Details

sample311.0ms

Algorithm

intervals

Results

178.0ms	101×	body	2560	valid
84.0ms	79×	body	1280	valid
18.0ms	44×	body	640	valid
10.0ms	256×	pre	80	true
7.0ms	22×	body	320	valid
2.0ms	10×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
2.9b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`times-frac`
12×	`add-cube-cbrt`
5×	`distribute-lft-out--`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`pow1`
1×	`tan-quot` `cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `associate-/r/` `frac-sub` `flip--`

Counts

2 → 50

Calls

2 calls:

23.0ms	(/ 1.0 (tan x))
28.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series221.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ 1.0 (tan x))
169.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify105.0ms

Counts: 56 → 56

prune151.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b

(+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x)))

0.1b

(* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5))

0.1b

(* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
29×	`add-exp-log`
26×	`associate-l`
25×	`times-frac`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`associate-r`
14×	`unswap-sqr`
13×	`add-cbrt-cube`
12×	`prod-exp`
10×	`unpow-prod-down`
8×	`add-log-exp`
7×	`associate-*l/`
6×	`div-exp` `sqr-pow`
5×	`cube-prod`
4×	`pow-to-exp` `frac-add` `pow-exp` `cbrt-unprod`
3×	`pow1` `sum-log`
2×	`cbrt-undiv` `flip3-+` `*-commutative` `flip-+` `div-inv`
1×	`+-commutative` `cube-mult` `associate-+r+` `unpow3`

Counts

3 → 109

Calls

3 calls:

49.0ms

(+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x)))

23.0ms

(* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5))

22.0ms

(* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3))

series192.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms

(+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x)))

64.0ms

(* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5))

44.0ms

(* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3))

simplify80.0ms

Counts: 118 → 118

prune504.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x)))) (cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x)))))
0.6b	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
0.6b	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
0.6b	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))

rewrite434.0ms

Algorithm

rewrite-expression-head

Rules

80×	`associate-*l/`
75×	`cbrt-div`
60×	`frac-add`
30×	`flip3-+` `flip-+`
25×	`cbrt-prod` `frac-times`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
5×	`associate-*r/`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 123

Calls

4 calls:

285.0ms	(* (cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x)))) (cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x)))))
33.0ms	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
47.0ms	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
61.0ms	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))

series1.4s

Counts

4 → 12

Calls

4 calls:

381.0ms	(* (cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x)))) (cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x)))))
345.0ms	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
395.0ms	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
308.0ms	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))

simplify156.0ms

Counts: 135 → 135

prune1.0s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.1b

localize70.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
0.6b	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
0.6b	(* 6405119470038039.0 (pow x 3))
2.1b	(* (* 6405119470038039.0 (pow x 3)) (* 2.305843009213694e+18 18014398509481984.0))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-exp-log`
21×	`prod-exp`
18×	`add-cbrt-cube`
17×	`add-sqr-sqrt`
13×	`associate-r`
10×	`add-cube-cbrt` `cbrt-div` `-un-lft-identity` `associate-l/`
9×	`pow1` `cbrt-unprod`
8×	`frac-add`
6×	`cbrt-prod`
4×	`unpow-prod-down` `flip3-+` `cube-prod` `associate-l` `flip-+` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `pow-prod-down` `pow-exp`
2×	`pow1/3` `*-commutative` `sqr-pow`
1×	`cube-mult` `unpow3`

Counts

4 → 87

Calls

4 calls:

53.0ms	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
52.0ms	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
22.0ms	(* 6405119470038039.0 (pow x 3))
52.0ms	(* (* 6405119470038039.0 (pow x 3)) (* 2.305843009213694e+18 18014398509481984.0))

series763.0ms

Counts

4 → 12

Calls

4 calls:

350.0ms	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
313.0ms	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
50.0ms	(* 6405119470038039.0 (pow x 3))
49.0ms	(* (* 6405119470038039.0 (pow x 3)) (* 2.305843009213694e+18 18014398509481984.0))

simplify95.0ms

Counts: 99 → 99

prune813.0ms

Pruning

16 alts after pruning (13 fresh and 3 done)

Merged error: 0.1b

regimes134.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify57.0ms

end0.0ms

sample11.7s

Algorithm

intervals

Results

7.4s	3296×	body	2560	valid
2.4s	2522×	body	1280	valid
1.1s	1223×	body	640	valid
237.0ms	601×	body	320	valid
188.0ms	8000×	pre	80	true
63.0ms	311×	body	160	valid
5.0ms	47×	body	80	valid