Details

sample138.0ms

Algorithm

intervals

Results

73.0ms	52×	body	2560	valid
34.0ms	85×	body	1280	valid
14.0ms	63×	body	640	valid
4.0ms	25×	body	320	valid
3.0ms	17×	body	160	valid
1.0ms	14×	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: 28.8b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.1b	(- 1.0 (cos x))

rewrite28.0ms

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:

19.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(- 1.0 (cos x))

series57.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(/ (- 1.0 (cos x)) (sin x))
24.0ms	(- 1.0 (cos x))

simplify35.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (7.0ms)

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

prune188.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

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)))
1.4b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.1b	(- 1.0 (cos x))

rewrite78.0ms

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:

20.0ms	(/ (- 1.0 (cos x)) (sin x))
20.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
23.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
11.0ms	(- 1.0 (cos x))

series129.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (- 1.0 (cos x)) (sin x))
45.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
34.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
17.0ms	(- 1.0 (cos x))

simplify41.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (31.0ms)

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

prune369.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

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	(pow (cos x) 3)
0.4b	(fma (cos x) (cos x) (* 1.0 (cos x)))
1.9b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite58.0ms

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:

9.0ms	(* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x))
6.0ms	(pow (cos x) 3)
0.0ms	(fma (cos x) (cos x) (* 1.0 (cos x)))
31.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series214.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x))
26.0ms	(pow (cos x) 3)
48.0ms	(fma (cos x) (cos x) (* 1.0 (cos x)))
44.0ms	(- (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	2913
1	2153	1995
2	5002	1966

prune371.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos x) 3)
0.4b	(fma (cos x) (cos x) (* 1.0 (cos x)))
0.4b	(pow (pow (cos x) 3) 3)
1.9b	(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

400×	`cbrt-prod`
396×	`prod-diff`
374×	`unpow-prod-down` `cube-prod`
277×	`add-sqr-sqrt`
214×	`*-un-lft-identity`
212×	`add-cube-cbrt`
97×	`sqr-pow`
74×	`cube-mult` `unpow3`
44×	`difference-of-squares`
12×	`fma-neg`
7×	`add-exp-log`
6×	`pow-unpow` `add-cbrt-cube` `add-log-exp`
5×	`pow1` `pow-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-to-exp`
2×	`pow-pow` `rem-cube-cbrt`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `fma-udef` `distribute-lft-out--`

Counts

4 → 547

Calls

4 calls:

3.0ms	(pow (cos x) 3)
0.0ms	(fma (cos x) (cos x) (* 1.0 (cos x)))
6.0ms	(pow (pow (cos x) 3) 3)
67.0ms	(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

series180.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow (cos x) 3)
50.0ms	(fma (cos x) (cos x) (* 1.0 (cos x)))
51.0ms	(pow (pow (cos x) 3) 3)
51.0ms	(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

simplify175.0ms

Algorithm

egg-herbie

Counts

559 → 559

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	895	9857
1	2483	5080
2	5002	4791

prune385.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

regimes199.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 29.6b

bsearch85.0ms

Steps

Iters	Range		Point
8	0.00015704816827310668	9.114942375872904	0.021515064933806238
9	-0.2945747773639613	-3.489101517161873e-08	-0.021580538691811514

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	43
1	43	43

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.1s	1575×	body	2560	valid
1.3s	2854×	body	1280	valid
431.0ms	1846×	body	640	valid
257.0ms	442×	body	160	valid
152.0ms	906×	body	320	valid
25.0ms	374×	body	80	valid
8.0ms	3×	body	5120	valid