Details

sample54.0ms

Algorithm

intervals

Results

18.0ms	42×	body	2560	valid
9.0ms	41×	body	1280	valid
7.0ms	48×	body	640	valid
6.0ms	67×	body	80	valid
4.0ms	39×	body	320	valid
1.0ms	19×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	4
1	21	4
2	26	4
3	28	4
4	28	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize6.0ms

Local error

Found 2 expressions with local error:

2.0b	(- 1.0 (cos x))
12.9b	(/ (- 1.0 (cos x)) (* x x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 58

Calls

2 calls:

7.0ms	(- 1.0 (cos x))
20.0ms	(/ (- 1.0 (cos x)) (* x x))

series59.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(- 1.0 (cos x))
43.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify32.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	279	446
1	1006	326
2	5001	317

prune183.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- 1.0 (cos x)))
2.0b	(- 1.0 (cos x))
2.0b	(- 1.0 (cos x))
2.0b	(- 1.0 (cos x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
26×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`fma-neg`
5×	`cbrt-prod`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 101

Calls

4 calls:

4.0ms	(cbrt (- 1.0 (cos x)))
7.0ms	(- 1.0 (cos x))
7.0ms	(- 1.0 (cos x))
7.0ms	(- 1.0 (cos x))

series164.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(cbrt (- 1.0 (cos x)))
20.0ms	(- 1.0 (cos x))
16.0ms	(- 1.0 (cos x))
17.0ms	(- 1.0 (cos x))

simplify97.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	208	863
1	622	569
2	2937	535
3	5002	482

prune428.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(log (exp (cbrt (- 1.0 (cos x)))))
2.0b	(- 1.0 (cos x))
2.0b	(- 1.0 (cos x))
2.0b	(- 1.0 (cos x))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt` `*-un-lft-identity`
28×	`add-cube-cbrt`
27×	`prod-diff`
10×	`add-log-exp`
9×	`fma-neg` `log-pow`
8×	`exp-prod`
5×	`pow1` `cbrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `log-prod` `flip3--` `diff-log` `flip--`
1×	`rem-log-exp`

Counts

4 → 106

Calls

4 calls:

15.0ms	(log (exp (cbrt (- 1.0 (cos x)))))
7.0ms	(- 1.0 (cos x))
10.0ms	(- 1.0 (cos x))
7.0ms	(- 1.0 (cos x))

series167.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(log (exp (cbrt (- 1.0 (cos x)))))
20.0ms	(- 1.0 (cos x))
16.0ms	(- 1.0 (cos x))
17.0ms	(- 1.0 (cos x))

simplify101.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	234	881
1	659	575
2	3010	541
3	5001	488

prune476.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos x) 3)
0.4b	(+ 1.0 (cos x))
1.8b	(- (pow 1.0 3) (pow (cos x) 3))
12.9b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (pow x 2) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))))

rewrite141.0ms

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×	`add-exp-log` `distribute-lft-out--`
12×	`fma-neg`
10×	`add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`difference-cubes` `pow-unpow` `fma-def` `prod-exp`
2×	`cbrt-undiv` `pow-to-exp` `flip3--` `pow-exp` `flip--` `associate-/l/`
1×	`+-commutative` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `div-sub` `clear-num` `associate-/r*` `sum-log` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 306

Calls

4 calls:

3.0ms	(pow (cos x) 3)
7.0ms	(+ 1.0 (cos x))
30.0ms	(- (pow 1.0 3) (pow (cos x) 3))
83.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (pow x 2) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))))

series214.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(pow (cos x) 3)
9.0ms	(+ 1.0 (cos x))
46.0ms	(- (pow 1.0 3) (pow (cos x) 3))
134.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (pow x 2) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))))

simplify134.0ms

Algorithm

egg-herbie

Counts

318 → 318

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	781	3805
1	3379	2851
2	5001	2798

prune619.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes74.0ms

Accuracy

99% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.9b

bsearch101.0ms

Steps

Iters	Range		Point
9	0.007285382865895221	15234496.061427226	0.03348525979632908
10	-569.2304264003914	-7.772245281701499e-10	-0.030567446252090087

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	20
1	32	20

end0.0ms

sample1.6s

Algorithm

intervals

Results

733.0ms	1563×	body	2560	valid
314.0ms	1296×	body	1280	valid
232.0ms	1490×	body	640	valid
101.0ms	932×	body	320	valid
83.0ms	2264×	body	80	valid
40.0ms	455×	body	160	valid