Details

sample315.0ms

Algorithm

intervals

Results

202.0ms	99×	body	2560	valid
64.0ms	77×	body	1280	valid
19.0ms	40×	body	640	valid
7.0ms	22×	body	320	valid
5.0ms	256×	pre	80	true
4.0ms	18×	body	160	valid

simplify22.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.4b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
4.2b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite79.0ms

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:

6.0ms	(/ 1.0 (tan x))
71.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series211.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(/ 1.0 (tan x))
157.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify899.0ms

Counts: 56 → 56

prune167.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

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))

rewrite123.0ms

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:

41.0ms

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

51.0ms

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

26.0ms

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

series232.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms

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

71.0ms

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

77.0ms

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

simplify1.5s

Counts: 118 → 118

prune503.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize32.0ms

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)))))
0.6b	(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))))

rewrite576.0ms

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:

414.0ms	(* (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)))))
40.0ms	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
54.0ms	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
49.0ms	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))

series1.6s

Counts

4 → 12

Calls

4 calls:

428.0ms	(* (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)))))
385.0ms	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
393.0ms	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
442.0ms	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))

simplify1.7s

Counts: 135 → 135

prune1.4s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.1b

localize87.0ms

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))))
0.7b	(cbrt (* (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 (* (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 (* (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))))))

rewrite492.0ms

Algorithm

rewrite-expression-head

Rules

290×	`cbrt-div`
200×	`associate-*l/`
148×	`frac-add`
75×	`frac-times`
74×	`flip3-+` `flip-+`
15×	`associate-*r/`
6×	`cbrt-prod`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`

Counts

4 → 148

Calls

4 calls:

37.0ms	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
110.0ms	(cbrt (* (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))))))
151.0ms	(cbrt (* (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))))))
172.0ms	(cbrt (* (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))))))

series2.0s

Counts

4 → 12

Calls

4 calls:

405.0ms	(cbrt (+ (* (/ 6405119470038039.0 2.8823037615171174e+17) (pow x 3)) (+ (* (/ 4880091024790887.0 2.305843009213694e+18) (pow x 5)) (* (/ 6004799503160661.0 18014398509481984.0) x))))
496.0ms	(cbrt (* (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))))))
594.0ms	(cbrt (* (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))))))
476.0ms	(cbrt (* (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))))))

simplify1.5s

Counts: 160 → 160

prune1.5s

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 0.1b

regimes185.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify815.0ms

end0.0ms

sample12.1s

Algorithm

intervals

Results

7.2s	3145×	body	2560	valid
2.5s	2546×	body	1280	valid
1.7s	1290×	body	640	valid
342.0ms	632×	body	320	valid
146.0ms	8000×	pre	80	true
74.0ms	337×	body	160	valid
6.0ms	50×	body	80	valid