Details

sample81.0ms

Algorithm

intervals

Results

41.0ms	113×	body	1280	valid
16.0ms	19×	body	2560	valid
11.0ms	55×	body	640	valid
3.0ms	23×	body	320	valid
2.0ms	42×	body	80	valid
0.0ms	4×	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: 36.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (tan (+ x eps)) (tan x))
2.6b	(tan (+ x eps))

rewrite11.0ms

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:

6.0ms	(- (tan (+ x eps)) (tan x))
4.0ms	(tan (+ x eps))

series143.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(- (tan (+ x eps)) (tan x))
54.0ms	(tan (+ x eps))

simplify79.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (22.0ms)

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

prune90.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.8b

localize15.0ms

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))

rewrite31.0ms

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:

8.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
4.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
12.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series757.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
91.0ms	(+ (tan x) (tan eps))
91.0ms	(* (tan x) (tan eps))
362.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify48.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (38.0ms)

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

prune463.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.6b

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))

rewrite37.0ms

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:

4.0ms	(+ (tan x) (tan eps))
6.0ms	(/ (* (sin x) (tan eps)) (cos x))
5.0ms	(* (sin x) (tan eps))
20.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

series614.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(+ (tan x) (tan eps))
96.0ms	(/ (* (sin x) (tan eps)) (cos x))
73.0ms	(* (sin x) (tan eps))
358.0ms	(- (/ (+ (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

prune272.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.3b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
3.0b	(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

5.0ms	(* (sin x) (sin eps))
8.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
8.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
25.0ms	(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

series591.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin x) (sin eps))
92.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
92.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
363.0ms	(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

simplify63.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	464	1846
1	2215	1611
2	5001	1611

prune288.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 14.6b

regimes174.0ms

Accuracy

83.9% (1.2b remaining)

Error of 15.6b against oracle of 14.4b and baseline of 21.7b

bsearch103.0ms

Steps

Iters	Range		Point
9	2.0162479452441862e-35	1.518081967238706e-29	3.0489110693032172e-33
6	-1.3342658890345104e-121	-1.7316235517029212e-122	-1.2673890691014833e-121

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	37
1	43	37

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.2s	3279×	body	1280	valid
546.0ms	634×	body	2560	valid
368.0ms	1821×	body	640	valid
100.0ms	754×	body	320	valid
49.0ms	1151×	body	80	valid
32.0ms	361×	body	160	valid