Details

sample163.0ms

Algorithm

intervals

Results

78.0ms	51×	body	2560	valid
47.0ms	87×	body	1280	valid
16.0ms	52×	body	640	valid
8.0ms	36×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	15×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize40.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.4b	(- 1.0 (cos x))

rewrite25.0ms

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:

18.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(- 1.0 (cos x))

series71.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (- 1.0 (cos x)) (sin x))
21.0ms	(- 1.0 (cos x))

simplify1.8s

Counts

74 → 74

Iterations

Iter	Nodes
done	5002
3	2334
2	774
1	308
0	134

prune443.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos x) (cos x)) (cos x))
0.3b	(* (cos x) (cos x))
0.5b	(+ (cos x) 1.0)
1.2b	(- (* (* 1.0 1.0) 1.0) (* (* (cos x) (cos x)) (cos x)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
13×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
11×	`add-cbrt-cube` `add-exp-log`
10×	`add-cube-cbrt`
8×	`add-log-exp`
7×	`pow-plus` `pow-prod-up`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`pow2` `fma-def` `swap-sqr` `pow3` `pow-sqr`
2×	`cos-mult` `*-commutative` `unswap-sqr`
1×	`difference-cubes` `+-commutative` `sqr-cos` `sum-log` `sub-neg` `flip3-+` `flip3--` `fma-neg` `diff-log` `prod-diff` `associate-*l/` `flip-+` `flip--` `distribute-lft-out`

Counts

4 → 94

Calls

4 calls:

20.0ms	(* (* (cos x) (cos x)) (cos x))
8.0ms	(* (cos x) (cos x))
9.0ms	(+ (cos x) 1.0)
39.0ms	(- (* (* 1.0 1.0) 1.0) (* (* (cos x) (cos x)) (cos x)))

series127.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (* (cos x) (cos x)) (cos x))
18.0ms	(* (cos x) (cos x))
11.0ms	(+ (cos x) 1.0)
63.0ms	(- (* (* 1.0 1.0) 1.0) (* (* (cos x) (cos x)) (cos x)))

simplify2.9s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
3	3415
2	1180
1	373
0	141

prune634.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (- (* (* 1.0 1.0) 1.0) (/ (fma (cos (+ x x)) (cos x) (cos x)) 2)) (fma (+ (cos x) 1.0) (cos x) (* 1.0 1.0))) (sin x))
0.4b	(fma (cos (+ x x)) (cos x) (cos x))
0.5b	(+ (cos x) 1.0)
1.2b	(- (* (* 1.0 1.0) 1.0) (/ (fma (cos (+ x x)) (cos x) (cos x)) 2))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
56×	`*-un-lft-identity`
54×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`prod-diff` `associate-/l*`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
6×	`div-inv`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `fma-def` `div-exp`
2×	`div-sub`
1×	`+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `flip3--` `fma-neg` `diff-log` `flip-+` `fma-udef` `flip--` `distribute-lft-out` `associate-/l/`

Counts

4 → 128

Calls

4 calls:

67.0ms	(/ (/ (- (* (* 1.0 1.0) 1.0) (/ (fma (cos (+ x x)) (cos x) (cos x)) 2)) (fma (+ (cos x) 1.0) (cos x) (* 1.0 1.0))) (sin x))
0.0ms	(fma (cos (+ x x)) (cos x) (cos x))
5.0ms	(+ (cos x) 1.0)
42.0ms	(- (* (* 1.0 1.0) 1.0) (/ (fma (cos (+ x x)) (cos x) (cos x)) 2))

series522.0ms

Counts

4 → 12

Calls

4 calls:

324.0ms	(/ (/ (- (* (* 1.0 1.0) 1.0) (/ (fma (cos (+ x x)) (cos x) (cos x)) 2)) (fma (+ (cos x) 1.0) (cos x) (* 1.0 1.0))) (sin x))
44.0ms	(fma (cos (+ x x)) (cos x) (cos x))
18.0ms	(+ (cos x) 1.0)
136.0ms	(- (* (* 1.0 1.0) 1.0) (/ (fma (cos (+ x x)) (cos x) (cos x)) 2))

simplify2.1s

Counts

140 → 140

Iterations

Iter	Nodes
done	5000
2	2730
1	891
0	350

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (- (* (* 1.0 1.0) 1.0) (* (+ 1/2 (* 1/2 (cos (+ x x)))) (cos x))) (fma (+ (cos x) 1.0) (cos x) (* 1.0 1.0))) (sin x))
0.4b	(+ 1/2 (* 1/2 (cos (+ x x))))
0.5b	(+ (cos x) 1.0)
1.2b	(- (* (* 1.0 1.0) 1.0) (* (+ 1/2 (* 1/2 (cos (+ x x)))) (cos x)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
50×	`*-un-lft-identity`
48×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`associate-/l*`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
6×	`fma-def`
5×	`div-inv`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
2×	`+-commutative` `sum-log` `flip3-+` `div-sub` `flip-+`
1×	`clear-num` `sub-neg` `frac-2neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip--` `distribute-lft-out` `associate-/l/`

Counts

4 → 122

Calls

4 calls:

53.0ms	(/ (/ (- (* (* 1.0 1.0) 1.0) (* (+ 1/2 (* 1/2 (cos (+ x x)))) (cos x))) (fma (+ (cos x) 1.0) (cos x) (* 1.0 1.0))) (sin x))
9.0ms	(+ 1/2 (* 1/2 (cos (+ x x))))
9.0ms	(+ (cos x) 1.0)
27.0ms	(- (* (* 1.0 1.0) 1.0) (* (+ 1/2 (* 1/2 (cos (+ x x)))) (cos x)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(/ (/ (- (* (* 1.0 1.0) 1.0) (* (+ 1/2 (* 1/2 (cos (+ x x)))) (cos x))) (fma (+ (cos x) 1.0) (cos x) (* 1.0 1.0))) (sin x))
31.0ms	(+ 1/2 (* 1/2 (cos (+ x x))))
14.0ms	(+ (cos x) 1.0)
103.0ms	(- (* (* 1.0 1.0) 1.0) (* (+ 1/2 (* 1/2 (cos (+ x x)))) (cos x)))

simplify1.7s

Counts

134 → 134

Iterations

Iter	Nodes
done	5001
2	2349
1	734
0	283

prune812.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes178.0ms

Accuracy

98.6% (0.4b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 30.1b

bsearch141.0ms

Steps

Iters	Range		Point
8	0.0004390994911134099	0.778402845272117	0.020699439208913106
9	-0.1501579911863904	-8.136897775944376e-09	-0.021867456850458863

simplify17.0ms

Iterations

Iter	Nodes
done	53
1	53
0	46

end0.0ms

sample8.2s

Algorithm

intervals

Results

3.4s	1546×	body	2560	valid
3.2s	2829×	body	1280	valid
944.0ms	1797×	body	640	valid
359.0ms	958×	body	320	valid
95.0ms	495×	body	160	valid
40.0ms	370×	body	80	valid
22.0ms	5×	body	5120	valid