Details

sample28.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify22.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
34.6b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`times-frac`
18×	`add-cube-cbrt` `*-un-lft-identity`
13×	`sqrt-prod`
8×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`pow1`
3×	`associate-/r` `sum-log` `associate-/l`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l+` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num`

Counts

3 → 67

Calls

3 calls:

55.0ms	(+ (+ (* x x) (* y y)) (* z z))
119.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
32.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series417.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(+ (+ (* x x) (* y y)) (* z z))
82.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
265.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.6s

Counts: 76 → 76

prune378.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.6b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.3b	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
34.6b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
29×	`sqrt-prod`
16×	`-un-lft-identity` `associate-r*`
14×	`add-cube-cbrt`
13×	`times-frac`
9×	`sqrt-div`
8×	`pow1` `add-log-exp` `unswap-sqr`
6×	`associate-l`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down` `sum-log`
2×	`frac-times` `associate-*l/`
1×	`+-commutative` `rem-sqrt-square` `associate-+l+` `sqrt-unprod` `associate-r/` `prod-exp` `-commutative` `cbrt-unprod` `div-inv`

Counts

3 → 77

Calls

3 calls:

38.0ms	(+ (+ (* x x) (* y y)) (* z z))
139.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
50.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series439.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(+ (+ (* x x) (* y y)) (* z z))
247.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
147.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.0s

Counts: 86 → 86

prune312.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 19.6b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
34.6b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
36×	`times-frac`
33×	`add-sqr-sqrt`
32×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-log-exp`
6×	`associate-/r` `associate-/l`
5×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `sqrt-div`
3×	`flip3-+` `sum-log` `flip-+`
2×	`associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `associate-+l+` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

3 → 91

Calls

3 calls:

62.0ms	(+ (+ (* x x) (* y y)) (* z z))
90.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
38.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series548.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(+ (+ (* x x) (* y y)) (* z z))
368.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
133.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.7s

Counts: 100 → 100

prune349.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 13.9b

localize11.0ms

Local error

Found 1 expressions with local error:

0.4b	(/ (* -1 x) (sqrt 3.0))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-exp-log` `times-frac` `associate-/r*` `sqrt-prod` `add-cbrt-cube`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
2×	`cbrt-undiv` `div-exp`
1×	`pow1` `frac-2neg` `mul-1-neg` `distribute-frac-neg` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*` `add-log-exp`

Counts

1 → 28

Calls

1 calls:

14.0ms

(/ (* -1 x) (sqrt 3.0))

series87.0ms

Counts

1 → 3

Calls

1 calls:

86.0ms

(/ (* -1 x) (sqrt 3.0))

simplify1.2s

Counts: 31 → 31

prune82.0ms

Pruning

13 alts after pruning (9 fresh and 4 done)

Merged error: 13.9b

regimes879.0ms

Accuracy

39.9% (15.1b remaining)

Error of 27.7b against oracle of 12.6b and baseline of 37.7b

bsearch249.0ms

Steps

Iters	Range		Point
8	5.371396990386091e+130	3.1850560457991193e+134	1.8192216904895108e+132
4	108.32890937213158	170.63804855109743	117.29549700725407
4	1.2154635330803314e-27	2.214974109293172e-27	1.821326997004851e-27
9	3.710986270645431e-163	2.2694274533444234e-157	1.886712735002693e-161
9	-1.5485501097512278e-105	-3.069833087712075e-111	-4.1790862257326374e-109
8	-1.3406402941326562e-14	-1.7042354074346654e-17	-5.7655042319482596e-15
8	-5.574189844595493e+137	-3.6562210107547913e+133	-6.836071970171613e+133

simplify50.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

908.0ms

8000×

body

valid