Details

sample1.6s

Algorithm

intervals

Results

1.3s	124×	body	10240	exit
52.0ms	51×	body	1280	nan
48.0ms	261×	body	80	valid
34.0ms	49×	body	640	nan
10.0ms	21×	body	320	nan
4.0ms	12×	body	160	nan
1.0ms	7×	body	80	nan

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	60	123
1	148	123
2	594	121
3	3627	88
done	5001	78

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize59.0ms

Local error

Found 4 expressions with local error:

6.3b	(- (- 1.0 z) 1.0)
6.3b	(- (- 1.0 z) 1.0)
6.3b	(- (- 1.0 z) 1.0)
6.3b	(- (- 1.0 z) 1.0)

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

116×	`*-un-lft-identity`
104×	`add-sqr-sqrt`
96×	`prod-diff`
64×	`add-cube-cbrt`
44×	`associate--l+`
28×	`distribute-lft-out--`
24×	`add-log-exp`
20×	`fma-neg` `difference-of-squares`
12×	`diff-log`
8×	`sub-neg`
4×	`pow1` `add-exp-log` `associate--l-` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

4 → 200

Calls

4 calls:

23.0ms	(- (- 1.0 z) 1.0)
27.0ms	(- (- 1.0 z) 1.0)
22.0ms	(- (- 1.0 z) 1.0)
23.0ms	(- (- 1.0 z) 1.0)

series50.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- (- 1.0 z) 1.0)
15.0ms	(- (- 1.0 z) 1.0)
11.0ms	(- (- 1.0 z) 1.0)
12.0ms	(- (- 1.0 z) 1.0)

simplify816.0ms

Counts

212 → 212

Iterations

Useful iterations: 3 (164.0ms)

Iter	Nodes	Cost
0	84	2848
1	164	2152
2	338	1656
3	1201	1132
done	5001	1132

prune1.7s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.6b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite9.6s

Algorithm

rewrite-expression-head

Rules

317×	`frac-add`
123×	`*-un-lft-identity` `associate-/l/`
121×	`frac-times`
111×	`flip3-+` `flip-+`
96×	`associate-*l/`
66×	`times-frac`
62×	`pow-sub`
61×	`associate-*r/`
42×	`fma-def`
40×	`add-exp-log`
36×	`add-sqr-sqrt`
25×	`prod-exp`
24×	`add-cube-cbrt` `add-cbrt-cube` `distribute-lft-out`
22×	`distribute-lft-out--`
14×	`div-exp`
11×	`add-log-exp`
9×	`cbrt-unprod`
7×	`pow1`
6×	`cbrt-undiv` `difference-of-squares`
5×	`associate-/r/`
4×	`expm1-log1p-u` `associate-/r*` `sum-log` `log1p-expm1-u`
3×	`pow-to-exp` `pow-exp` `div-inv`
2×	`+-commutative` `flip3--` `sqrt-pow1` `exp-sum` `flip--`
1×	`associate-+r-` `associate-+r+` `frac-2neg` `pow1/2` `exp-diff` `pow-prod-down` `clear-num` `sqrt-prod` `associate-/l*`

Counts

4 → 263

Calls

4 calls:

149.0ms	(+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
50.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
2.0ms	(sqrt (* PI 2.0))
9.3s	(/ (* (* (* (/ PI (sin (* PI z))) (sqrt (* PI 2.0))) (pow (+ 0.5 (- 7.0 z)) (- 0.5 z))) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))) (+ (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z)))) (/ 771.3234287776531 (- 3.0 z))))) (exp (+ 0.5 (- 7.0 z))))

series942.0ms

Counts

4 → 10

Calls

4 calls:

111.0ms	(+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
77.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
0.0ms	(sqrt (* PI 2.0))
754.0ms	(/ (* (* (* (/ PI (sin (* PI z))) (sqrt (* PI 2.0))) (pow (+ 0.5 (- 7.0 z)) (- 0.5 z))) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))) (+ (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z)))) (/ 771.3234287776531 (- 3.0 z))))) (exp (+ 0.5 (- 7.0 z))))

simplify574.0ms

Counts

273 → 273

Iterations

Useful iterations: done (551.0ms)

Iter	Nodes	Cost
0	629	17437
1	2110	15772
done	5000	15747

prune3.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.6s

Algorithm

rewrite-expression-head

Rules

154×	`*-un-lft-identity`
95×	`distribute-lft-out`
79×	`frac-add`
30×	`associate-*r/`
28×	`flip3-+` `flip-+`
27×	`add-exp-log` `associate-r`
24×	`add-sqr-sqrt`
23×	`times-frac`
21×	`fma-def`
17×	`prod-exp`
16×	`add-cube-cbrt`
15×	`add-cbrt-cube`
11×	`pow1`
7×	`cbrt-unprod` `distribute-lft-out--`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u`
3×	`pow-prod-down` `difference-of-squares`
2×	`pow-to-exp` `sqrt-pow1` `pow-exp` `sqrt-prod` `associate-/r/` `*-commutative`
1×	`+-commutative` `distribute-rgt-in` `flip3--` `distribute-lft-in` `pow1/2` `sum-log` `flip--` `div-inv` `unswap-sqr`

Counts

4 → 151

Calls

4 calls:

51.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
23.5s	(* (* (* PI (sqrt (* PI 2.0))) (pow (+ 0.5 (- 7.0 z)) 0.5)) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))) (+ (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z)))) (/ 771.3234287776531 (- 3.0 z)))))
2.0ms	(sqrt (* PI 2.0))
10.0ms	(* PI (sqrt (* PI 2.0)))

series671.0ms

Counts

4 → 8

Calls

4 calls:

73.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
597.0ms	(* (* (* PI (sqrt (* PI 2.0))) (pow (+ 0.5 (- 7.0 z)) 0.5)) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))) (+ (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (- 2.0 z))) (/ -176.6150291621406 (- 4.0 z)))) (/ 771.3234287776531 (- 3.0 z)))))
0.0ms	(sqrt (* PI 2.0))
0.0ms	(* PI (sqrt (* PI 2.0)))

simplify534.0ms

Counts

159 → 159

Iterations

Useful iterations: done (515.0ms)

Iter	Nodes	Cost
0	453	9818
1	1813	8982
done	5000	8974

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize116.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
1.0b	(pow (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))) 3)
1.0b	(sqrt (* PI 2.0))
1.0b	(* PI (sqrt (* PI 2.0)))

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

91×	`*-un-lft-identity`
40×	`times-frac`
32×	`add-sqr-sqrt`
24×	`associate-l`
19×	`add-cube-cbrt`
15×	`distribute-lft-out` `distribute-lft-out--`
12×	`pow1` `add-exp-log` `associate-r` `add-cbrt-cube`
8×	`unpow-prod-down` `cube-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cube-div` `frac-times` `pow-unpow` `flip3-+` `associate-*r/` `pow-prod-down` `frac-add` `prod-exp` `cbrt-unprod` `flip-+` `difference-of-squares` `unswap-sqr`
2×	`sqrt-pow1` `sqrt-prod` `associate-/r/` `*-commutative`
1×	`cbrt-undiv` `distribute-rgt-in` `cube-mult` `pow-to-exp` `flip3--` `pow-pow` `distribute-lft-in` `pow1/2` `unpow3` `div-exp` `associate-*l/` `pow-exp` `flip--` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 127

Calls

4 calls:

172.0ms	(* (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
81.0ms	(pow (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))) 3)
2.0ms	(sqrt (* PI 2.0))
7.0ms	(* PI (sqrt (* PI 2.0)))

series235.0ms

Counts

4 → 8

Calls

4 calls:

123.0ms	(* (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
111.0ms	(pow (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))) 3)
0.0ms	(sqrt (* PI 2.0))
0.0ms	(* PI (sqrt (* PI 2.0)))

simplify1.3s

Counts

135 → 135

Iterations

Useful iterations: 2 (493.0ms)

Iter	Nodes	Cost
0	301	3098
1	930	2815
2	3939	2673
done	5000	2673

prune2.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes247.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	86	383
1	113	383
done	113	383

end0.0ms

sample45.7s

Algorithm

intervals

Results

40.8s	3835×	body	10240	exit
1.6s	1525×	body	1280	nan
1.5s	8100×	body	80	valid
898.0ms	1275×	body	640	nan
307.0ms	597×	body	320	nan
116.0ms	328×	body	160	nan
53.0ms	304×	body	80	nan