Details

sample205.0ms

Algorithm

intervals

Results

92.0ms	48×	body	2560	valid
59.0ms	89×	body	1280	valid
26.0ms	62×	body	640	valid
7.0ms	27×	body	320	valid
3.0ms	19×	body	160	valid
1.0ms	11×	body	80	valid

simplify13.0ms

Counts

1 → 1

Iterations

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

prune53.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize27.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
2.1b	(- 1.0 (cos x))

rewrite45.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*` `fma-neg`
2×	`expm1-log1p-u` `pow1` `flip3--` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 68

Calls

2 calls:

29.0ms	(/ (- 1.0 (cos x)) (sin x))
12.0ms	(- 1.0 (cos x))

series112.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(/ (- 1.0 (cos x)) (sin x))
36.0ms	(- 1.0 (cos x))

simplify1.4s

Counts

74 → 74

Iterations

Iter	Nodes
done	5001
2	1211
1	309
0	134

prune480.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x))) (fma (cos x) (+ (cos x) 1.0) (* 1.0 1.0)))
0.3b	(* (cos x) (cos x))
0.5b	(+ (cos x) 1.0)
1.9b	(- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
12×	`times-frac`
11×	`pow1`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`difference-cubes` `cube-unmult` `pow3`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r` `fma-def` `swap-sqr` `associate-r` `associate-l*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`pow2` `cbrt-undiv` `+-commutative` `sqr-cos` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `pow-plus` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `pow-prod-down` `prod-exp` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

63.0ms	(/ (- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x))) (fma (cos x) (+ (cos x) 1.0) (* 1.0 1.0)))
8.0ms	(* (cos x) (cos x))
6.0ms	(+ (cos x) 1.0)
39.0ms	(- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ (- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x))) (fma (cos x) (+ (cos x) 1.0) (* 1.0 1.0)))
24.0ms	(* (cos x) (cos x))
11.0ms	(+ (cos x) 1.0)
63.0ms	(- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))

simplify3.3s

Counts

111 → 111

Iterations

Iter	Nodes
done	5001
2	3152
1	497
0	187

prune818.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.1b

localize76.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos x) (cos x))
0.3b	(exp (log (/ (- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x))) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))))
0.5b	(+ 1.0 (cos x))
1.9b	(- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
16×	`log-prod` `exp-sum`
12×	`pow1` `times-frac`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `difference-cubes` `exp-prod` `cube-unmult` `pow3` `log1p-expm1-u`
3×	`fma-def` `swap-sqr` `associate-r` `associate-l`
1×	`pow2` `+-commutative` `log-div` `sqr-cos` `sum-log` `sub-neg` `flip3-+` `pow-plus` `flip3--` `exp-diff` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `prod-exp` `pow-sqr` `log-pow` `cos-mult` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `div-inv` `flip--` `distribute-lft-out` `unswap-sqr` `rem-exp-log`

Counts

4 → 94

Calls

4 calls:

8.0ms	(* (cos x) (cos x))
22.0ms	(exp (log (/ (- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x))) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))))
5.0ms	(+ 1.0 (cos x))
35.0ms	(- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (cos x) (cos x))
176.0ms	(exp (log (/ (- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x))) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))))
11.0ms	(+ 1.0 (cos x))
67.0ms	(- (* 1.0 (* 1.0 1.0)) (* (* (cos x) (cos x)) (cos x)))

simplify2.7s

Counts

106 → 106

Iterations

Iter	Nodes
done	5002
2	3146
1	552
0	237

prune790.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.1b

localize89.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (log (/ (- (* 1.0 (* 1.0 1.0)) (* (log (exp (* (cos x) (cos x)))) (cos x))) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))))
0.5b	(+ 1.0 (cos x))
0.5b	(log (exp (* (cos x) (cos x))))
1.9b	(- (* 1.0 (* 1.0 1.0)) (* (log (exp (* (cos x) (cos x)))) (cos x)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

17×	`log-prod`
16×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `exp-sum` `add-cube-cbrt`
9×	`times-frac` `add-log-exp`
6×	`pow1`
5×	`exp-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log-pow` `log1p-expm1-u`
3×	`fma-def`
1×	`+-commutative` `log-div` `sqr-cos` `sum-log` `sub-neg` `flip3-+` `flip3--` `exp-to-pow` `exp-diff` `fma-neg` `diff-log` `rem-log-exp` `prod-diff` `flip-+` `div-inv` `flip--` `distribute-lft-out` `rem-exp-log`

Counts

4 → 78

Calls

4 calls:

29.0ms	(exp (log (/ (- (* 1.0 (* 1.0 1.0)) (* (log (exp (* (cos x) (cos x)))) (cos x))) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))))
10.0ms	(+ 1.0 (cos x))
7.0ms	(log (exp (* (cos x) (cos x))))
27.0ms	(- (* 1.0 (* 1.0 1.0)) (* (log (exp (* (cos x) (cos x)))) (cos x)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(exp (log (/ (- (* 1.0 (* 1.0 1.0)) (* (log (exp (* (cos x) (cos x)))) (cos x))) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))))
19.0ms	(+ 1.0 (cos x))
30.0ms	(log (exp (* (cos x) (cos x))))
92.0ms	(- (* 1.0 (* 1.0 1.0)) (* (log (exp (* (cos x) (cos x)))) (cos x)))

simplify1.9s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	1996
1	457
0	210

prune626.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 0.1b

regimes356.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.2b

bsearch114.0ms

Steps

Iters	Range		Point
9	5.1798647897020696e-05	160.65039477392645	0.02306599559720159
8	-0.9341403346610884	-0.003292329160956242	-0.020666341506661655

simplify20.0ms

Iterations

Iter	Nodes
done	45
1	45
0	39

end0.0ms

sample8.6s

Algorithm

intervals

Results

4.0s	1619×	body	2560	valid
2.6s	2702×	body	1280	valid
1.1s	1905×	body	640	valid
368.0ms	923×	body	320	valid
158.0ms	502×	body	160	valid
38.0ms	345×	body	80	valid
20.0ms	4×	body	5120	valid