Details

sample172.0ms

Algorithm

intervals

Results

73.0ms	96×	body	1280	valid
52.0ms	31×	body	2560	valid
26.0ms	64×	body	640	valid
5.0ms	21×	body	320	valid
2.0ms	31×	body	80	valid
2.0ms	13×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (tan (+ x eps)) (tan x))
4.7b	(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:

7.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series142.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(- (tan (+ x eps)) (tan x))
56.0ms	(tan (+ x eps))

simplify79.0ms

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

prune80.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.4b

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))
0.3b	(* (tan x) (tan eps))
2.2b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite62.0ms

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:

11.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
3.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
41.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series731.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
90.0ms	(+ (tan x) (tan eps))
91.0ms	(* (tan x) (tan eps))
346.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify52.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (39.0ms)

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

prune291.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 15.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
0.3b	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.2b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
45×	`tan-quot`
21×	`frac-times`
20×	`add-exp-log` `add-cbrt-cube`
19×	`pow-prod-down`
15×	`associate-*r/`
14×	`associate-*l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`frac-sub`
4×	`pow-sqr` `pow-prod-up`
3×	`*-commutative`
2×	`flip3-+` `pow-plus` `associate--l+` `flip-+` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `swap-sqr` `flip--`

Counts

4 → 110

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
20.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
10.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (tan x) (tan eps))
90.0ms	(* (tan x) (tan eps))
110.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
893.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify83.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	599	1358
1	3021	1222
2	5001	1222

prune352.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin x) 2)
0.3b	(pow (cos eps) 2)
0.3b	(pow (sin eps) 2)
2.2b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down` `pow-unpow`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
5×	`tan-quot` `frac-sub`
4×	`add-cbrt-cube`
3×	`pow-to-exp` `pow-pow` `pow-exp` `unpow2` `sqr-pow`
2×	`frac-times` `flip3-+` `associate-*r/` `associate--l+` `flip-+`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `associate-*l/` `flip--`

Counts

4 → 73

Calls

4 calls:

1.0ms	(pow (sin x) 2)
1.0ms	(pow (cos eps) 2)
1.0ms	(pow (sin eps) 2)
20.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series983.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin x) 2)
16.0ms	(pow (cos eps) 2)
19.0ms	(pow (sin eps) 2)
930.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos eps) 2) (pow (cos x) 2))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify65.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	527	1109
1	2291	991
2	5001	991

prune368.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 15.3b

regimes174.0ms

Accuracy

88.5% (0.8b remaining)

Error of 15.7b against oracle of 14.9b and baseline of 22.1b

bsearch167.0ms

Steps

Iters	Range		Point
9	1.9540685346212126e-24	9.316647860064626e-18	1.047829285418837e-23
8	-5.529960614046254e-31	-1.2848272222116945e-35	-4.67846670432253e-32

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	59
1	58	59

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.5s	3364×	body	1280	valid
1.1s	667×	body	2560	valid
742.0ms	1800×	body	640	valid
206.0ms	787×	body	320	valid
83.0ms	1032×	body	80	valid
62.0ms	350×	body	160	valid