Details

sample79.0ms

Algorithm

intervals

Results

45.0ms

256×

body

valid

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	37
1	55	37
2	138	37
3	448	37
4	1537	37
done	5000	37

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
0.1b	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
25.3b	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite369.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`associate-r` `associate-l`
8×	`associate-*l/` `associate-/l/`
7×	`flip3-+` `flip-+`
4×	`frac-times` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`flip3--` `times-frac` `pow-prod-down` `associate-/r` `-commutative` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `associate-*r/` `div-exp` `associate-/r/`
1×	`frac-2neg` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 91

Calls

4 calls:

112.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
27.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
58.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
168.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series628.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
108.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
65.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
345.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify1.7s

Counts

103 → 103

Iterations

Useful iterations: 2 (548.0ms)

Iter	Nodes	Cost
0	227	2664
1	654	2592
2	2778	2274
done	5002	2274

prune569.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
0.1b	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
0.3b	(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))
22.0b	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

rewrite399.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
110×	`add-sqr-sqrt`
106×	`*-un-lft-identity`
74×	`add-cube-cbrt`
18×	`associate-/r*`
16×	`distribute-lft-out--` `difference-of-squares`
15×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
10×	`flip3-+` `flip-+`
8×	`pow1` `div-inv` `associate-/l*`
6×	`associate-r` `associate-l`
4×	`cbrt-undiv` `div-exp` `associate-*l/` `associate-/l/` `add-log-exp`
2×	`frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`flip3--` `div-sub` `flip--`

Counts

4 → 184

Calls

4 calls:

26.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
52.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
158.0ms	(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))
154.0ms	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

series618.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
59.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
290.0ms	(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))
179.0ms	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

simplify2.0s

Counts

196 → 196

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	346	9875
1	951	9725
2	3451	9291
done	5002	9281

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
0.1b	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
2.8b	(/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
22.0b	(* (/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

rewrite558.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
31×	`times-frac`
28×	`add-cube-cbrt`
27×	`associate-l`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`associate-r`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`flip3-+` `flip-+`
5×	`associate-l/` `associate-/l`
4×	`prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `-commutative`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `div-inv` `associate-/l/`
1×	`distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `div-sub` `clear-num` `flip--`

Counts

4 → 126

Calls

4 calls:

27.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
54.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
65.0ms	(/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
407.0ms	(* (/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

series531.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
63.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
86.0ms	(/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
290.0ms	(* (/ (- x 2.0) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

simplify2.2s

Counts

138 → 138

Iterations

Useful iterations: 2 (728.0ms)

Iter	Nodes	Cost
0	273	4168
1	852	4118
2	2996	3750
done	5002	3750

prune809.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

localize72.0ms

Local error

Found 4 expressions with local error:

7.7b	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
7.7b	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
13.4b	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
22.0b	(* (* (/ 1 (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

rewrite828.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
38×	`add-exp-log`
30×	`times-frac`
26×	`add-cube-cbrt`
24×	`sqrt-prod` `add-cbrt-cube`
17×	`prod-exp`
11×	`pow1`
9×	`frac-times` `div-exp` `cbrt-unprod`
7×	`flip3-+` `flip-+` `distribute-lft-out--` `difference-of-squares`
6×	`sqrt-div` `associate-l/` `associate-/r`
5×	`cbrt-undiv` `associate-r/` `associate-/l`
4×	`add-log-exp`
3×	`associate-r` `pow-prod-down`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-/r/` `associate-/l/`
1×	`distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `div-sub` `associate-l` `clear-num` `*-commutative` `flip--` `div-inv`

Counts

4 → 129

Calls

4 calls:

47.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
62.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
86.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
622.0ms	(* (* (/ 1 (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

series713.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
92.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
194.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
321.0ms	(* (* (/ 1 (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

simplify2.1s

Counts

141 → 141

Iterations

Useful iterations: 2 (689.0ms)

Iter	Nodes	Cost
0	288	6410
1	771	5946
2	2882	4642
done	5000	4642

prune732.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes368.0ms

Accuracy

97.6% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 24.7b

bsearch366.0ms

Steps

Iters	Range		Point
11	1.9138944455855922e+68	4.7705286842092256e+92	1.9308694312533926e+69
7	-3.807880116067595e+71	-3.6274401496220754e+69	-9.168391507400123e+69

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	42	67
1	60	57
done	60	57

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.7s

8010×

body

valid