Details

sample147.0ms

Algorithm

intervals

Results

70.0ms	103×	body	1280	valid
27.0ms	16×	body	2560	valid
23.0ms	58×	body	640	valid
7.0ms	30×	body	320	valid
6.0ms	40×	body	80	valid
1.0ms	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

localize9.0ms

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

4×	`tan-quot` `add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `tan-sum` `frac-sub` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 25

Calls

2 calls:

17.0ms	(- (tan (+ x eps)) (tan x))
7.0ms	(tan (+ x eps))

series135.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(- (tan (+ x eps)) (tan x))
52.0ms	(tan (+ x eps))

simplify80.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (23.0ms)

Iter	Nodes	Cost
0	134	211
1	295	202
2	757	200
3	2482	199
4	5001	199

prune91.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.6b

localize16.0ms

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))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3--` `flip3-+` `frac-add` `associate-/r/` `flip--` `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` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

31.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
9.0ms	(+ (tan x) (tan eps))
16.0ms	(* (tan x) (tan eps))
81.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series684.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
83.0ms	(+ (tan x) (tan eps))
83.0ms	(* (tan x) (tan eps))
324.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify45.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	397	1050
1	1432	1005
2	5001	995

prune291.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.3b	(pow (* (tan x) (tan eps)) 3)
3.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
25.1b	(cbrt (pow (* (tan x) (tan eps)) 3))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`tan-quot`
10×	`*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt`
6×	`cube-div` `add-log-exp`
3×	`frac-times` `pow-unpow` `cbrt-div` `associate-r/` `associate-r` `associate-l` `associate-l/`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `difference-of-squares` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `times-frac` `pow1/3` `diff-log` `*-commutative` `frac-sub` `flip--` `rem-cbrt-cube` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

15.0ms	(* (tan x) (tan eps))
12.0ms	(pow (* (tan x) (tan eps)) 3)
163.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
8.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

series612.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (tan x) (tan eps))
115.0ms	(pow (* (tan x) (tan eps)) 3)
331.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (pow (* (tan x) (tan eps)) 3)))) (tan x))
80.0ms	(cbrt (pow (* (tan x) (tan eps)) 3))

simplify51.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	384	787
1	1733	744
2	5002	743

prune311.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(/ (* (sin x) (tan eps)) (cos x))
0.2b	(* (sin x) (tan eps))
3.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1`
5×	`tan-quot`
4×	`times-frac`
3×	`associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `difference-of-squares`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `frac-add` `clear-num` `sum-log` `-commutative` `frac-sub` `flip--` `flip-+` `div-inv` `associate-/l/` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 70

Calls

4 calls:

8.0ms	(+ (tan x) (tan eps))
15.0ms	(/ (* (sin x) (tan eps)) (cos x))
14.0ms	(* (sin x) (tan eps))
156.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

series599.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(+ (tan x) (tan eps))
97.0ms	(/ (* (sin x) (tan eps)) (cos x))
73.0ms	(* (sin x) (tan eps))
343.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

simplify42.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	389	785
1	1406	711
2	5001	699

prune246.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.4b

regimes169.0ms

Accuracy

82.7% (1.3b remaining)

Error of 15.4b against oracle of 14.1b and baseline of 21.6b

bsearch167.0ms

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	39	23
1	39	23

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.4s	3258×	body	1280	valid
1.1s	635×	body	2560	valid
745.0ms	1847×	body	640	valid
221.0ms	787×	body	320	valid
95.0ms	1115×	body	80	valid
67.0ms	358×	body	160	valid