Details

sample154.0ms

Algorithm

intervals

Results

80.0ms	54×	body	2560	valid
40.0ms	90×	body	1280	valid
11.0ms	51×	body	640	valid
8.0ms	2×	body	5120	valid
4.0ms	28×	body	320	valid
2.0ms	21×	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: 29.2b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.6b	(- 1.0 (cos x))

rewrite13.0ms

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:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series57.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 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

prune178.0ms

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))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
0.9b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.6b	(- 1.0 (cos x))

rewrite29.0ms

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:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series134.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (- 1.0 (cos x)) (sin x))
39.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
38.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
18.0ms	(- 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

prune347.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
0.9b	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
1.6b	(- 1.0 (cos x))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

339×	`times-frac`
230×	`add-sqr-sqrt` `*-un-lft-identity`
168×	`add-cube-cbrt`
136×	`exp-prod`
69×	`log-pow`
31×	`distribute-lft-out--` `difference-of-squares`
23×	`associate-/r/`
21×	`associate-/r*`
15×	`add-exp-log`
13×	`div-inv`
11×	`flip3--` `flip--`
9×	`prod-diff` `add-cbrt-cube`
7×	`div-exp` `add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `log-prod` `fma-neg` `associate-/l*`
2×	`rec-exp` `1-exp`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `rem-log-exp` `clear-num` `rem-exp-log` `inv-pow`

Counts

4 → 298

Calls

4 calls:

9.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
13.0ms	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
15.0ms	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
4.0ms	(- 1.0 (cos x))

series131.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
45.0ms	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
33.0ms	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
18.0ms	(- 1.0 (cos x))

simplify75.0ms

Algorithm

egg-herbie

Counts

310 → 310

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	691	2770
1	2749	2429
2	5002	2180

prune686.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.6b	(- 1.0 (cos x))

rewrite13.0ms

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:

7.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series55.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(/ (- 1.0 (cos x)) (sin x))
22.0ms	(- 1.0 (cos x))

simplify35.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

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

prune120.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

regimes131.0ms

Accuracy

98.3% (0.5b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 30.3b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	32
1	36	32

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.0s	1576×	body	2560	valid
1.4s	2771×	body	1280	valid
425.0ms	1890×	body	640	valid
141.0ms	912×	body	320	valid
51.0ms	484×	body	160	valid
24.0ms	362×	body	80	valid
18.0ms	5×	body	5120	valid