Details

sample135.0ms

Algorithm

intervals

Results

59.0ms	46×	body	2560	valid
43.0ms	94×	body	1280	valid
17.0ms	66×	body	640	valid
6.0ms	33×	body	320	valid
1.0ms	8×	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: 31.0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.8b	(- 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))
3.0ms	(- 1.0 (cos x))

series55.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify41.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (8.0ms)

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

prune184.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

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)))
1.2b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.8b	(- 1.0 (cos x))

rewrite42.0ms

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:

9.0ms	(/ (- 1.0 (cos x)) (sin x))
12.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
12.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

series144.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
49.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
36.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
24.0ms	(- 1.0 (cos x))

simplify42.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (32.0ms)

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

prune356.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sqrt (- 1.0 (cos x))) (sin x)) (sqrt (- 1.0 (cos x))))
0.2b	(/ (sqrt (- 1.0 (cos x))) (sin x))
1.8b	(- 1.0 (cos x))
1.8b	(- 1.0 (cos x))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
52×	`add-cube-cbrt` `times-frac`
45×	`sqrt-prod`
28×	`associate-l`
18×	`prod-diff`
11×	`add-exp-log` `add-cbrt-cube`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-r` `associate-/l*` `add-log-exp`
6×	`pow1` `fma-neg` `sqrt-div` `unswap-sqr`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r*`
2×	`cbrt-undiv` `frac-times` `sub-neg` `diff-log` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

4 → 169

Calls

4 calls:

30.0ms	(* (/ (sqrt (- 1.0 (cos x))) (sin x)) (sqrt (- 1.0 (cos x))))
8.0ms	(/ (sqrt (- 1.0 (cos x))) (sin x))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series179.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (/ (sqrt (- 1.0 (cos x))) (sin x)) (sqrt (- 1.0 (cos x))))
101.0ms	(/ (sqrt (- 1.0 (cos x))) (sin x))
19.0ms	(- 1.0 (cos x))
24.0ms	(- 1.0 (cos x))

simplify67.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	485	1718
1	1950	1400
2	5002	1383

prune413.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(cbrt (pow (/ (- 1.0 (cos x)) (sin x)) 3))
0.4b	(pow (/ (- 1.0 (cos x)) (sin x)) 3)
1.8b	(- 1.0 (cos x))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

93×	`add-sqr-sqrt` `*-un-lft-identity`
75×	`times-frac`
59×	`add-cube-cbrt`
44×	`cbrt-prod`
38×	`unpow-prod-down` `cube-prod`
17×	`distribute-lft-out--` `difference-of-squares`
9×	`add-exp-log` `prod-diff` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `div-inv` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `fma-neg` `associate-/r*`
2×	`cbrt-undiv` `cube-div` `cube-mult` `flip3--` `unpow3` `div-exp` `pow-exp` `flip--` `associate-/l/` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-sub` `clear-num` `rem-cbrt-cube`

Counts

4 → 184

Calls

4 calls:

9.0ms	(/ (- 1.0 (cos x)) (sin x))
13.0ms	(cbrt (pow (/ (- 1.0 (cos x)) (sin x)) 3))
8.0ms	(pow (/ (- 1.0 (cos x)) (sin x)) 3)
4.0ms	(- 1.0 (cos x))

series166.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (- 1.0 (cos x)) (sin x))
35.0ms	(cbrt (pow (/ (- 1.0 (cos x)) (sin x)) 3))
70.0ms	(pow (/ (- 1.0 (cos x)) (sin x)) 3)
19.0ms	(- 1.0 (cos x))

simplify75.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	596	1705
1	2601	1523
2	5002	1505

prune322.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes126.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.2b

bsearch91.0ms

Steps

Iters	Range		Point
9	2.0114125408603258e-10	0.4954286465087044	0.02145283746761365
10	-1.7081313977704333	-1.7977825652338532e-10	-0.019990581307716814

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	22
1	31	22

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.2s	1621×	body	2560	valid
1.6s	2805×	body	1280	valid
486.0ms	1822×	body	640	valid
161.0ms	909×	body	320	valid
61.0ms	469×	body	160	valid
35.0ms	370×	body	80	valid
14.0ms	4×	body	5120	valid