Details

sample42.0ms

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	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9
done	105	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize13.0ms

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))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-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` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

65.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
23.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series302.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
47.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	403	779
1	1514	685
2	5002	674
done	5002	674

prune219.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.4b

localize14.0ms

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))))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`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 → 154

Calls

4 calls:

22.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
83.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
59.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series478.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
148.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
180.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify96.0ms

Counts

166 → 166

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	640	2692
1	2944	2439
2	5001	2426
done	5001	2426

prune388.0ms

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))))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

100.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
9.0ms	(- (* b b) (* 4.0 (* a c)))
20.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
45.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify59.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	479	920
1	2139	790
2	5002	777
done	5002	777

prune221.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.3b

localize18.0ms

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))))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt`
102×	`times-frac`
86×	`*-un-lft-identity`
42×	`add-cube-cbrt`
33×	`associate-/l*` `difference-of-squares`
22×	`log-prod` `exp-sum` `distribute-lft-out--`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
9×	`associate-/r*`
8×	`add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`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 → 165

Calls

4 calls:

100.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))) (* 2.0 a))
67.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))))
27.0ms	(- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series498.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))) (* 2.0 a))
188.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c))))))))
83.0ms	(- (- b) (exp (log (sqrt (- (* b b) (* 4.0 (* a c)))))))
76.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify103.0ms

Counts

177 → 177

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	687	3374
1	3001	2930
2	5002	2873
done	5002	2873

prune456.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.3b

regimes208.0ms

Accuracy

83.7% (4.4b remaining)

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

bsearch75.0ms

Steps

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

simplify1.0ms

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

249.0ms	1119×	body	2560	valid
229.0ms	5759×	body	80	valid
165.0ms	900×	body	1280	valid
100.0ms	2850×	body	80	nan
72.0ms	476×	body	640	valid
35.0ms	129×	body	5120	valid
25.0ms	216×	body	320	valid
8.0ms	108×	body	160	valid