Details

sample89.0ms

Algorithm

intervals

Results

38.0ms	289×	body	80	valid
12.0ms	104×	body	80	nan

simplify215.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	20	38
1	39	38
2	79	37
3	143	37
4	179	37
5	189	37
6	193	37
done	193	37

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.3b

localize137.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
1.0b	(- (* b b) (* (* 4.0 a) c))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 66

Calls

4 calls:

18.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(- (* b b) (* (* 4.0 a) c))
24.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
28.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* (* 4.0 a) c))
72.0ms	(- (* b b) (* (* 4.0 a) c))
104.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
120.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify951.0ms

Counts

78 → 78

Iterations

Useful iterations: 2 (152.0ms)

Iter	Nodes	Cost
0	71	1146
1	185	1058
2	843	952
done	5000	952

prune566.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.8b

localize150.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
4.1b	(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
6.8b	(/ (* a c) b)
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
14×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `times-frac`
7×	`associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r*` `log1p-expm1-u` `distribute-lft-out--`
3×	`flip3--` `sqrt-prod` `flip--`
2×	`distribute-rgt-neg-in` `frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l/` `difference-of-squares`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff`

Counts

4 → 88

Calls

4 calls:

11.0ms	(- (* b b) (* (* 4.0 a) c))
110.0ms	(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
21.0ms	(/ (* a c) b)
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- (* b b) (* (* 4.0 a) c))
116.0ms	(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
37.0ms	(/ (* a c) b)
120.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

100 → 100

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	179	1531
1	489	1459
2	2640	1285
done	5000	1255

prune739.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.6b

localize119.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite134.0ms

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-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 89

Calls

4 calls:

77.0ms	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
28.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series546.0ms

Counts

4 → 12

Calls

4 calls:

270.0ms	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
103.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
66.0ms	(- (* b b) (* (* 4.0 a) c))
107.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts

101 → 101

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	157	1641
1	424	1527
2	2032	1308
done	5001	1291

prune684.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.5b

localize116.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
10.3b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

18.0ms	(- (* b b) (* (* 4.0 a) c))
24.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (* b b) (* (* 4.0 a) c))
133.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
125.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
84.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts

87 → 87

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	107	1507
1	295	1094
2	1512	993
done	5000	986

prune557.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 7.5b

regimes505.0ms

Accuracy

92.2% (1.1b remaining)

Error of 7.5b against oracle of 6.3b and baseline of 20.6b

bsearch282.0ms

Steps

Iters	Range		Point
8	1.051086597250448e+104	1.8086281629461872e+108	2.750597423682243e+107
9	-5.388960530500634e+155	-8.097032161796104e+150	-1.3613714418567412e+154

simplify19.0ms

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	49	134
1	61	134
2	62	132
done	62	132

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.7s	8766×	body	80	valid
306.0ms	2950×	body	80	nan