Details

sample147.0ms

Algorithm

intervals

Results

72.0ms	103×	body	1280	valid
27.0ms	16×	body	2560	valid
24.0ms	58×	body	640	valid
8.0ms	30×	body	320	valid
3.0ms	40×	body	80	valid
2.0ms	9×	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: 36.1b

localize14.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (tan (+ x eps)) (tan x))
4.7b	(tan (+ x eps))

rewrite24.0ms

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:

17.0ms	(- (tan (+ x eps)) (tan x))
6.0ms	(tan (+ x eps))

series125.0ms

Counts

2 → 6

Calls

2 calls:

77.0ms	(- (tan (+ x eps)) (tan x))
48.0ms	(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

prune110.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.6b

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))
3.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite149.0ms

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:

28.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
8.0ms	(+ (tan x) (tan eps))
14.0ms	(* (tan x) (tan eps))
92.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series689.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
79.0ms	(+ (tan x) (tan eps))
84.0ms	(* (tan x) (tan eps))
327.0ms	(- (/ (+ (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	2915
1	2054	2366
2	5001	2345

prune395.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.4b

localize16.0ms

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)))
3.0b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite99.0ms

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:

16.0ms	(* (tan x) (tan eps))
14.0ms	(* (tan x) (tan eps))
66.0ms	(* (* (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)))

series803.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (tan x) (tan eps))
78.0ms	(* (tan x) (tan eps))
106.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
535.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify53.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	432	1111
1	1952	927
2	5001	872

prune343.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.4b

localize21.0ms

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))
3.0b	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (* (tan x) (tan eps)) (tan x)) (tan eps)))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

14.0ms	(* (tan x) (tan eps))
17.0ms	(* (tan x) (tan eps))
37.0ms	(* (* (tan x) (tan eps)) (tan x))
0.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (* (tan x) (tan eps)) (tan x)) (tan eps)))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

series780.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (tan x) (tan eps))
77.0ms	(* (tan x) (tan eps))
91.0ms	(* (* (tan x) (tan eps)) (tan x))
525.0ms	(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (* (tan x) (tan eps)) (tan x)) (tan eps)))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	369	913
1	1634	775
2	5001	743

prune284.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 13.4b

regimes168.0ms

Accuracy

81.1% (1.4b remaining)

Error of 15.4b against oracle of 14.0b and baseline of 21.5b

bsearch169.0ms

Steps

Iters	Range		Point
7	1.0926285726175518e-119	1.4988070402197298e-117	1.4767289533588029e-117
8	-1.868688662916188e-68	-1.4402068522716586e-72	-1.8367694074004902e-68

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	42
1	44	42

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.4s	3258×	body	1280	valid
1.1s	635×	body	2560	valid
755.0ms	1847×	body	640	valid
234.0ms	787×	body	320	valid
104.0ms	1115×	body	80	valid
71.0ms	358×	body	160	valid