Details

sample42.0ms

Algorithm

intervals

Results

10.0ms	205×	body	80	valid
5.0ms	26×	body	2560	valid
4.0ms	26×	body	1280	valid
3.0ms	83×	body	80	nan
1.0ms	11×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	9
done	148	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.8b	(- (* b b) (* 4.0 (* a c)))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

67.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
26.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series309.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
82.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
51.0ms	(- (* b b) (* 4.0 (* a c)))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	404	890
1	1481	801
2	5001	796
done	5001	796

prune269.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
1.8b	(- (* b b) (* 4.0 (* a c)))
5.9b	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
10×	`times-frac`
9×	`add-exp-log` `add-cube-cbrt` `sqrt-prod` `add-cbrt-cube`
8×	`add-log-exp`
6×	`associate-/l*`
5×	`pow1`
4×	`flip3--` `sqrt-div` `flip--`
3×	`div-inv` `distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-out--` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `frac-sub` `cbrt-unprod` `sub-div` `difference-of-squares`

Counts

4 → 76

Calls

4 calls:

21.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
10.0ms	(- (* b b) (* 4.0 (* a c)))
60.0ms	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series380.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
48.0ms	(- (* b b) (* 4.0 (* a c)))
116.0ms	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
77.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify42.0ms

Counts

88 → 88

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	419	882
1	1458	817
2	5001	806
done	5001	806

prune269.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.1b

localize16.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (* b b) (* 4.0 (* a c)))
11.5b	(- (/ (- b) (* 2.0 a)) (/ (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (/ (* 2.0 a) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`*-un-lft-identity` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
3×	`times-frac`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`
1×	`associate--l-` `neg-sub0` `div-sub` `frac-sub` `distribute-lft-out--`

Counts

4 → 61

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
170.0ms	(- (/ (- b) (* 2.0 a)) (/ (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (/ (* 2.0 a) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series318.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* 4.0 (* a c)))
116.0ms	(- (/ (- b) (* 2.0 a)) (/ (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (/ (* 2.0 a) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))))
78.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
77.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify132.0ms

Counts

73 → 73

Iterations

Useful iterations: 3 (123.0ms)

Iter	Nodes	Cost
0	310	1004
1	1079	940
2	4846	887
3	5002	871
done	5002	871

prune293.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.1b

localize15.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (* b b) (* 4.0 (* a c)))
7.5b	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))
24.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
9×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
3×	`diff-log`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate--l-` `neg-sub0` `neg-log` `difference-of-squares`

Counts

4 → 57

Calls

4 calls:

12.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
9.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
10.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series283.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* 4.0 (* a c)))
86.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
77.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify122.0ms

Counts

69 → 69

Iterations

Useful iterations: 3 (116.0ms)

Iter	Nodes	Cost
0	240	693
1	924	594
2	4083	573
3	5001	554
done	5001	554

prune235.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 7.1b

regimes291.0ms

Accuracy

88.6% (3.3b remaining)

Error of 8.8b against oracle of 5.6b and baseline of 34.2b

bsearch164.0ms

Steps

Iters	Range		Point
6	9.002760019060421e+93	3.662435776182418e+94	2.3684713380299e+94
11	-1.7080554663773614e-124	-7.974260657123443e-153	-3.5252839655411165e-144
6	-1.1479397783227414e+56	-2.609655750368231e+55	-3.8603554551533365e+55

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	28
1	41	28
done	41	28

end0.0ms

sample1.2s

Algorithm

intervals

Results

238.0ms	1084×	body	2560	valid
223.0ms	5914×	body	80	valid
156.0ms	871×	body	1280	valid
105.0ms	2851×	body	80	nan
63.0ms	452×	body	640	valid
30.0ms	112×	body	5120	valid
22.0ms	209×	body	320	valid
7.0ms	103×	body	160	valid