Details

sample23.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify129.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
5.8b	(- (* x x) (* (* y 4.0) y))
31.8b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 55

Calls

3 calls:

10.0ms	(+ (* x x) (* (* y 4.0) y))
8.0ms	(- (* x x) (* (* y 4.0) y))
30.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series156.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ (* x x) (* (* y 4.0) y))
47.0ms	(- (* x x) (* (* y 4.0) y))
70.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify2.5s

Counts: 64 → 64

prune159.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify12.0ms

Counts: 0 → 0

prune5.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
0.0b	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
23.3b	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
26.3b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

9.0ms	(+ (* x x) (* (* y 4.0) y))
80.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
34.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
18.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (* x x) (* (* y 4.0) y))
78.0ms	(- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y))))
56.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
55.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

simplify806.0ms

Counts: 91 → 91

prune187.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))) 3))
0.0b	(pow (- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))) 3)
23.3b	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
26.3b	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

rewrite261.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
24×	`cbrt-prod`
22×	`*-un-lft-identity`
20×	`associate-/r/`
19×	`add-exp-log` `add-cbrt-cube`
18×	`unpow-prod-down` `cube-prod`
14×	`add-cube-cbrt`
12×	`distribute-rgt-out--`
10×	`flip3-+` `times-frac` `flip-+` `div-inv`
8×	`cube-div` `difference-of-squares`
6×	`associate-/r*`
5×	`pow1` `cbrt-undiv` `div-exp`
4×	`cbrt-div` `prod-exp` `cbrt-unprod` `distribute-lft-out--` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `flip3--` `frac-2neg` `unpow3` `clear-num` `frac-sub` `flip--` `associate-/l*` `sub-div` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 124

Calls

4 calls:

98.0ms	(cbrt (pow (- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))) 3))
104.0ms	(pow (- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))) 3)
28.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
23.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(cbrt (pow (- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))) 3))
144.0ms	(pow (- (/ (* x x) (+ (* x x) (* (* y 4.0) y))) (/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))) 3)
72.0ms	(/ (* (* y 4.0) y) (+ (* x x) (* (* y 4.0) y)))
81.0ms	(/ (* x x) (+ (* x x) (* (* y 4.0) y)))

simplify1.0s

Counts: 136 → 136

prune412.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

regimes207.0ms

Accuracy

59.9% (12.7b remaining)

Error of 13.1b against oracle of 0.4b and baseline of 32.2b

bsearch244.0ms

Steps

Iters	Range		Point
9	2.4695173491361562e+123	1.0540223684506411e+130	1.0420907489457317e+130
8	0.0020412052054215894	0.8658429469844214	0.0031347165249641634
9	-3.551065177746875e-106	-3.477066808752501e-113	-5.3011610319498124e-111
10	-2.230909400099993e+156	-4.616428544046371e+146	-2.03762022030659e+149

simplify1.3s

end0.0ms

sample710.0ms

Algorithm

intervals

Results

455.0ms

8000×

body

valid