Details

sample236.0ms

Algorithm

intervals

Results

99.0ms	51×	body	2560	valid
88.0ms	86×	body	1280	valid
25.0ms	65×	body	640	valid
7.0ms	27×	body	320	valid
3.0ms	18×	body	160	valid
1.0ms	9×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.5b	(- 1.0 (cos x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

20.0ms	(/ (- 1.0 (cos x)) (sin x))
13.0ms	(- 1.0 (cos x))

series109.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(/ (- 1.0 (cos x)) (sin x))
30.0ms	(- 1.0 (cos x))

simplify2.2s

Counts

74 → 74

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	134	964
1	295	831
2	743	731
3	2333	692
done	5000	683

prune292.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x)))))
0.3b	(pow (cos x) 3)
0.4b	(+ 1.0 (cos x))
1.3b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

233×	`add-sqr-sqrt`
165×	`*-un-lft-identity`
144×	`prod-diff`
138×	`unpow-prod-down` `cube-prod`
113×	`add-cube-cbrt`
80×	`difference-of-squares`
75×	`times-frac`
66×	`sqr-pow`
26×	`cube-mult` `unpow3`
25×	`associate-/l*` `distribute-lft-out--`
12×	`fma-neg`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `difference-cubes`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `flip-+` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 354

Calls

4 calls:

143.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x)))))
7.0ms	(pow (cos x) 3)
15.0ms	(+ 1.0 (cos x))
55.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series340.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x)))))
36.0ms	(pow (cos x) 3)
19.0ms	(+ 1.0 (cos x))
66.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify2.4s

Counts

366 → 366

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	378	11554
1	816	7927
2	2347	6842
done	5000	6120

prune1.0s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 0.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.4b	(+ 1.0 (cos x))
0.4b	(+ 1.0 (cos x))
1.4b	(- (/ (pow 1.0 3) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))) (/ (pow (cos x) 3) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))

rewrite577.0ms

Algorithm

rewrite-expression-head

Rules

2986×	`times-frac`
1881×	`add-sqr-sqrt`
1837×	`*-un-lft-identity`
1801×	`add-cube-cbrt`
1600×	`prod-diff`
754×	`unpow-prod-down` `cube-prod`
254×	`sqr-pow`
244×	`cube-mult` `unpow3`
83×	`div-inv`
40×	`fma-neg`
25×	`difference-of-squares`
16×	`distribute-lft-out--`
10×	`add-log-exp`
6×	`fma-def`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow`
2×	`+-commutative` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`
1×	`pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `pow-pow` `diff-log` `pow-exp` `frac-sub` `flip--` `sub-div` `rem-cube-cbrt`

Counts

4 → 1757

Calls

4 calls:

3.0ms	(pow (cos x) 3)
7.0ms	(+ 1.0 (cos x))
7.0ms	(+ 1.0 (cos x))
254.0ms	(- (/ (pow 1.0 3) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))) (/ (pow (cos x) 3) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))

series444.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (cos x) 3)
11.0ms	(+ 1.0 (cos x))
13.0ms	(+ 1.0 (cos x))
389.0ms	(- (/ (pow 1.0 3) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))) (/ (pow (cos x) 3) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))

simplify2.2s

Counts

1769 → 1769

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	1340	225648
1	2785	196041
done	5000	133498

prune1.4s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 0.2b

localize64.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ 1.0 (cos x))
0.4b	(+ 1.0 (cos x))
0.6b	(expm1 (pow (cos x) 3))
1.4b	(- (/ (pow 1.0 3) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))) (/ (log1p (expm1 (pow (cos x) 3))) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

883×	`times-frac`
627×	`add-sqr-sqrt`
608×	`*-un-lft-identity`
596×	`add-cube-cbrt`
520×	`prod-diff`
128×	`unpow-prod-down` `cube-prod`
56×	`div-inv`
44×	`sqr-pow`
42×	`cube-mult` `unpow3`
40×	`fma-neg`
10×	`add-log-exp` `difference-of-squares`
6×	`fma-def`
5×	`log1p-expm1-u`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `distribute-lft-out--`
2×	`+-commutative` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`
1×	`sub-neg` `expm1-log1p` `flip3--` `distribute-rgt-out--` `diff-log` `frac-sub` `flip--` `expm1-udef` `sub-div`

Counts

4 → 636

Calls

4 calls:

7.0ms	(+ 1.0 (cos x))
7.0ms	(+ 1.0 (cos x))
0.0ms	(expm1 (pow (cos x) 3))
151.0ms	(- (/ (pow 1.0 3) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))) (/ (log1p (expm1 (pow (cos x) 3))) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))

series886.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ 1.0 (cos x))
12.0ms	(+ 1.0 (cos x))
81.0ms	(expm1 (pow (cos x) 3))
782.0ms	(- (/ (pow 1.0 3) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))) (/ (log1p (expm1 (pow (cos x) 3))) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))

simplify2.4s

Counts

648 → 648

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	664	79288
1	1424	64412
2	2789	41440
done	5001	34441

prune1.4s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 0.2b

regimes179.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.0b

bsearch150.0ms

Steps

Iters	Range		Point
9	5.155942382976535e-09	0.21963308938311268	0.021287987873600457
11	-2445851338.3862987	-4.2674702477225e-16	-0.023540467143693854

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	81
1	39	81
done	39	81

end0.0ms

sample8.7s

Algorithm

intervals

Results

3.9s	1589×	body	2560	valid
3.0s	2733×	body	1280	valid
1.0s	1880×	body	640	valid
330.0ms	944×	body	320	valid
92.0ms	476×	body	160	valid
42.0ms	375×	body	80	valid
13.0ms	3×	body	5120	valid