Details

sample100.0ms

Algorithm

intervals

Results

22.0ms	40×	body	2560	valid
16.0ms	183×	body	80	valid
15.0ms	35×	body	1280	valid
7.0ms	79×	body	80	nan
5.0ms	16×	body	640	valid
1.0ms	2×	body	5120	valid
1.0ms	5×	body	160	valid
0.0ms	2×	body	320	valid

simplify101.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	104
5	104
4	96
3	76
2	41
1	21
0	12

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.2b	(* (* 3.0 a) c)
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
14×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `add-log-exp`
6×	`distribute-lft-out`
5×	`times-frac` `associate-/l*`
4×	`prod-exp` `cbrt-unprod`
3×	`distribute-rgt-neg-in` `associate-r` `pow-prod-down` `sqrt-prod`
2×	`neg-sub0` `cbrt-undiv` `sum-log` `flip3-+` `sqrt-div` `div-exp` `associate-+l-` `flip-+` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `div-sub` `associate-l` `neg-log` `-commutative` `div-inv` `flip--`

Counts

4 → 76

Calls

4 calls:

88.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
27.0ms	(* (* 3.0 a) c)
39.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
13.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
23.0ms	(* (* 3.0 a) c)
117.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
103.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.4s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	2544
1	448
0	164

prune443.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 3.0 a) c))
0.2b	(* (* 3.0 a) c)
1.3b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
24.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite75.0ms

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`
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 → 60

Calls

4 calls:

6.0ms	(- (* b b) (* (* 3.0 a) c))
13.0ms	(* (* 3.0 a) c)
43.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (* b b) (* (* 3.0 a) c))
21.0ms	(* (* 3.0 a) c)
137.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
97.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify975.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1549
1	302
0	120

prune375.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.7b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.4b	(/ (/ 1 3.0) a)
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
52×	`*-un-lft-identity`
49×	`add-sqr-sqrt`
48×	`add-cube-cbrt`
18×	`add-exp-log`
14×	`add-cbrt-cube`
13×	`associate-/l*`
10×	`pow1`
8×	`add-log-exp`
6×	`div-exp`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/r` `associate-r*` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`sum-log` `sqrt-div` `distribute-lft-out`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `rec-exp` `clear-num` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `1-exp` `associate-l` `neg-log` `*-commutative` `associate-+l-` `flip-+` `flip--` `associate-/l/`

Counts

4 → 120

Calls

4 calls:

24.0ms	(* (* 3.0 a) c)
20.0ms	(/ (/ 1 3.0) a)
43.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (* 3.0 a) c)
33.0ms	(/ (/ 1 3.0) a)
120.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
106.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.8s

Counts

132 → 132

Iterations

Iter	Nodes
done	5002
2	3122
1	630
0	249

prune654.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.7b

localize55.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b) (sqrt (- (* b b) (* (* 3.0 c) a))))
3.5b	(* (/ (+ 0 (* (* 3.0 c) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 c) a))))) (/ (/ 1 3.0) a))
7.8b	(/ (+ 0 (* (* 3.0 c) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 c) a)))))
24.2b	(sqrt (- (* b b) (* (* 3.0 c) a)))

rewrite259.0ms

Algorithm

rewrite-expression-head

Rules

124×	`add-sqr-sqrt`
122×	`times-frac`
97×	`*-un-lft-identity`
63×	`add-cube-cbrt`
43×	`associate-r`
41×	`add-exp-log`
27×	`add-cbrt-cube` `associate-l`
18×	`div-exp`
16×	`distribute-lft-out--` `difference-of-squares`
11×	`sqrt-prod`
10×	`cbrt-undiv` `prod-exp`
8×	`distribute-rgt-neg-in` `add-log-exp` `unswap-sqr`
7×	`pow1` `associate-/r*`
6×	`cbrt-unprod` `div-inv`
4×	`flip3--` `associate-/r/` `flip--`
3×	`associate-/l*`
2×	`rec-exp` `sqrt-div` `diff-log` `1-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `frac-times` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `neg-log` `associate-l/` `associate-r/` `*-commutative` `flip-+`

Counts

4 → 186

Calls

4 calls:

35.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 c) a))))
151.0ms	(* (/ (+ 0 (* (* 3.0 c) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 c) a))))) (/ (/ 1 3.0) a))
51.0ms	(/ (+ 0 (* (* 3.0 c) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 c) a)))))
7.0ms	(sqrt (- (* b b) (* (* 3.0 c) a)))

series798.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 c) a))))
269.0ms	(* (/ (+ 0 (* (* 3.0 c) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 c) a))))) (/ (/ 1 3.0) a))
285.0ms	(/ (+ 0 (* (* 3.0 c) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 c) a)))))
122.0ms	(sqrt (- (* b b) (* (* 3.0 c) a)))

simplify548.0ms

Counts

198 → 198

Iterations

Iter	Nodes
done	5000
1	1089
0	344

prune1.2s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 3.6b

regimes634.0ms

Accuracy

83.3% (4.6b remaining)

Error of 9.9b against oracle of 5.4b and baseline of 32.6b

bsearch149.0ms

Steps

Iters	Range		Point
7	1.726360512453143e-63	2.3465896586148578e-61	8.08526583505735e-63
9	-3.845605078781637e+76	-1.2146338677939432e+68	-7.943482039519134e+75

simplify3.0ms

Iterations

Iter	Nodes
done	36
1	36
0	30

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.0s	5775×	body	80	valid
559.0ms	1095×	body	2560	valid
400.0ms	933×	body	1280	valid
277.0ms	2884×	body	80	nan
207.0ms	446×	body	640	valid
50.0ms	92×	body	5120	valid
45.0ms	228×	body	320	valid
18.0ms	127×	body	160	valid