Details

sample219.0ms

Algorithm

intervals

Results

151.0ms	112×	body	2560	valid
41.0ms	74×	body	1280	valid
12.0ms	44×	body	640	valid
4.0ms	21×	body	320	valid
3.0ms	256×	pre	80	true
1.0ms	4×	body	160	valid
0.0ms	1×	body	80	valid

simplify13.0ms

Counts: 1 → 1

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.2b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
2.1b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite36.0ms

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:

5.0ms	(/ 1.0 (tan x))
29.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series139.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ 1.0 (tan x))
104.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify615.0ms

Counts: 56 → 56

prune108.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 4 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)))
0.0b	(+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))
0.0b	(* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5))
0.1b	(* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

35.0ms	(+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x)))
12.0ms	(+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))
18.0ms	(* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5))
24.0ms	(* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3))

series276.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x)))
130.0ms	(+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))
47.0ms	(* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5))
39.0ms	(* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3))

simplify970.0ms

Counts: 133 → 133

prune346.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (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)))))
0.7b	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
0.7b	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
0.7b	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))

rewrite329.0ms

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:

232.0ms	(* (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)))))
30.0ms	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
28.0ms	(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))))

series1.1s

Counts

4 → 12

Calls

4 calls:

288.0ms	(* (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)))))
263.0ms	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
257.0ms	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
256.0ms	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))

simplify1.1s

Counts: 135 → 135

prune695.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.7b	(* 4880091024790887.0 (pow x 5))
0.8b	(* (* 4880091024790887.0 (pow x 5)) 18014398509481984.0)
0.8b	(* 6405119470038039.0 (pow x 3))
1.9b	(* (* 6405119470038039.0 (pow x 3)) (* 2.305843009213694e+18 18014398509481984.0))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
31×	`prod-exp`
25×	`add-cbrt-cube`
24×	`add-sqr-sqrt`
23×	`associate-r`
13×	`cbrt-unprod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
8×	`unpow-prod-down` `associate-l`
7×	`unswap-sqr`
5×	`pow-to-exp` `pow-exp`
4×	`cube-prod` `pow-prod-down` `*-commutative` `add-log-exp` `sqr-pow`
1×	`cube-mult` `unpow3`

Counts

4 → 99

Calls

4 calls:

10.0ms	(* 4880091024790887.0 (pow x 5))
20.0ms	(* (* 4880091024790887.0 (pow x 5)) 18014398509481984.0)
14.0ms	(* 6405119470038039.0 (pow x 3))
29.0ms	(* (* 6405119470038039.0 (pow x 3)) (* 2.305843009213694e+18 18014398509481984.0))

series174.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* 4880091024790887.0 (pow x 5))
51.0ms	(* (* 4880091024790887.0 (pow x 5)) 18014398509481984.0)
36.0ms	(* 6405119470038039.0 (pow x 3))
41.0ms	(* (* 6405119470038039.0 (pow x 3)) (* 2.305843009213694e+18 18014398509481984.0))

simplify647.0ms

Counts: 111 → 111

prune433.0ms

Pruning

19 alts after pruning (16 fresh and 3 done)

Merged error: 0.1b

regimes143.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify588.0ms

end0.0ms

sample8.3s

Algorithm

intervals

Results

5.6s	3255×	body	2560	valid
1.7s	2509×	body	1280	valid
465.0ms	1271×	body	640	valid
133.0ms	8000×	pre	80	true
123.0ms	609×	body	320	valid
43.0ms	314×	body	160	valid
3.0ms	42×	body	80	valid