Details

sample41.0ms

Algorithm

intervals

Results

8.0ms	36×	body	2560	valid
7.0ms	191×	body	80	valid
4.0ms	20×	body	1280	valid
3.0ms	77×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	4×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9
done	121	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.5b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

68.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
22.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series325.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
51.0ms	(- (* b b) (* 4.0 (* a c)))
85.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify52.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	438	854
1	1658	750
2	5001	735
done	5001	735

prune501.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.7b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.5b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
24.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 232

Calls

4 calls:

30.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
87.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
60.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series498.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
155.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
188.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify131.0ms

Counts

244 → 244

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	818	5119
1	3560	3863
2	5001	3860
done	5001	3860

prune546.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.5b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cbrt-cube`
11×	`add-cube-cbrt`
10×	`fma-def` `prod-exp` `add-log-exp`
7×	`pow1` `associate-r`
5×	`distribute-rgt-neg-in` `associate-l`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out`
3×	`distribute-lft-neg-in` `flip3-+` `times-frac` `sqrt-prod` `flip-+`
2×	`cbrt-undiv` `frac-times` `rec-exp` `flip3--` `sqrt-div` `1-exp` `associate-*l/` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-r/` `prod-diff` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

103.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
11.0ms	(- (* b b) (* 4.0 (* a c)))
22.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series320.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
47.0ms	(- (* b b) (* 4.0 (* a c)))
83.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify64.0ms

Counts

112 → 112

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	515	1011
1	2277	856
2	5001	843
done	5001	843

prune306.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.3b

localize19.0ms

Local error

Found 4 expressions with local error:

5.7b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))) (* 2.0 a))
10.7b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))))
18.6b	(- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))
24.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

169×	`add-sqr-sqrt`
146×	`*-un-lft-identity`
102×	`add-cube-cbrt` `times-frac`
90×	`prod-diff`
82×	`log-prod` `exp-sum`
44×	`sqrt-prod`
41×	`distribute-rgt-neg-in`
33×	`associate-/l*` `difference-of-squares`
30×	`distribute-lft-neg-in`
22×	`distribute-lft-out--`
18×	`add-exp-log` `add-cbrt-cube`
10×	`neg-mul-1` `fma-neg`
9×	`associate-/r*`
8×	`add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 273

Calls

4 calls:

104.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))) (* 2.0 a))
70.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))))
40.0ms	(- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series519.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))) (* 2.0 a))
197.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))))
86.0ms	(- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify142.0ms

Counts

285 → 285

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	967	7740
1	3761	4917
2	5001	4914
done	5001	4914

prune630.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.3b

regimes234.0ms

Accuracy

83.7% (4.4b remaining)

Error of 10.1b against oracle of 5.8b and baseline of 32.5b

bsearch81.0ms

Steps

Iters	Range		Point
5	3.8896208850456714e-71	9.054856756550336e-71	6.485606601696406e-71
8	-3.9507459177053075e+109	-4.2638646006519825e+105	-1.2447742914077108e+109

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	16
1	38	16
done	38	16

end0.0ms

sample1.2s

Algorithm

intervals

Results

248.0ms	1119×	body	2560	valid
228.0ms	5759×	body	80	valid
159.0ms	900×	body	1280	valid
105.0ms	2850×	body	80	nan
70.0ms	476×	body	640	valid
39.0ms	129×	body	5120	valid
23.0ms	216×	body	320	valid
8.0ms	108×	body	160	valid