Details

sample45.0ms

Algorithm

intervals

Results

21.0ms

256×

body

valid

simplify40.0ms

Counts: 1 → 1

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.4b

localize24.0ms

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)
37.5b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite239.0ms

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:

50.0ms	(+ (+ (* x x) (* y y)) (* z z))
127.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
59.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series430.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(+ (+ (* x x) (* y y)) (* z z))
73.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
292.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.6s

Counts: 76 → 76

prune313.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 20.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.1b	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
37.5b	(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))

rewrite346.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
51×	`add-exp-log` `times-frac`
37×	`*-un-lft-identity`
34×	`add-cube-cbrt`
24×	`cbrt-prod`
22×	`associate-r`
20×	`prod-exp`
19×	`add-cbrt-cube`
16×	`div-exp`
9×	`pow1` `add-log-exp` `unswap-sqr`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`associate-l`
6×	`associate-/r*`
4×	`rec-exp` `1-exp`
3×	`sqrt-div` `sum-log` `div-inv` `associate-/l*`
2×	`frac-times` `sqrt-pow1` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+l+` `frac-2neg` `pow1/2` `clear-num` `sqrt-prod` `*-commutative`

Counts

4 → 138

Calls

4 calls:

32.0ms	(+ (+ (* x x) (* y y)) (* z z))
129.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))
95.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
85.0ms	(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))

series946.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(+ (+ (* x x) (* y y)) (* z z))
181.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))
197.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
505.0ms	(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))

simplify1.3s

Counts: 150 → 150

prune483.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 20.3b

localize16.0ms

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 (/ 1 3.0)))
37.5b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite191.0ms

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:

43.0ms	(+ (+ (* x x) (* y y)) (* z z))
112.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
32.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series411.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(+ (+ (* x x) (* y y)) (* z z))
225.0ms	(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
137.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.8s

Counts: 86 → 86

prune302.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 20.3b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
16×	`associate-r` `sqrt-prod`
11×	`*-un-lft-identity` `times-frac`
10×	`add-cube-cbrt`
4×	`unswap-sqr`
3×	`pow1` `add-exp-log` `associate-l` `add-cbrt-cube`
1×	`sqrt-div` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `div-inv` `add-log-exp`

Counts

1 → 35

Calls

1 calls:

35.0ms

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

series60.0ms

Counts

1 → 3

Calls

1 calls:

60.0ms

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

simplify831.0ms

Counts: 38 → 38

prune94.0ms

Pruning

13 alts after pruning (9 fresh and 4 done)

Merged error: 20.3b

regimes1.2s

Accuracy

58.7% (8.2b remaining)

Error of 27.0b against oracle of 18.9b and baseline of 38.6b

bsearch154.0ms

Steps

Iters	Range		Point
7	2.343630355969629e+63	3.913008940742602e+64	3.871233825359606e+64
6	-1.2800795360934752e-306	-2.5092550594592027e-307	-8.416887720474182e-307
9	-2.849107293399729e-271	-2.591365672246518e-278	-2.623547536657377e-278
10	-1.474096976152395e+169	-2.086363706554303e+150	-9.893983514208573e+152

simplify3.7s

end0.0ms

sample973.0ms

Algorithm

intervals

Results

612.0ms

8000×

body

valid