Details

sample174.0ms

Algorithm

intervals

Results

124.0ms

520×

body

valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
6	2452
5	1745
4	1125
3	543
2	196
1	66
0	28

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.9b

localize90.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (- (* c b) (* (* 27.0 j) k)) (* 4.0 (* x i))) (* (- (* (* x 18.0) (* y z)) (* a 4.0)) t))
0.2b	(* (* 27.0 j) k)
3.5b	(* (* x 18.0) (* y z))
3.9b	(* (- (* (* x 18.0) (* y z)) (* a 4.0)) t)

rewrite315.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1` `add-cbrt-cube` `add-exp-log`
13×	`add-log-exp`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt`
7×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
6×	`associate-*l/`
5×	`flip3--` `associate-l` `flip--`
4×	`associate-+l+` `frac-add`
3×	`sum-log` `diff-log` `*-commutative`
2×	`sub-neg` `associate--l+`
1×	`+-commutative` `flip3-+` `associate-+l-` `flip-+` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

132.0ms	(+ (- (- (* c b) (* (* 27.0 j) k)) (* 4.0 (* x i))) (* (- (* (* x 18.0) (* y z)) (* a 4.0)) t))
25.0ms	(* (* 27.0 j) k)
39.0ms	(* (* x 18.0) (* y z))
115.0ms	(* (- (* (* x 18.0) (* y z)) (* a 4.0)) t)

series11.5s

Counts

4 → 12

Calls

4 calls:

11.3s	(+ (- (- (* c b) (* (* 27.0 j) k)) (* 4.0 (* x i))) (* (- (* (* x 18.0) (* y z)) (* a 4.0)) t))
29.0ms	(* (* 27.0 j) k)
37.0ms	(* (* x 18.0) (* y z))
118.0ms	(* (- (* (* x 18.0) (* y z)) (* a 4.0)) t)

simplify976.0ms

Counts

94 → 94

Iterations

Iter	Nodes
2	2715
1	623
0	209

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 1.6b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 27.0 j) k)
0.3b	(* (* y z) 18.0)
3.5b	(* x (* (* y z) 18.0))
3.9b	(* (- (* x (* (* y z) 18.0)) (* a 4.0)) t)

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1` `add-cbrt-cube` `add-exp-log`
13×	`pow-prod-down` `prod-exp` `cbrt-unprod`
11×	`add-sqr-sqrt`
10×	`associate-r`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-l`
4×	`*-commutative` `add-log-exp`
2×	`associate-*l/`
1×	`flip3--` `flip--` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

12.0ms	(* (* 27.0 j) k)
13.0ms	(* (* y z) 18.0)
64.0ms	(* x (* (* y z) 18.0))
163.0ms	(* (- (* x (* (* y z) 18.0)) (* a 4.0)) t)

series193.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (* 27.0 j) k)
20.0ms	(* (* y z) 18.0)
34.0ms	(* x (* (* y z) 18.0))
115.0ms	(* (- (* x (* (* y z) 18.0)) (* a 4.0)) t)

simplify4.0s

Counts

89 → 89

Iterations

Iter	Nodes
3	5781
2	1399
1	393
0	149

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.6b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y (* z 18.0))
0.2b	(* (* 27.0 j) k)
3.5b	(* x (* y (* z 18.0)))
3.9b	(* (- (* x (* y (* z 18.0))) (* a 4.0)) t)

rewrite516.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1` `add-cbrt-cube` `add-exp-log`
13×	`pow-prod-down` `prod-exp` `cbrt-unprod`
11×	`add-sqr-sqrt`
10×	`associate-l`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-r`
4×	`*-commutative` `add-log-exp`
2×	`associate-*l/`
1×	`flip3--` `flip--` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

11.0ms	(* y (* z 18.0))
12.0ms	(* (* 27.0 j) k)
40.0ms	(* x (* y (* z 18.0)))
451.0ms	(* (- (* x (* y (* z 18.0))) (* a 4.0)) t)

series185.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* y (* z 18.0))
22.0ms	(* (* 27.0 j) k)
35.0ms	(* x (* y (* z 18.0)))
107.0ms	(* (- (* x (* y (* z 18.0))) (* a 4.0)) t)

simplify2.1s

Counts

89 → 89

Iterations

Iter	Nodes
3	5787
2	1314
1	377
0	147

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.6b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (- (* c b) (* 27.0 (* j k))) (* 4.0 (* x i))) (* (- (* (* x 18.0) (* y z)) (* a 4.0)) t))
0.3b	(* 27.0 (* j k))
3.5b	(* (* x 18.0) (* y z))
3.9b	(* (- (* (* x 18.0) (* y z)) (* a 4.0)) t)

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1` `add-cbrt-cube` `add-exp-log`
13×	`add-log-exp`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt`
7×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
6×	`associate-*l/`
5×	`flip3--` `associate-r` `flip--`
4×	`associate-+l+` `frac-add`
3×	`sum-log` `diff-log` `*-commutative`
2×	`sub-neg` `associate--l+`
1×	`+-commutative` `flip3-+` `associate-+l-` `flip-+` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

154.0ms	(+ (- (- (* c b) (* 27.0 (* j k))) (* 4.0 (* x i))) (* (- (* (* x 18.0) (* y z)) (* a 4.0)) t))
12.0ms	(* 27.0 (* j k))
24.0ms	(* (* x 18.0) (* y z))
83.0ms	(* (- (* (* x 18.0) (* y z)) (* a 4.0)) t)

series10.4s

Counts

4 → 12

Calls

4 calls:

10.3s	(+ (- (- (* c b) (* 27.0 (* j k))) (* 4.0 (* x i))) (* (- (* (* x 18.0) (* y z)) (* a 4.0)) t))
26.0ms	(* 27.0 (* j k))
34.0ms	(* (* x 18.0) (* y z))
111.0ms	(* (- (* (* x 18.0) (* y z)) (* a 4.0)) t)

simplify618.0ms

Counts

94 → 94

Iterations

Iter	Nodes
2	2641
1	610
0	206

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 1.6b

regimes1.3s

Accuracy

36.3% (1.9b remaining)

Error of 5.2b against oracle of 3.3b and baseline of 6.3b

bsearch386.0ms

Steps

Iters	Range		Point
10	9.567420893965084e-101	2.8088593333065733e-88	1.95010356846324e-100
10	-8.404003850832203e-286	-4.5843098450401264e-297	-7.711355120201642e-286

simplify16.0ms

Iterations

Iter	Nodes
4	67
3	67
2	64
1	54
0	37

end0.0ms

sample4.3s

Algorithm

intervals

Results

3.1s

16164×

body

valid