Details

sample92.0ms

Algorithm

intervals

Results

23.0ms	198×	body	80	valid
16.0ms	29×	body	1280	valid
11.0ms	17×	body	2560	valid
9.0ms	82×	body	80	nan
6.0ms	13×	body	640	valid
4.0ms	10×	body	320	valid
3.0ms	4×	body	5120	valid
2.0ms	10×	body	160	valid

simplify155.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	93
7	93
6	92
5	90
4	82
3	66
2	40
1	21
0	12

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
1.2b	(- (* b b) (* (* 3 a) c))
2.7b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
22.2b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite112.0ms

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:

64.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
9.0ms	(- (* b b) (* (* 3 a) c))
30.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
51.0ms	(- (* b b) (* (* 3 a) c))
92.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
92.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify3.4s

Counts

88 → 88

Iterations

Iter	Nodes
3	4888
2	1249
1	396
0	157

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* 3 a) (- (sqrt (- (* b b) (* (* 3 a) c))) b))
1.2b	(- (* b b) (* (* 3 a) c))
2.7b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
22.2b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite132.0ms

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×	`associate-/r*` `times-frac` `sqrt-prod` `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-/r/`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 75

Calls

4 calls:

39.0ms	(/ (* 3 a) (- (sqrt (- (* b b) (* (* 3 a) c))) b))
7.0ms	(- (* b b) (* (* 3 a) c))
69.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
14.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series548.0ms

Counts

4 → 12

Calls

4 calls:

294.0ms	(/ (* 3 a) (- (sqrt (- (* b b) (* (* 3 a) c))) b))
61.0ms	(- (* b b) (* (* 3 a) c))
113.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
81.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify3.3s

Counts

87 → 87

Iterations

Iter	Nodes
3	4310
2	1176
1	370
0	150

prune947.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* 3 (/ a (- (sqrt (- (* b b) (* (* 3 a) c))) b))))
1.2b	(- (* b b) (* (* 3 a) c))
2.7b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
22.2b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

90.0ms	(/ 1 (* 3 (/ a (- (sqrt (- (* b b) (* (* 3 a) c))) b))))
8.0ms	(- (* b b) (* (* 3 a) c))
38.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(/ 1 (* 3 (/ a (- (sqrt (- (* b b) (* (* 3 a) c))) b))))
65.0ms	(- (* b b) (* (* 3 a) c))
103.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
111.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify3.1s

Counts

91 → 91

Iterations

Iter	Nodes
3	4421
2	1177
1	390
0	159

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3 a) c)
1.2b	(- (* b b) (* (* 3 a) c))
2.7b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
22.2b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod` `insert-posit16`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

20.0ms	(* (* 3 a) c)
14.0ms	(- (* b b) (* (* 3 a) c))
34.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (* 3 a) c)
65.0ms	(- (* b b) (* (* 3 a) c))
107.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
96.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.0s

Counts

76 → 76

Iterations

Iter	Nodes
3	3440
2	958
1	297
0	123

prune758.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.3b

regimes650.0ms

Accuracy

77.7% (6.2b remaining)

Error of 12.0b against oracle of 5.8b and baseline of 33.6b

bsearch645.0ms

Steps

Iters	Range		Point
3	1.897422751335727e-16	2.3824489835354504e-16	1.922674299151799e-16
7	4.1266326978064226e-111	9.799836324706106e-110	4.186415469310955e-111
8	9.808312070140145e-191	3.260010576758525e-187	3.207624111695675e-187
9	-9.113678877832951e+119	-2.8363346747228946e+114	-1.5936256221995724e+117

simplify8.0ms

Iterations

Iter	Nodes
2	49
1	49
0	38

end0.0ms

sample3.8s

Algorithm

intervals

Results

965.0ms	884×	body	1280	valid
860.0ms	1045×	body	2560	valid
788.0ms	5930×	body	80	valid
412.0ms	2880×	body	80	nan
268.0ms	497×	body	640	valid
110.0ms	200×	body	320	valid
99.0ms	121×	body	5120	valid
25.0ms	116×	body	160	valid