Details

sample207.0ms

Algorithm

intervals

Results

97.0ms	46×	body	2560	valid
65.0ms	92×	body	1280	valid
22.0ms	63×	body	640	valid
7.0ms	29×	body	320	valid
2.0ms	11×	body	160	valid
1.0ms	15×	body	80	valid

simplify8.0ms

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

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.8b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.1b	(- 1.0 (cos x))

rewrite44.0ms

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:

29.0ms	(/ (- 1.0 (cos x)) (sin x))
10.0ms	(- 1.0 (cos x))

series112.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(/ (- 1.0 (cos x)) (sin x))
33.0ms	(- 1.0 (cos x))

simplify2.4s

Counts

74 → 74

Iterations

Useful iterations: done (2.4s)

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

prune331.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
0.4b	(pow (cos x) 3)
0.4b	(+ 1.0 (cos x))
0.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
144×	`prod-diff`
117×	`*-un-lft-identity`
114×	`unpow-prod-down` `cube-prod`
85×	`add-cube-cbrt`
50×	`sqr-pow`
48×	`difference-of-squares`
26×	`cube-mult` `unpow3`
25×	`times-frac` `associate-/l*`
15×	`distribute-lft-out--`
12×	`fma-neg`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`difference-cubes` `pow-unpow` `fma-def`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`+-commutative` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 304

Calls

4 calls:

126.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
4.0ms	(pow (cos x) 3)
7.0ms	(+ 1.0 (cos x))
64.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series374.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
39.0ms	(pow (cos x) 3)
11.0ms	(+ 1.0 (cos x))
79.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify2.0s

Counts

316 → 316

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	342	9345
1	787	5855
2	2429	4730
done	5001	4728

prune820.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (* (pow (cos x) 2) (cos x))) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
0.3b	(pow (cos x) 2)
0.4b	(+ 1.0 (cos x))
0.9b	(- (pow 1.0 3) (* (pow (cos x) 2) (cos x)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
15×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`fma-neg` `prod-diff`
10×	`add-exp-log`
9×	`unpow-prod-down` `add-cbrt-cube`
8×	`add-log-exp`
6×	`cube-prod`
5×	`pow1`
4×	`expm1-log1p-u` `times-frac` `log1p-expm1-u` `associate-/l*` `unpow2`
3×	`difference-cubes` `pow-unpow` `fma-def` `pow3` `sqr-pow`
2×	`cbrt-undiv` `cube-mult` `flip3--` `unpow3` `div-exp` `flip--` `associate-/l/`
1×	`+-commutative` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 104

Calls

4 calls:

87.0ms	(/ (- (pow 1.0 3) (* (pow (cos x) 2) (cos x))) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
7.0ms	(pow (cos x) 2)
12.0ms	(+ 1.0 (cos x))
23.0ms	(- (pow 1.0 3) (* (pow (cos x) 2) (cos x)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(/ (- (pow 1.0 3) (* (pow (cos x) 2) (cos x))) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
27.0ms	(pow (cos x) 2)
13.0ms	(+ 1.0 (cos x))
72.0ms	(- (pow 1.0 3) (* (pow (cos x) 2) (cos x)))

simplify1.6s

Counts

116 → 116

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	202	2071
1	515	1647
2	1727	1440
done	5000	1439

prune623.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3)))) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
0.4b	(pow (cos x) 3)
0.4b	(+ 1.0 (cos x))
26.1b	(- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
18×	`unpow-prod-down` `cube-prod`
12×	`fma-neg` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
8×	`times-frac` `associate-/l*` `add-log-exp` `sqr-pow`
5×	`pow1` `cube-mult` `unpow3`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `distribute-lft-out--`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`+-commutative` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `div-sub` `pow-exp` `prod-exp` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out` `expm1-udef` `associate--r-` `rem-cube-cbrt`

Counts

4 → 146

Calls

4 calls:

77.0ms	(/ (- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3)))) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
14.0ms	(pow (cos x) 3)
7.0ms	(+ 1.0 (cos x))
23.0ms	(- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3))))

series886.0ms

Counts

4 → 12

Calls

4 calls:

558.0ms	(/ (- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3)))) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
31.0ms	(pow (cos x) 3)
11.0ms	(+ 1.0 (cos x))
286.0ms	(- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3))))

simplify2.0s

Counts

158 → 158

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	238	4063
1	580	2448
2	2018	2067
done	5001	1885

prune632.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.1b

regimes167.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 29.9b

bsearch155.0ms

Steps

Iters	Range		Point
9	0.0033303272193615503	311302.39110615524	0.021388816407749943
9	-7.35943201301068	-4.403108084983288e-07	-0.02304827811785197

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	85
1	52	85
done	52	85

end0.0ms

sample7.7s

Algorithm

intervals

Results

3.5s	1590×	body	2560	valid
2.7s	2797×	body	1280	valid
835.0ms	1830×	body	640	valid
240.0ms	961×	body	320	valid
145.0ms	477×	body	160	valid
33.0ms	341×	body	80	valid
21.0ms	4×	body	5120	valid