Details

sample178.0ms

Algorithm

intervals

Results

73.0ms	92×	body	1280	valid
41.0ms	23×	body	2560	valid
40.0ms	73×	body	640	valid
7.0ms	21×	body	320	valid
4.0ms	36×	body	80	valid
3.0ms	11×	body	160	valid

simplify6.0ms

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: 38.7b

localize9.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (tan (+ x eps)) (tan x))
3.4b	(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))

series144.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(- (tan (+ x eps)) (tan x))
55.0ms	(tan (+ x eps))

simplify88.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (83.0ms)

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

prune131.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.9b	(- (/ (+ (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))
52.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series779.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
95.0ms	(+ (tan x) (tan eps))
94.0ms	(* (tan x) (tan eps))
369.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify74.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (53.0ms)

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

prune471.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 16.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
4.0b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite36.0ms

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))
21.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

series906.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (tan x) (tan eps))
96.0ms	(* (tan x) (tan eps))
119.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
597.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify62.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (46.0ms)

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

prune407.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 16.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(/ (* (sin x) (tan eps)) (cos x))
0.3b	(* (* (tan x) (tan eps)) (/ (* (sin x) (tan eps)) (cos x)))
4.0b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (/ (* (sin x) (tan eps)) (cos x))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(/ (* (sin x) (tan eps)) (cos x))
17.0ms	(* (* (tan x) (tan eps)) (/ (* (sin x) (tan eps)) (cos x)))
0.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (/ (* (sin x) (tan eps)) (cos x))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

series965.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (tan x) (tan eps))
104.0ms	(/ (* (sin x) (tan eps)) (cos x))
149.0ms	(* (* (tan x) (tan eps)) (/ (* (sin x) (tan eps)) (cos x)))
617.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (/ (* (sin x) (tan eps)) (cos x))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify75.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	545	1309
1	2925	1060
2	5002	1059

prune407.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 16.1b

regimes187.0ms

Accuracy

87.8% (0.9b remaining)

Error of 15.9b against oracle of 15.0b and baseline of 22.5b

bsearch168.0ms

Steps

Iters	Range		Point
8	1.4969758855213984e-44	4.87546518652314e-42	2.69186416397234e-43
7	-3.9570119562060503e-20	-1.6549662793807668e-21	-2.859692106909577e-20

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	49
1	46	49

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.6s	3275×	body	1280	valid
1.2s	660×	body	2560	valid
861.0ms	1796×	body	640	valid
254.0ms	795×	body	320	valid
146.0ms	1120×	body	80	valid
82.0ms	354×	body	160	valid