Details

sample185.0ms

Algorithm

intervals

Results

105.0ms	136×	body	1280	valid
26.0ms	61×	body	640	valid
16.0ms	256×	pre	80	true
6.0ms	22×	body	320	valid
3.0ms	33×	body	80	valid
1.0ms	4×	body	160	valid

simplify25.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	33	5
3	39	5
4	50	5
5	70	5
6	99	5
7	124	5
8	166	5
9	259	5
10	260	5
11	260	5
done	260	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
3.2b	(tan (+ y z))

rewrite50.0ms

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×	`pow1` `add-exp-log` `expm1-log1p-u` `fma-def` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `tan-sum` `diff-log` `sum-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:

17.0ms	(+ x (- (tan (+ y z)) (tan a)))
23.0ms	(- (tan (+ y z)) (tan a))
7.0ms	(tan (+ y z))

series351.0ms

Counts

3 → 9

Calls

3 calls:

147.0ms	(+ x (- (tan (+ y z)) (tan a)))
142.0ms	(- (tan (+ y z)) (tan a))
62.0ms	(tan (+ y z))

simplify99.0ms

Counts

81 → 81

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	276	685
1	732	540
2	3128	507
3	5001	488
done	5001	488

prune247.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite302.0ms

Algorithm

rewrite-expression-head

Rules

165×	`*-un-lft-identity`
115×	`add-sqr-sqrt`
108×	`add-cube-cbrt` `prod-diff`
97×	`times-frac`
56×	`associate-+r+`
27×	`distribute-lft-out`
18×	`fma-neg`
16×	`associate-/r/`
11×	`add-log-exp`
9×	`flip3--` `flip--`
8×	`add-exp-log` `add-cbrt-cube` `div-inv`
7×	`tan-quot`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`sub-neg` `flip3-+` `diff-log` `sum-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `associate-+r-` `frac-2neg` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `*-commutative` `frac-sub` `cbrt-unprod` `unswap-sqr`

Counts

4 → 227

Calls

4 calls:

148.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
28.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
98.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
16.0ms	(* (tan y) (tan z))

series1.3s

Counts

4 → 12

Calls

4 calls:

432.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
249.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
461.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
111.0ms	(* (tan y) (tan z))

simplify86.0ms

Counts

239 → 239

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	704	4490
1	2293	3769
2	5002	3667
done	5002	3667

prune781.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (tan a))
0.6b	(cbrt (tan a))
0.6b	(cbrt (tan a))
60.7b	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`tan-quot` `cbrt-div` `pow1/3`
1×	`fma-udef`

Counts

4 → 52

Calls

4 calls:

2.0ms	(cbrt (tan a))
2.0ms	(cbrt (tan a))
2.0ms	(cbrt (tan a))
0.0ms	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

series638.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(cbrt (tan a))
136.0ms	(cbrt (tan a))
138.0ms	(cbrt (tan a))
221.0ms	(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

simplify112.0ms

Counts

64 → 64

Iterations

Useful iterations: 4 (107.0ms)

Iter	Nodes	Cost
0	102	427
1	211	373
2	675	363
3	2633	349
4	5002	337
done	5002	337

prune478.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
0.2b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))
2.7b	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

rewrite599.0ms

Algorithm

rewrite-expression-head

Rules

105×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg` `distribute-lft-out`
12×	`add-log-exp`
10×	`associate-/r/`
8×	`add-exp-log` `add-cbrt-cube`
7×	`tan-quot`
6×	`pow1` `flip3--` `flip--`
5×	`exp-prod` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `rem-exp-log` `associate-/l/`
2×	`diff-log` `sum-log` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `frac-times` `associate-+r-` `sub-neg` `frac-2neg` `flip3-+` `exp-diff` `associate-r/` `div-exp` `exp-sum` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 170

Calls

4 calls:

30.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
94.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
15.0ms	(* (tan y) (tan z))
451.0ms	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

series1.3s

Counts

4 → 12

Calls

4 calls:

252.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
465.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
108.0ms	(* (tan y) (tan z))
520.0ms	(exp (+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))

simplify83.0ms

Counts

182 → 182

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	583	3094
1	2037	2523
2	5001	2496
done	5001	2496

prune629.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes272.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	14
1	22	14
done	22	14

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.1s	3956×	body	1280	valid
877.0ms	1966×	body	640	valid
341.0ms	8000×	pre	80	true
207.0ms	674×	body	320	valid
109.0ms	1135×	body	80	valid
56.0ms	269×	body	160	valid