Details

sample190.0ms

Algorithm

intervals

Results

88.0ms	108×	body	1280	valid
48.0ms	25×	body	2560	valid
31.0ms	54×	body	640	valid
7.0ms	21×	body	320	valid
3.0ms	36×	body	80	valid
2.0ms	12×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

localize9.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (tan (+ x eps)) (tan x))
2.2b	(tan (+ x eps))

rewrite14.0ms

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:

9.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series143.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(- (tan (+ x eps)) (tan x))
50.0ms	(tan (+ x eps))

simplify82.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (72.0ms)

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

prune111.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(- 1 (* (tan x) (tan eps)))
0.2b	(* (tan x) (tan eps))
3.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
74×	`add-sqr-sqrt`
67×	`add-cube-cbrt`
61×	`times-frac`
57×	`prod-diff`
21×	`fma-neg`
16×	`distribute-lft-out`
10×	`associate-/r/`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`tan-quot` `flip3--` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`sub-neg` `diff-log` `difference-of-squares`
1×	`cbrt-undiv` `frac-times` `frac-2neg` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 171

Calls

4 calls:

11.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
2.0ms	(- 1 (* (tan x) (tan eps)))
5.0ms	(* (tan x) (tan eps))
48.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series795.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
116.0ms	(- 1 (* (tan x) (tan eps)))
93.0ms	(* (tan x) (tan eps))
366.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify76.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	566	2988
1	2124	2419
2	5002	2397

prune423.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))
0.2b	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
0.2b	(* (sin x) (sin eps))
3.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (tan x))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

191×	`*-un-lft-identity`
148×	`add-sqr-sqrt`
108×	`prod-diff`
101×	`times-frac`
90×	`add-cube-cbrt`
36×	`difference-of-squares`
33×	`fma-neg`
24×	`distribute-lft-out`
18×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
12×	`associate-/r/`
8×	`div-inv` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `cos-mult` `log1p-expm1-u`
3×	`associate-r` `associate-l`
2×	`sub-neg` `diff-log` `sin-mult`
1×	`tan-quot` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `frac-sub` `associate-/l/` `associate-/l*` `unswap-sqr`

Counts

4 → 222

Calls

4 calls:

9.0ms	(- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))
6.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
4.0ms	(* (sin x) (sin eps))
123.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (tan x))

series853.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))
303.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
47.0ms	(* (sin x) (sin eps))
389.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (tan x))

simplify124.0ms

Algorithm

egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	774	5495
1	3323	4198
2	5002	4155

prune556.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))
0.2b	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
0.2b	(* (sin x) (sin eps))
3.4b	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (- (tan x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
18×	`add-exp-log` `prod-diff` `add-cbrt-cube`
16×	`add-cube-cbrt`
6×	`pow1` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `times-frac` `div-exp` `associate-/r/` `cos-mult` `log1p-expm1-u` `div-inv`
3×	`fma-neg` `associate-r` `associate-l`
2×	`sin-mult` `difference-of-squares`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `flip--` `fma-udef` `associate-/l/` `associate-/l*` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 94

Calls

4 calls:

8.0ms	(- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))
6.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
4.0ms	(* (sin x) (sin eps))
0.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (- (tan x)))

series564.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))
98.0ms	(/ (* (sin x) (sin eps)) (* (cos eps) (cos x)))
46.0ms	(* (sin x) (sin eps))
302.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))))) (- (tan x)))

simplify80.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	488	1592
1	2453	1140
2	5001	1138

prune319.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.3b

regimes153.0ms

Accuracy

87.8% (0.9b remaining)

Error of 15.1b against oracle of 14.2b and baseline of 21.6b

bsearch150.0ms

Steps

Iters	Range		Point
8	1.412343169719264e-20	6.157903029658734e-17	5.66748466896462e-20
7	-5.424898332662606e-53	-2.572039402824119e-55	-1.803646814354997e-54

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	35
1	40	35

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.5s	3321×	body	1280	valid
1.1s	618×	body	2560	valid
792.0ms	1844×	body	640	valid
209.0ms	707×	body	320	valid
92.0ms	1109×	body	80	valid
73.0ms	401×	body	160	valid