Details

sample77.0ms

Algorithm

intervals

Results

21.0ms	210×	body	80	valid
14.0ms	23×	body	2560	valid
12.0ms	25×	body	1280	valid
7.0ms	84×	body	80	nan
3.0ms	8×	body	640	valid
3.0ms	9×	body	320	valid
2.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify114.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	93
7	93
6	92
5	90
4	82
3	66
2	40
1	21
0	12

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
0.8b	(- (* b b) (* (* 3 a) c))
1.0b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
20.8b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 76

Calls

4 calls:

59.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
7.0ms	(- (* b b) (* (* 3 a) c))
31.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series332.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
48.0ms	(- (* b b) (* (* 3 a) c))
81.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
91.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.1s

Counts

88 → 88

Iterations

Iter	Nodes
done	5013
2	1265
1	396
0	157

prune447.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) 3)
0.8b	(- (* b b) (* (* 3 a) c))
1.0b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
20.8b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 88

Calls

4 calls:

66.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) 3)
13.0ms	(- (* b b) (* (* 3 a) c))
53.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
11.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) 3)
69.0ms	(- (* b b) (* (* 3 a) c))
120.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
87.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.8s

Counts

100 → 100

Iterations

Iter	Nodes
done	5003
3	4592
2	1049
1	373
0	157

prune516.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (sqrt (+ (* b b) (* -3 (* a c)))) b) 3)
0.8b	(+ (* b b) (* -3 (* a c)))
1.0b	(- (sqrt (+ (* b b) (* -3 (* a c)))) b)
20.8b	(sqrt (+ (* b b) (* -3 (* a c))))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`insert-posit16`
3×	`associate-/r*`
2×	`flip3-+` `flip3--` `sqrt-div` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 87

Calls

4 calls:

75.0ms	(/ (- (sqrt (+ (* b b) (* -3 (* a c)))) b) 3)
8.0ms	(+ (* b b) (* -3 (* a c)))
46.0ms	(- (sqrt (+ (* b b) (* -3 (* a c)))) b)
11.0ms	(sqrt (+ (* b b) (* -3 (* a c))))

series387.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (- (sqrt (+ (* b b) (* -3 (* a c)))) b) 3)
58.0ms	(+ (* b b) (* -3 (* a c)))
105.0ms	(- (sqrt (+ (* b b) (* -3 (* a c)))) b)
87.0ms	(sqrt (+ (* b b) (* -3 (* a c))))

simplify2.7s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
3	4334
2	1167
1	385
0	156

prune440.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
0.8b	(- (* b b) (* (* 3 a) c))
1.0b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
20.8b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 76

Calls

4 calls:

77.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
16.0ms	(- (* b b) (* (* 3 a) c))
31.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
69.0ms	(- (* b b) (* (* 3 a) c))
94.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
93.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.1s

Counts

88 → 88

Iterations

Iter	Nodes
done	5013
2	1265
1	396
0	157

prune439.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.5b

regimes305.0ms

Accuracy

82.8% (4.8b remaining)

Error of 10.5b against oracle of 5.7b and baseline of 33.4b

bsearch354.0ms

Steps

Iters	Range		Point
8	5.451909898538592e-70	5.081728108716245e-67	3.5051690294214705e-69
7	6.366271362828677e-80	2.0474353944207673e-78	4.020455841328689e-79
8	1.9015403840268286e-125	4.787339246176752e-121	3.7535994007355634e-122
7	-6.914140684613533e+154	-2.006932639140506e+153	-1.343328406152013e+154

simplify14.0ms

Iterations

Iter	Nodes
done	58
1	58
0	45

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.2s	1084×	body	2560	valid
734.0ms	5867×	body	80	valid
695.0ms	908×	body	1280	valid
373.0ms	3007×	body	80	nan
262.0ms	446×	body	640	valid
108.0ms	101×	body	5120	valid
79.0ms	236×	body	320	valid
24.0ms	108×	body	160	valid