Details

sample166.0ms

Algorithm

intervals

Results

84.0ms	105×	body	1280	valid
31.0ms	18×	body	2560	valid
28.0ms	62×	body	640	valid
6.0ms	17×	body	320	valid
5.0ms	40×	body	80	valid
3.0ms	14×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize8.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (tan (+ x eps)) (tan x))
4.4b	(tan (+ x eps))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `tan-sum` `frac-sub` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

8.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series152.0ms

Counts

2 → 6

Calls

2 calls:

95.0ms	(- (tan (+ x eps)) (tan x))
56.0ms	(tan (+ x eps))

simplify76.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	192	420
1	538	319
2	2593	310
3	5001	255

prune123.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 169

Calls

4 calls:

11.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
3.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
53.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series784.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
95.0ms	(+ (tan x) (tan eps))
95.0ms	(* (tan x) (tan eps))
368.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify77.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	559	2915
1	2054	2366
2	5001	2345

prune441.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(/ (* (sin x) (tan eps)) (cos x))
0.2b	(* (sin x) (tan eps))
3.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

183×	`*-un-lft-identity`
138×	`add-sqr-sqrt`
100×	`times-frac`
90×	`prod-diff`
83×	`add-cube-cbrt`
34×	`difference-of-squares`
30×	`fma-neg`
25×	`distribute-lft-out`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r/` `add-log-exp`
6×	`pow1`
5×	`tan-quot` `flip3--` `flip--` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `clear-num` `sum-log` `-commutative` `frac-sub` `flip-+` `associate-/l/` `associate-/l` `unswap-sqr`

Counts

4 → 201

Calls

4 calls:

3.0ms	(+ (tan x) (tan eps))
4.0ms	(/ (* (sin x) (tan eps)) (cos x))
5.0ms	(* (sin x) (tan eps))
103.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

series676.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(+ (tan x) (tan eps))
108.0ms	(/ (* (sin x) (tan eps)) (cos x))
82.0ms	(* (sin x) (tan eps))
391.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

simplify89.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	678	4171
1	2545	3274
2	5002	3234

prune536.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(/ (* (sin x) (tan eps)) (cos x))
0.2b	(* (sin x) (tan eps))
3.5b	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (sin x) (tan eps)) (cos x))))) (tan x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

16×	`tan-quot`
12×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt`
8×	`frac-sub` `add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`frac-times` `fma-def` `flip3-+` `times-frac` `associate-r/` `associate-r` `associate-l` `prod-diff` `associate-l/` `frac-add` `associate-/r*` `flip-+`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `fma-neg` `diff-log` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `flip--` `div-inv` `associate-/l/` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

3.0ms	(+ (tan x) (tan eps))
5.0ms	(/ (* (sin x) (tan eps)) (cos x))
4.0ms	(* (sin x) (tan eps))
17.0ms	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (sin x) (tan eps)) (cos x))))) (tan x))

series673.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(+ (tan x) (tan eps))
106.0ms	(/ (* (sin x) (tan eps)) (cos x))
81.0ms	(* (sin x) (tan eps))
390.0ms	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (sin x) (tan eps)) (cos x))))) (tan x))

simplify70.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	547	1092
1	2392	969
2	5002	963

prune393.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.4b

regimes175.0ms

Accuracy

85.7% (1.1b remaining)

Error of 15.6b against oracle of 14.5b and baseline of 22.1b

bsearch194.0ms

Steps

Iters	Range		Point
9	2.450734406407808e-49	1.8905107981278726e-44	1.8371289099221047e-44
8	-2.2913029590799255e-75	-9.949878853385243e-80	-1.9052490692525806e-75

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	63
1	67	63
2	73	63
3	73	63

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.9s	3341×	body	1280	valid
1.1s	636×	body	2560	valid
880.0ms	1845×	body	640	valid
234.0ms	729×	body	320	valid
136.0ms	1101×	body	80	valid
85.0ms	348×	body	160	valid