 (- z 1.0))))
334.0ms	(/ (pow (+ 0.5 (+ 7.0 (- z 1.0))) (+ 0.5 (- z 1.0))) (exp (+ 0.5 (+ 7.0 (- z 1.0)))))
3.0ms	(sqrt (* 2.0 PI))
1.1m	(* (+ (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)) (+ (+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) (/ -0.13857109526572012 (+ 6.0 (- z 1.0)))) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -176.6150291621406 (+ 4.0 (- z 1.0)))) (+ (/ 771.3234287776531 (+ 3.0 (- z 1.0))) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 676.5203681218851 z) 0.9999999999998099)))))) (/ (pow (+ 0.5 (+ 7.0 (- z 1.0))) (+ 0.5 (- z 1.0))) (exp (+ 0.5 (+ 7.0 (- z 1.0))))))

series649.0ms

Counts

4 → 10

Calls

4 calls:

73.0ms	(+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) (/ -0.13857109526572012 (+ 6.0 (- z 1.0))))
174.0ms	(/ (pow (+ 0.5 (+ 7.0 (- z 1.0))) (+ 0.5 (- z 1.0))) (exp (+ 0.5 (+ 7.0 (- z 1.0)))))
0.0ms	(sqrt (* 2.0 PI))
401.0ms	(* (+ (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)) (+ (+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) (/ -0.13857109526572012 (+ 6.0 (- z 1.0)))) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -176.6150291621406 (+ 4.0 (- z 1.0)))) (+ (/ 771.3234287776531 (+ 3.0 (- z 1.0))) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (/ 676.5203681218851 z) 0.9999999999998099)))))) (/ (pow (+ 0.5 (+ 7.0 (- z 1.0))) (+ 0.5 (- z 1.0))) (exp (+ 0.5 (+ 7.0 (- z 1.0))))))

simplify8.7s

Counts

366 → 366

Iterations

Iter	Nodes
done	5000
1	4678
0	1234

prune5.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize123.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (fma 338.26018406094255 (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (/ z (/ (exp 6.5) (* (log 6.5) (log 6.5))))) (fma 2581.191799681222 (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (/ z (exp 6.5))) (fma 676.5203681218851 (* (/ (log 6.5) (exp 6.5)) (pow (/ 1 (pow 6.5 1.0)) 0.5)) (fma 676.5203681218851 (/ (* (pow (/ 1 (pow 6.5 1.0)) 0.5) 1) (* z (exp 6.5))) (* (* 169.13009203047127 (/ z (exp 6.5))) (pow (/ 1 (pow 6.5 5.0)) 0.5)))))) (* 1656.8104518737205 (+ (* (/ z (/ (exp 6.5) (log 6.5))) (pow (/ 1 (pow 6.5 1.0)) 0.5)) (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (exp (- 6.5)))))) (sqrt (* 2.0 PI)))
1.0b	(* 1656.8104518737205 (+ (* (/ z (/ (exp 6.5) (log 6.5))) (pow (/ 1 (pow 6.5 1.0)) 0.5)) (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (exp (- 6.5)))))
1.0b	(* (/ (log 6.5) (exp 6.5)) (pow (/ 1 (pow 6.5 1.0)) 0.5))
1.0b	(sqrt (* 2.0 PI))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
54×	`times-frac` `add-exp-log`
52×	`unpow-prod-down`
37×	`*-un-lft-identity`
36×	`associate-r`
31×	`add-cube-cbrt`
26×	`pow-exp` `prod-exp`
24×	`div-exp`
22×	`associate-l`
20×	`unswap-sqr`
14×	`pow1`
13×	`add-cbrt-cube`
10×	`sqr-pow`
8×	`pow-to-exp`
7×	`associate-*r/`
6×	`rec-exp` `1-exp` `associate-*l/`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `frac-add` `log-pow` `*-commutative`
2×	`exp-neg` `sqrt-pow1` `sqrt-prod` `div-inv`
1×	`neg-sub0` `distribute-rgt-in` `cbrt-undiv` `distribute-lft-in` `flip3-+` `flip3--` `pow1/2` `exp-diff` `un-div-inv` `flip-+` `flip--`

Counts

4 → 163

Calls

4 calls:

22.0ms	(* (- (fma 338.26018406094255 (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (/ z (/ (exp 6.5) (* (log 6.5) (log 6.5))))) (fma 2581.191799681222 (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (/ z (exp 6.5))) (fma 676.5203681218851 (* (/ (log 6.5) (exp 6.5)) (pow (/ 1 (pow 6.5 1.0)) 0.5)) (fma 676.5203681218851 (/ (* (pow (/ 1 (pow 6.5 1.0)) 0.5) 1) (* z (exp 6.5))) (* (* 169.13009203047127 (/ z (exp 6.5))) (pow (/ 1 (pow 6.5 5.0)) 0.5)))))) (* 1656.8104518737205 (+ (* (/ z (/ (exp 6.5) (log 6.5))) (pow (/ 1 (pow 6.5 1.0)) 0.5)) (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (exp (- 6.5)))))) (sqrt (* 2.0 PI)))
85.0ms	(* 1656.8104518737205 (+ (* (/ z (/ (exp 6.5) (log 6.5))) (pow (/ 1 (pow 6.5 1.0)) 0.5)) (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (exp (- 6.5)))))
50.0ms	(* (/ (log 6.5) (exp 6.5)) (pow (/ 1 (pow 6.5 1.0)) 0.5))
3.0ms	(sqrt (* 2.0 PI))

series4.2s

Counts

4 → 8

Calls

4 calls:

2.4s	(* (- (fma 338.26018406094255 (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (/ z (/ (exp 6.5) (* (log 6.5) (log 6.5))))) (fma 2581.191799681222 (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (/ z (exp 6.5))) (fma 676.5203681218851 (* (/ (log 6.5) (exp 6.5)) (pow (/ 1 (pow 6.5 1.0)) 0.5)) (fma 676.5203681218851 (/ (* (pow (/ 1 (pow 6.5 1.0)) 0.5) 1) (* z (exp 6.5))) (* (* 169.13009203047127 (/ z (exp 6.5))) (pow (/ 1 (pow 6.5 5.0)) 0.5)))))) (* 1656.8104518737205 (+ (* (/ z (/ (exp 6.5) (log 6.5))) (pow (/ 1 (pow 6.5 1.0)) 0.5)) (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (exp (- 6.5)))))) (sqrt (* 2.0 PI)))
1.8s	(* 1656.8104518737205 (+ (* (/ z (/ (exp 6.5) (log 6.5))) (pow (/ 1 (pow 6.5 1.0)) 0.5)) (* (pow (/ 1 (pow 6.5 1.0)) 0.5) (exp (- 6.5)))))
0.0ms	(* (/ (log 6.5) (exp 6.5)) (pow (/ 1 (pow 6.5 1.0)) 0.5))
0.0ms	(sqrt (* 2.0 PI))

simplify2.2s

Counts

171 → 171

Iterations

Iter	Nodes
done	5002
2	3783
1	1081
0	390

prune1.8s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes223.0ms

Accuracy

0% (1.0b remaining)

Error of 1.0b against oracle of 0.0b and baseline of 1.0b

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	73
1	73
0	53

end0.0ms

sample22.9s

Algorithm

intervals

Results

8.6s	3996×	body	10240	exit
4.5s	3391×	body	1280	valid
3.2s	2516×	body	640	valid
2.1s	1521×	body	1280	nan
1.4s	1218×	body	320	valid
1.1s	1266×	body	640	nan
913.0ms	625×	body	320	nan
271.0ms	301×	body	160	nan
216.0ms	639×	body	160	valid
54.0ms	316×	body	80	valid
47.0ms	301×	body	80	nan