Details

sample463.0ms

Algorithm

intervals

Results

101.0ms	46×	body	2560	valid
70.0ms	95×	body	1280	valid
26.0ms	65×	body	640	valid
9.0ms	33×	body	320	valid
2.0ms	8×	body	160	valid
1.0ms	9×	body	80	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.5b	(- x (sin x))
1.5b	(- x (tan x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 110

Calls

3 calls:

13.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (sin x))
7.0ms	(- x (tan x))

series174.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ (- x (sin x)) (- x (tan x)))
30.0ms	(- x (sin x))
68.0ms	(- x (tan x))

simplify55.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	472	1059
1	1737	854
2	5001	854

prune236.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 27/2800 (pow x 4) 1/2)
16.6b	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma 27/2800 (pow x 4) 1/2)
0.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

series134.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(fma 27/2800 (pow x 4) 1/2)
50.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify146.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	51	133
1	162	117
2	626	117
3	3552	117
4	5001	117

prune69.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ (- x (sin x)) (- x (tan x))) 3)
0.0b	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
1.5b	(- x (sin x))
1.5b	(- x (tan x))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

148×	`add-sqr-sqrt` `*-un-lft-identity`
100×	`times-frac`
68×	`cbrt-prod`
64×	`add-cube-cbrt`
62×	`unpow-prod-down` `cube-prod`
42×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`associate-/r/` `add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
6×	`flip3--` `fma-neg` `flip--`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `sub-neg` `diff-log` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `div-exp` `rem-cbrt-cube`

Counts

4 → 220

Calls

4 calls:

14.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
15.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
4.0ms	(- x (sin x))
3.0ms	(- x (tan x))

series255.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
78.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
36.0ms	(- x (sin x))
49.0ms	(- x (tan x))

simplify98.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	853	2547
1	3624	2257
2	5001	2239

prune354.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (pow (/ (- x (sin x)) (- x (tan x))) (* (cbrt 3) (cbrt 3))) (cbrt 3))
0.0b	(cbrt (pow (pow (/ (- x (sin x)) (- x (tan x))) (* (cbrt 3) (cbrt 3))) (cbrt 3)))
1.5b	(- x (sin x))
1.5b	(- x (tan x))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

132×	`unpow-prod-down`
89×	`add-sqr-sqrt` `*-un-lft-identity`
50×	`times-frac`
45×	`add-cube-cbrt`
42×	`cbrt-prod`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`add-exp-log` `add-log-exp`
6×	`pow-unpow` `fma-neg` `pow-exp`
4×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--` `log1p-expm1-u` `sqr-pow`
2×	`pow-to-exp` `sub-neg` `diff-log` `div-inv`
1×	`pow-pow` `pow1/3` `div-exp`

Counts

4 → 162

Calls

4 calls:

29.0ms	(pow (pow (/ (- x (sin x)) (- x (tan x))) (* (cbrt 3) (cbrt 3))) (cbrt 3))
33.0ms	(cbrt (pow (pow (/ (- x (sin x)) (- x (tan x))) (* (cbrt 3) (cbrt 3))) (cbrt 3)))
4.0ms	(- x (sin x))
3.0ms	(- x (tan x))

series1.0s

Counts

4 → 12

Calls

4 calls:

395.0ms	(pow (pow (/ (- x (sin x)) (- x (tan x))) (* (cbrt 3) (cbrt 3))) (cbrt 3))
531.0ms	(cbrt (pow (pow (/ (- x (sin x)) (- x (tan x))) (* (cbrt 3) (cbrt 3))) (cbrt 3)))
30.0ms	(- x (sin x))
54.0ms	(- x (tan x))

simplify85.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	888	2916
1	2883	2680
2	5001	2665

prune515.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes68.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.0b

bsearch107.0ms

Steps

Iters	Range		Point
9	2.0114125408603258e-10	0.4954286465087044	0.024314219703607573
10	-1.7081313977704333	-1.7977825652338532e-10	-1.5623918316578669

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	24

end0.0ms

sample7.2s

Algorithm

intervals

Results

3.7s	1630×	body	2560	valid
2.1s	2795×	body	1280	valid
745.0ms	1823×	body	640	valid
248.0ms	905×	body	320	valid
99.0ms	474×	body	160	valid
68.0ms	373×	body	80	valid