Details

sample137.0ms

Algorithm

intervals

Results

72.0ms	51×	body	2560	valid
36.0ms	84×	body	1280	valid
14.0ms	59×	body	640	valid
5.0ms	30×	body	320	valid
3.0ms	22×	body	160	valid
1.0ms	10×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.4b	(- 1.0 (cos x))

rewrite15.0ms

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:

9.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series62.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify37.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	292	569
1	965	460
2	5002	460

prune185.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.5b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.4b	(- 1.0 (cos x))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
40×	`add-cube-cbrt`
38×	`exp-prod`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
9×	`prod-diff`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `fma-neg` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 132

Calls

4 calls:

13.0ms	(/ (- 1.0 (cos x)) (sin x))
12.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
13.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series140.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (- 1.0 (cos x)) (sin x))
48.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
36.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms	(- 1.0 (cos x))

simplify43.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	368	1009
1	1099	873
2	5002	871

prune350.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x))
0.3b	(pow (cos x) 3)
0.4b	(fma (cos x) (cos x) (* 1.0 (cos x)))
2.2b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

144×	`prod-diff`
110×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
90×	`unpow-prod-down` `cube-prod`
84×	`add-cube-cbrt`
34×	`sqr-pow`
26×	`cube-mult` `unpow3`
16×	`difference-of-squares`
12×	`fma-neg`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `associate-r` `associate-l`
1×	`difference-cubes` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 247

Calls

4 calls:

7.0ms	(* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x))
2.0ms	(pow (cos x) 3)
0.0ms	(fma (cos x) (cos x) (* 1.0 (cos x)))
22.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series231.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x))
29.0ms	(pow (cos x) 3)
52.0ms	(fma (cos x) (cos x) (* 1.0 (cos x)))
48.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify109.0ms

Algorithm

egg-herbie

Counts

259 → 259

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	616	2931
1	2145	2011
2	5002	1989

prune345.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x))
0.4b	(+ (cos x) 1.0)
0.4b	(fma (cos x) (cos x) (* 1.0 (cos x)))
2.4b	(- 1.0 (cos x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
9×	`prod-diff`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `fma-neg` `associate-r` `associate-l`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `fma-udef` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

3.0ms	(* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x))
3.0ms	(+ (cos x) 1.0)
0.0ms	(fma (cos x) (cos x) (* 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

series182.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x))
10.0ms	(+ (cos x) 1.0)
52.0ms	(fma (cos x) (cos x) (* 1.0 (cos x)))
19.0ms	(- 1.0 (cos x))

simplify42.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	324	643
1	1201	490
2	5001	489

prune258.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

regimes170.0ms

Accuracy

97.4% (0.8b remaining)

Error of 1.0b against oracle of 0.2b and baseline of 29.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	40
1	41	40

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.0s	1546×	body	2560	valid
1.2s	2704×	body	1280	valid
474.0ms	1935×	body	640	valid
151.0ms	949×	body	320	valid
56.0ms	512×	body	160	valid
22.0ms	351×	body	80	valid
16.0ms	3×	body	5120	valid