Details

sample1.6s

Algorithm

intervals

Results

1.4s	128×	body	10240	exit
49.0ms	44×	body	1280	nan
45.0ms	259×	body	80	valid
29.0ms	42×	body	640	nan
8.0ms	17×	body	320	nan
4.0ms	12×	body	160	nan
2.0ms	10×	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

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize53.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
0.9b	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
1.0b	(sqrt (* PI 2.0))
1.1b	(/ (* (* (* (/ 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))))

rewrite9.4s

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:

147.0ms	(+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
48.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
2.0ms	(sqrt (* PI 2.0))
9.2s	(/ (* (* (* (/ 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))))

series931.0ms

Counts

4 → 10

Calls

4 calls:

110.0ms	(+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
76.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
0.0ms	(sqrt (* PI 2.0))
745.0ms	(/ (* (* (* (/ 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))))

simplify575.0ms

Counts

273 → 273

Iterations

Useful iterations: done (551.0ms)

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

prune3.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (/ 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 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)))))
1.0b	(sqrt (* PI 2.0))
1.0b	(* PI (sqrt (* PI 2.0)))

rewrite23.2s

Algorithm

rewrite-expression-head

Rules

157×	`frac-add`
154×	`*-un-lft-identity`
95×	`distribute-lft-out`
61×	`associate-*r/`
55×	`flip3-+` `flip-+`
31×	`pow-sub`
30×	`frac-times`
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` `associate-*l/` `sum-log` `flip--` `div-inv` `unswap-sqr`

Counts

4 → 182

Calls

4 calls:

49.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
23.1s	(* (* (* PI (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)))))
2.0ms	(sqrt (* PI 2.0))
7.0ms	(* PI (sqrt (* PI 2.0)))

series625.0ms

Counts

4 → 8

Calls

4 calls:

78.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
547.0ms	(* (* (* PI (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)))))
0.0ms	(sqrt (* PI 2.0))
0.0ms	(* PI (sqrt (* PI 2.0)))

simplify673.0ms

Counts

190 → 190

Iterations

Useful iterations: done (648.0ms)

Iter	Nodes	Cost
0	543	19202
1	2418	17336
done	5000	17332

prune2.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize87.0ms

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)))

rewrite261.0ms

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:

167.0ms	(* (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
80.0ms	(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)))

series226.0ms

Counts

4 → 8

Calls

4 calls:

119.0ms	(* (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z))))
107.0ms	(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)))

simplify1.2s

Counts

135 → 135

Iterations

Useful iterations: 2 (495.0ms)

Iter	Nodes	Cost
0	292	2954
1	897	2709
2	3780	2567
done	5000	2567

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
1.0b	(* (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)))))
1.0b	(sqrt (* PI 2.0))
1.0b	(* PI (sqrt (* PI 2.0)))

rewrite30.2s

Algorithm

rewrite-expression-head

Rules

167×	`*-un-lft-identity`
157×	`frac-add`
97×	`distribute-lft-out`
55×	`flip3-+` `flip-+`
37×	`add-sqr-sqrt`
31×	`pow-sub`
30×	`frac-times` `associate-*r/`
27×	`associate-r`
24×	`add-cube-cbrt`
23×	`times-frac` `associate-l`
21×	`fma-def`
11×	`unpow-prod-up` `add-exp-log`
9×	`pow1` `prod-diff`
8×	`add-cbrt-cube` `distribute-lft-out--`
6×	`unpow-prod-down` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `unswap-sqr`
3×	`difference-of-squares`
2×	`sqrt-pow1` `pow-prod-down` `sqrt-prod` `associate-/r/` `*-commutative` `cbrt-unprod` `sqr-pow`
1×	`+-commutative` `distribute-rgt-in` `pow-to-exp` `sub-neg` `flip3--` `distribute-lft-in` `pow1/2` `associate-*l/` `pow-exp` `sum-log` `flip--` `div-inv`

Counts

4 → 197

Calls

4 calls:

48.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
30.2s	(* (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)))))
2.0ms	(sqrt (* PI 2.0))
7.0ms	(* PI (sqrt (* PI 2.0)))

series398.0ms

Counts

4 → 8

Calls

4 calls:

75.0ms	(+ (/ 9.984369578019572e-06 (- 7.0 z)) (/ -0.13857109526572012 (- 6.0 z)))
323.0ms	(* (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)))))
0.0ms	(sqrt (* PI 2.0))
0.0ms	(* PI (sqrt (* PI 2.0)))

simplify630.0ms

Counts

205 → 205

Iterations

Useful iterations: 1 (211.0ms)

Iter	Nodes	Cost
0	544	19276
1	2263	17437
done	5000	17437

prune2.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes291.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	78
1	72	78
done	72	78

end0.0ms

sample46.3s

Algorithm

intervals

Results

41.5s	3928×	body	10240	exit
1.5s	1486×	body	1280	nan
1.5s	8096×	body	80	valid
914.0ms	1273×	body	640	nan
315.0ms	605×	body	320	nan
105.0ms	318×	body	160	nan
54.0ms	318×	body	80	nan
0.0ms	1×	body	160	valid