Details

sample346.0ms

Algorithm

intervals

Results

135.0ms	105×	body	1280	valid
122.0ms	82×	body	640	valid
18.0ms	256×	pre	80	true
13.0ms	21×	body	320	valid
7.0ms	38×	body	80	valid
3.0ms	10×	body	160	valid

simplify7.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
9	4724
8	1354
7	446
6	193
5	89
4	39
3	33
2	22
1	15
0	9

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize27.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
2.5b	(tan (+ y z))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`prod-diff`
17×	`add-cube-cbrt`
11×	`associate-+r+`
10×	`add-log-exp`
4×	`tan-quot`
3×	`expm1-log1p-u` `pow1` `fma-def` `add-cbrt-cube` `fma-neg` `add-exp-log` `log1p-expm1-u`
2×	`tan-sum` `sum-log` `sub-neg` `diff-log` `frac-sub` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip3--` `flip-+` `flip--` `difference-of-squares`

Counts

3 → 72

Calls

3 calls:

14.0ms	(+ x (- (tan (+ y z)) (tan a)))
22.0ms	(- (tan (+ y z)) (tan a))
18.0ms	(tan (+ y z))

series468.0ms

Counts

3 → 9

Calls

3 calls:

181.0ms	(+ x (- (tan (+ y z)) (tan a)))
196.0ms	(- (tan (+ y z)) (tan a))
91.0ms	(tan (+ y z))

simplify786.0ms

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
2	1003
1	284
0	128

prune505.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan z) (tan y))
0.1b	(+ x (- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a)))
0.2b	(- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a))
0.2b	(* (tan z) (tan y))

rewrite278.0ms

Algorithm

rewrite-expression-head

Rules

151×	`*-un-lft-identity`
108×	`prod-diff`
107×	`add-sqr-sqrt`
100×	`add-cube-cbrt`
85×	`times-frac`
56×	`associate-+r+`
24×	`distribute-lft-out`
18×	`fma-neg`
14×	`associate-/r/`
13×	`add-log-exp`
8×	`flip3--` `flip--`
7×	`tan-quot` `div-inv`
6×	`pow1` `fma-def` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sum-log` `associate-r` `associate-l`
2×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `unswap-sqr`

Counts

4 → 207

Calls

4 calls:

7.0ms	(+ (tan z) (tan y))
143.0ms	(+ x (- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a)))
107.0ms	(- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a))
12.0ms	(* (tan z) (tan y))

series1.8s

Counts

4 → 12

Calls

4 calls:

188.0ms	(+ (tan z) (tan y))
628.0ms	(+ x (- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a)))
826.0ms	(- (/ (+ (tan z) (tan y)) (- 1 (* (tan z) (tan y)))) (tan a))
134.0ms	(* (tan z) (tan y))

simplify2.5s

Counts

219 → 219

Iterations

Iter	Nodes
done	5000
2	2655
1	701
0	298

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (tan z) (tan y))) (cbrt (* (tan z) (tan y))))
8.1b	(cbrt (* (tan z) (tan y)))
8.1b	(cbrt (* (tan z) (tan y)))
8.1b	(cbrt (* (tan z) (tan y)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

44×	`tan-quot`
33×	`cbrt-div`
20×	`frac-times`
14×	`associate-l/` `associate-r/`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

41.0ms	(* (cbrt (* (tan z) (tan y))) (cbrt (* (tan z) (tan y))))
7.0ms	(cbrt (* (tan z) (tan y)))
7.0ms	(cbrt (* (tan z) (tan y)))
7.0ms	(cbrt (* (tan z) (tan y)))

series998.0ms

Counts

4 → 12

Calls

4 calls:

329.0ms	(* (cbrt (* (tan z) (tan y))) (cbrt (* (tan z) (tan y))))
236.0ms	(cbrt (* (tan z) (tan y)))
228.0ms	(cbrt (* (tan z) (tan y)))
204.0ms	(cbrt (* (tan z) (tan y)))

simplify628.0ms

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
2	1126
1	289
0	122

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (pow (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (tan a)) 3) (pow x 3))
0.3b	(* (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (+ (tan a) x)) (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (tan a)))
0.4b	(/ (+ (pow (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (tan a)) 3) (pow x 3)) (fma x x (* (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (+ (tan a) x)) (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (tan a)))))
0.6b	(pow (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (tan a)) 3)

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

271×	`*-un-lft-identity`
142×	`add-sqr-sqrt`
117×	`times-frac`
110×	`add-cube-cbrt`
96×	`prod-diff`
64×	`distribute-lft-out`
52×	`unpow-prod-down` `cube-prod`
50×	`distribute-rgt-in` `distribute-lft-in`
27×	`distribute-lft-out--`
18×	`fma-def`
14×	`frac-sub`
13×	`associate-/l*`
12×	`frac-times` `difference-of-squares`
10×	`flip3--` `flip--`
9×	`add-cbrt-cube` `add-exp-log`
7×	`pow1` `associate-l` `div-inv`
6×	`flip3-+` `associate-r` `tan-quot` `flip-+` `add-log-exp`
5×	`sum-cubes`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u`
3×	`cube-div` `pow-unpow` `associate-/r` `associate-r/`
2×	`cube-mult` `sub-neg` `unpow3` `sqr-pow` `associate-/l/`
1×	`pow-to-exp` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `pow-pow` `frac-2neg` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 292

Calls

4 calls:

432.0ms	(+ (pow (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (tan a)) 3) (pow x 3))
318.0ms	(* (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (+ (tan a) x)) (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (tan a)))
791.0ms	(/ (+ (pow (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (tan a)) 3) (pow x 3)) (fma x x (* (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (+ (tan a) x)) (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (tan a)))))
49.0ms	(pow (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (tan a)) 3)

series23.7s

Counts

4 → 12

Calls

4 calls:

12.4s	(+ (pow (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (tan a)) 3) (pow x 3))
2.1s	(* (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (+ (tan a) x)) (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (tan a)))
8.3s	(/ (+ (pow (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (tan a)) 3) (pow x 3)) (fma x x (* (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (+ (tan a) x)) (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (tan a)))))
878.0ms	(pow (- (/ (+ (tan z) (tan y)) (fma (- (tan y)) (tan z) 1)) (tan a)) 3)

simplify694.0ms

Counts

304 → 304

Iterations

Iter	Nodes
done	5000
1	1837
0	587

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes420.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	23
1	23
0	17

end0.0ms

sample8.3s

Algorithm

intervals

Results

4.6s	3831×	body	1280	valid
1.9s	2070×	body	640	valid
867.0ms	8000×	pre	80	true
287.0ms	688×	body	320	valid
172.0ms	1139×	body	80	valid
106.0ms	272×	body	160	valid