Details

sample127.0ms

Algorithm

intervals

Results

69.0ms	59×	body	2560	valid
27.0ms	67×	body	1280	valid
14.0ms	62×	body	640	valid
7.0ms	42×	body	320	valid
2.0ms	17×	body	160	valid
1.0ms	9×	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: 30.9b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.6b	(- 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))

series64.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify37.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (9.0ms)

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

prune193.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
2.6b	(- 1.0 (cos x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 177

Calls

3 calls:

14.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
7.0ms	(/ (sin x) (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

series97.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
36.0ms	(/ (sin x) (- 1.0 (cos x)))
19.0ms	(- 1.0 (cos x))

simplify68.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	572	1779
1	2636	1549
2	5001	1441

prune321.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- 1.0 (cos x)))
0.2b	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
1.7b	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
2.6b	(- 1.0 (cos x))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

231×	`times-frac`
166×	`add-sqr-sqrt` `*-un-lft-identity`
136×	`exp-prod`
120×	`add-cube-cbrt`
69×	`log-pow`
23×	`distribute-lft-out--` `difference-of-squares`
16×	`associate-/r/`
9×	`prod-diff` `div-inv`
8×	`flip3--` `flip--`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `fma-neg` `associate-/l*`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 227

Calls

4 calls:

7.0ms	(/ (sin x) (- 1.0 (cos x)))
24.0ms	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
31.0ms	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
4.0ms	(- 1.0 (cos x))

series145.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (sin x) (- 1.0 (cos x)))
43.0ms	(exp (/ 1 (/ (sin x) (- 1.0 (cos x)))))
41.0ms	(log (exp (/ 1 (/ (sin x) (- 1.0 (cos x))))))
19.0ms	(- 1.0 (cos x))

simplify63.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	593	1886
1	2179	1647
2	5002	1502

prune684.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (sin x))
0.2b	(* (- 1.0 (cos x)) (/ 1 (sin x)))
2.6b	(- 1.0 (cos x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
26×	`add-cube-cbrt`
20×	`times-frac`
16×	`add-exp-log`
13×	`associate-r`
10×	`add-cbrt-cube`
9×	`prod-diff`
6×	`pow1`
5×	`associate-l` `add-log-exp`
4×	`div-exp` `prod-exp`
3×	`expm1-log1p-u` `flip3--` `fma-neg` `associate-/r` `flip--` `log1p-expm1-u` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

3 → 105

Calls

3 calls:

2.0ms	(/ 1 (sin x))
20.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
3.0ms	(- 1.0 (cos x))

series69.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/ 1 (sin x))
36.0ms	(* (- 1.0 (cos x)) (/ 1 (sin x)))
19.0ms	(- 1.0 (cos x))

simplify53.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	381	728
1	1613	574
2	5002	548

prune193.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 0.1b

regimes359.0ms

Accuracy

97.9% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 30.3b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	31
1	35	31

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.1s	1600×	body	2560	valid
1.2s	2746×	body	1280	valid
449.0ms	1888×	body	640	valid
154.0ms	937×	body	320	valid
51.0ms	445×	body	160	valid
24.0ms	383×	body	80	valid
3.0ms	1×	body	5120	valid