Details

sample179.0ms

Algorithm

intervals

Results

90.0ms	119×	body	1280	valid
49.0ms	29×	body	2560	valid
21.0ms	55×	body	640	valid
5.0ms	18×	body	320	valid
3.0ms	30×	body	80	valid
1.0ms	5×	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: 40.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.6b	(- (tan (+ x eps)) (tan x))
2.9b	(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:

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

series140.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(- (tan (+ x eps)) (tan x))
54.0ms	(tan (+ x eps))

simplify73.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (69.0ms)

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: 19.0b

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))
2.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite77.0ms

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))
7.0ms	(* (tan x) (tan eps))
48.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series732.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
89.0ms	(+ (tan x) (tan eps))
89.0ms	(* (tan x) (tan eps))
347.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify73.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	559	2923
1	2054	2373
2	5001	2349

prune442.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 18.8b

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)))
2.1b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite35.0ms

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))
22.0ms	(* (* (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)))

series852.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (tan x) (tan eps))
90.0ms	(* (tan x) (tan eps))
109.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
560.0ms	(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 (47.0ms)

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

prune381.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 18.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (sin eps))
0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
2.1b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (tan x) (tan eps)) (* (tan x) (sin eps))) (cos eps)))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

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

series888.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (tan x) (sin eps))
103.0ms	(* (tan x) (tan eps))
88.0ms	(* (tan x) (tan eps))
609.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (tan x) (tan eps)) (* (tan x) (sin eps))) (cos eps)))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify40.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	323	837
1	1306	718
2	5001	686

prune351.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 18.8b

regimes232.0ms

Accuracy

83.8% (1.2b remaining)

Error of 15.9b against oracle of 14.7b and baseline of 22.0b

bsearch158.0ms

Steps

Iters	Range		Point
7	2.723980583389076e-66	6.7695755698382385e-65	5.600552306151778e-65
8	-5.3548116028992445e-65	-1.1477498591415104e-67	-5.289064774366373e-65

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	32
1	45	32

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.5s	3323×	body	1280	valid
1.1s	663×	body	2560	valid
787.0ms	1849×	body	640	valid
213.0ms	749×	body	320	valid
88.0ms	1069×	body	80	valid
61.0ms	347×	body	160	valid