Details

sample86.0ms

Algorithm

intervals

Results

39.0ms	100×	body	1280	valid
21.0ms	22×	body	2560	valid
12.0ms	57×	body	640	valid
2.0ms	17×	body	320	valid
2.0ms	45×	body	80	valid
1.0ms	15×	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: 34.0b

localize8.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (tan (+ x eps)) (tan x))
3.5b	(tan (+ x eps))

rewrite12.0ms

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:

7.0ms	(- (tan (+ x eps)) (tan x))
4.0ms	(tan (+ x eps))

series133.0ms

Counts

2 → 6

Calls

2 calls:

85.0ms	(- (tan (+ x eps)) (tan x))
47.0ms	(tan (+ x eps))

simplify74.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (67.0ms)

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

prune103.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.0b

localize13.0ms

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))
2.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite38.0ms

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:

8.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
4.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
14.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series727.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
86.0ms	(+ (tan x) (tan eps))
86.0ms	(* (tan x) (tan eps))
337.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify70.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (48.0ms)

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

prune367.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.2b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.4b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
40×	`tan-quot`
20×	`add-exp-log` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
13×	`associate-r/` `associate-l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-plus` `unswap-sqr`
1×	`pow2` `swap-sqr` `fma-udef`

Counts

4 → 107

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
11.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

series835.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (tan x) (tan eps))
89.0ms	(* (tan x) (tan eps))
110.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
546.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify58.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	432	1098
1	1952	917
2	5001	864

prune336.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.2b	(* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps)))
2.4b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log` `add-cbrt-cube`
16×	`tan-quot`
14×	`add-sqr-sqrt`
13×	`pow1` `associate-r` `prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `*-un-lft-identity`
7×	`frac-times` `associate-l` `associate-*l/`
5×	`associate-*r/` `pow-prod-down`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `*-commutative`
2×	`unswap-sqr`
1×	`fma-udef` `div-inv`

Counts

4 → 95

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
10.0ms	(* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps)))
1.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

series970.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (tan x) (tan eps))
92.0ms	(* (tan x) (tan eps))
165.0ms	(* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps)))
621.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify70.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	516	1245
1	2744	1012
2	5001	1011

prune384.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.9b

regimes113.0ms

Accuracy

87.6% (0.9b remaining)

Error of 15.4b against oracle of 14.5b and baseline of 22.0b

bsearch130.0ms

Steps

Iters	Range		Point
8	2.7379472383092327e-72	1.7149841608833565e-68	7.60268013552436e-69
11	-1.5073415317839904e-10	-5.397704668065765e-30	-6.425365041334478e-20

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	53
1	58	53
2	58	53

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.2s	3283×	body	1280	valid
563.0ms	663×	body	2560	valid
372.0ms	1812×	body	640	valid
100.0ms	755×	body	320	valid
44.0ms	1105×	body	80	valid
34.0ms	382×	body	160	valid