Details

sample560.0ms

Algorithm

intervals

Results

126.0ms	52×	body	2560	valid
55.0ms	85×	body	1280	valid
45.0ms	63×	body	640	valid
6.0ms	25×	body	320	valid
5.0ms	17×	body	160	valid
1.0ms	14×	body	80	valid

simplify11.0ms

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: 29.8b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.7b	(- x (tan x))
1.7b	(- x (sin x))

rewrite57.0ms

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:

34.0ms	(/ (- x (sin x)) (- x (tan x)))
7.0ms	(- x (tan x))
10.0ms	(- x (sin x))

series171.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(/ (- x (sin x)) (- x (tan x)))
57.0ms	(- x (tan x))
41.0ms	(- x (sin x))

simplify58.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (11.0ms)

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

prune253.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 27/2800 (pow x 4) 1/2)
16.3b	(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)))

series127.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(fma 27/2800 (pow x 4) 1/2)
44.0ms	(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

prune75.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin x) (sin x))
1.7b	(- x (tan x))
1.7b	(- (* x x) (* (sin x) (sin x)))
15.8b	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`prod-diff`
8×	`associate-/r/` `add-log-exp`
6×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-times` `times-frac` `fma-neg` `log1p-expm1-u` `associate-/l*` `difference-of-squares`
3×	`flip3-+` `swap-sqr` `associate-r` `associate-l` `flip-+`
2×	`cbrt-undiv` `sub-neg` `diff-log` `associate-r/` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod` `sqr-sin` `associate-/l/`
1×	`pow2` `frac-2neg` `pow-plus` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `pow-sqr` `-commutative` `pow-prod-up` `div-inv` `sin-mult` `distribute-lft-out--` `associate--r-` `unswap-sqr`

Counts

4 → 111

Calls

4 calls:

14.0ms	(* (sin x) (sin x))
7.0ms	(- x (tan x))
9.0ms	(- (* x x) (* (sin x) (sin x)))
32.0ms	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

series280.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (sin x) (sin x))
54.0ms	(- x (tan x))
65.0ms	(- (* x x) (* (sin x) (sin x)))
142.0ms	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

simplify84.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	638	1099
1	3208	889
2	5001	883

prune312.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (* x x) (* (sin x) (sin x)))
15.2b	(sqrt (- (* x x) (* (sin x) (sin x))))
15.2b	(sqrt (- (* x x) (* (sin x) (sin x))))
15.8b	(/ (* (sqrt (- (* x x) (* (sin x) (sin x)))) (sqrt (- (* x x) (* (sin x) (sin x))))) (* (- x (tan x)) (+ x (sin x))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
12×	`flip3--` `flip--`
8×	`add-sqr-sqrt` `frac-times` `sqrt-prod` `associate-/r/` `associate-/l/`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-r/` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`flip3-+` `flip-+` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `frac-2neg` `times-frac` `fma-neg` `diff-log` `prod-diff` `clear-num` `associate-/r` `sqr-sin` `div-inv` `associate-/l` `associate--r-`

Counts

4 → 93

Calls

4 calls:

9.0ms	(- (* x x) (* (sin x) (sin x)))
12.0ms	(sqrt (- (* x x) (* (sin x) (sin x))))
14.0ms	(sqrt (- (* x x) (* (sin x) (sin x))))
46.0ms	(/ (* (sqrt (- (* x x) (* (sin x) (sin x)))) (sqrt (- (* x x) (* (sin x) (sin x))))) (* (- x (tan x)) (+ x (sin x))))

series368.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (* x x) (* (sin x) (sin x)))
73.0ms	(sqrt (- (* x x) (* (sin x) (sin x))))
79.0ms	(sqrt (- (* x x) (* (sin x) (sin x))))
151.0ms	(/ (* (sqrt (- (* x x) (* (sin x) (sin x)))) (sqrt (- (* x x) (* (sin x) (sin x))))) (* (- x (tan x)) (+ x (sin x))))

simplify71.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	592	1383
1	2949	1170
2	5001	1117

prune376.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes59.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.7b

bsearch78.0ms

Steps

Iters	Range		Point
8	0.00015704816827310668	9.114942375872904	0.01861232521167047
9	-0.2945747773639613	-3.489101517161873e-08	-0.024389077621678308

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	10
1	25	10

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.5s	1584×	body	2560	valid
2.0s	2847×	body	1280	valid
678.0ms	1840×	body	640	valid
214.0ms	907×	body	320	valid
74.0ms	445×	body	160	valid
37.0ms	377×	body	80	valid