Details

sample44.0ms

Algorithm

intervals

Results

15.0ms	189×	body	80	valid
5.0ms	26×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	8×	body	1280	valid
1.0ms	8×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
14	4122
13	3069
12	2474
11	2032
10	1843
9	1602
8	1334
7	972
6	535
5	248
4	118
3	71
2	33
1	16
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
2.7b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
6.6b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 63

Calls

3 calls:

21.0ms	(* (- 1.0 x) y)
17.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
24.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series195.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(* (- 1.0 x) y)
92.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
54.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify1.2s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1286
1	346
0	128

prune375.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) (/ y (+ y 1.0)))
0.0b	(/ y (+ y 1.0))
2.7b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
25×	`times-frac`
21×	`add-cube-cbrt`
18×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
7×	`distribute-lft-out`
5×	`pow1` `associate-l` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`flip3--` `flip--` `associate-/l*`
2×	`frac-times` `cbrt-undiv` `flip3-+` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `pow-prod-down` `associate-r/` `-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 88

Calls

3 calls:

62.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
12.0ms	(/ y (+ y 1.0))
6.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series196.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
50.0ms	(/ y (+ y 1.0))
99.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify1.4s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1637
1	425
0	157

prune413.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ y (- y 1.0))
0.0b	(* (/ (- 1.0 x) (+ y 1.0)) (/ y (- y 1.0)))
0.1b	(* (* (/ (- 1.0 x) (+ y 1.0)) (/ y (- y 1.0))) (- y 1.0))
4.9b	(- 1.0 (* (* (/ (- 1.0 x) (+ y 1.0)) (/ y (- y 1.0))) (- y 1.0)))

rewrite259.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
68×	`*-un-lft-identity`
54×	`times-frac`
36×	`add-cbrt-cube` `add-exp-log`
34×	`add-cube-cbrt`
27×	`associate-l`
26×	`associate-r`
13×	`prod-exp` `cbrt-unprod`
12×	`distribute-lft-out--` `difference-of-squares`
11×	`pow1`
10×	`frac-times`
9×	`cbrt-undiv` `div-exp`
7×	`flip3--` `associate-*l/` `flip--`
6×	`associate-*r/` `associate-/r/` `add-log-exp`
5×	`associate-/r*` `sub-neg` `distribute-lft-out`
4×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate--r+` `unswap-sqr`
3×	`div-inv` `associate-/l*`
2×	`*-commutative`
1×	`clear-num` `frac-2neg` `flip3-+` `diff-log` `flip-+`

Counts

4 → 165

Calls

4 calls:

17.0ms	(/ y (- y 1.0))
78.0ms	(* (/ (- 1.0 x) (+ y 1.0)) (/ y (- y 1.0)))
143.0ms	(* (* (/ (- 1.0 x) (+ y 1.0)) (/ y (- y 1.0))) (- y 1.0))
9.0ms	(- 1.0 (* (* (/ (- 1.0 x) (+ y 1.0)) (/ y (- y 1.0))) (- y 1.0)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ y (- y 1.0))
145.0ms	(* (/ (- 1.0 x) (+ y 1.0)) (/ y (- y 1.0)))
49.0ms	(* (* (/ (- 1.0 x) (+ y 1.0)) (/ y (- y 1.0))) (- y 1.0))
113.0ms	(- 1.0 (* (* (/ (- 1.0 x) (+ y 1.0)) (/ y (- y 1.0))) (- y 1.0)))

simplify2.1s

Counts

177 → 177

Iterations

Iter	Nodes
done	5002
2	3808
1	831
0	260

prune867.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* (/ y (+ y 1.0)) (/ y (+ y 1.0))) (/ y (+ y 1.0)))
0.0b	(* (/ y (+ y 1.0)) (/ y (+ y 1.0)))
2.7b	(- 1.0 (* (- 1.0 x) (cbrt (* (* (/ y (+ y 1.0)) (/ y (+ y 1.0))) (/ y (+ y 1.0))))))
19.9b	(cbrt (* (* (/ y (+ y 1.0)) (/ y (+ y 1.0))) (/ y (+ y 1.0))))

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

96×	`*-un-lft-identity`
77×	`times-frac`
63×	`add-sqr-sqrt`
57×	`add-cbrt-cube` `add-exp-log`
48×	`add-cube-cbrt`
36×	`associate-r`
30×	`pow1`
24×	`swap-sqr`
22×	`prod-exp` `cbrt-unprod`
21×	`distribute-lft-out`
19×	`associate-l`
17×	`cbrt-undiv` `div-exp`
11×	`frac-times` `associate-*l/`
10×	`associate-/r/`
7×	`cbrt-div` `pow-plus` `associate-*r/` `pow-prod-up`
6×	`add-log-exp` `unswap-sqr`
5×	`flip3-+` `flip-+` `div-inv`
4×	`pow-prod-down`
3×	`pow2` `pow-sqr`
2×	`pow3` `*-commutative`
1×	`cbrt-prod` `sub-neg` `flip3--` `pow1/3` `diff-log` `rem-cbrt-cube` `flip--`

Counts

4 → 184

Calls

4 calls:

81.0ms	(* (* (/ y (+ y 1.0)) (/ y (+ y 1.0))) (/ y (+ y 1.0)))
58.0ms	(* (/ y (+ y 1.0)) (/ y (+ y 1.0)))
9.0ms	(- 1.0 (* (- 1.0 x) (cbrt (* (* (/ y (+ y 1.0)) (/ y (+ y 1.0))) (/ y (+ y 1.0))))))
77.0ms	(cbrt (* (* (/ y (+ y 1.0)) (/ y (+ y 1.0))) (/ y (+ y 1.0))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (* (/ y (+ y 1.0)) (/ y (+ y 1.0))) (/ y (+ y 1.0)))
49.0ms	(* (/ y (+ y 1.0)) (/ y (+ y 1.0)))
95.0ms	(- 1.0 (* (- 1.0 x) (cbrt (* (* (/ y (+ y 1.0)) (/ y (+ y 1.0))) (/ y (+ y 1.0))))))
69.0ms	(cbrt (* (* (/ y (+ y 1.0)) (/ y (+ y 1.0))) (/ y (+ y 1.0))))

simplify2.8s

Counts

196 → 196

Iterations

Iter	Nodes
done	5003
2	3174
1	868
0	270

prune872.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

regimes231.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.5b

bsearch135.0ms

Steps

Iters	Range		Point
9	12146952.384825662	1779227265816.5227	108523950.22793227
9	-62218760779908.9	-733100.9210806559	-140476787.34337726

simplify4.0ms

Iterations

Iter	Nodes
done	28
1	28
0	22

end0.0ms

sample950.0ms

Algorithm

intervals

Results

431.0ms	6080×	body	80	valid
152.0ms	730×	body	640	valid
78.0ms	370×	body	1280	valid
64.0ms	535×	body	320	valid
24.0ms	285×	body	160	valid