Details

sample150.0ms

Algorithm

intervals

Results

78.0ms	113×	body	1280	valid
23.0ms	59×	body	640	valid
21.0ms	13×	body	2560	valid
7.0ms	35×	body	80	valid
6.0ms	23×	body	320	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.4b

localize8.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (tan (+ x eps)) (tan x))
3.5b	(tan (+ x eps))

rewrite23.0ms

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:

16.0ms	(- (tan (+ x eps)) (tan x))
6.0ms	(tan (+ x eps))

series129.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(- (tan (+ x eps)) (tan x))
50.0ms	(tan (+ x eps))

simplify74.0ms

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

prune82.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.3b	(* (tan x) (tan eps))
2.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite131.0ms

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))
28.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
15.0ms	(* (tan x) (tan eps))
78.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series683.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(+ (tan x) (tan eps))
195.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
85.0ms	(* (tan x) (tan eps))
318.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify45.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (36.0ms)

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

prune288.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
0.2b	(/ (* (tan x) (sin eps)) (cos eps))
0.2b	(* (tan x) (sin eps))
2.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

41.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
16.0ms	(/ (* (tan x) (sin eps)) (cos eps))
14.0ms	(* (tan x) (sin eps))
149.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series668.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
86.0ms	(/ (* (tan x) (sin eps)) (cos eps))
56.0ms	(* (tan x) (sin eps))
329.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify64.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	494	1549
1	1980	1464
2	5002	1464

prune371.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
0.3b	(* (tan x) (tan eps))
0.3b	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
4.9b	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 178

Calls

4 calls:

22.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
16.0ms	(* (tan x) (tan eps))
26.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
133.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

series873.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
85.0ms	(* (tan x) (tan eps))
203.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
338.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

simplify88.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	703	2793
1	3290	2509
2	5001	2506

prune351.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.3b

regimes191.0ms

Accuracy

86.3% (1.0b remaining)

Error of 15.6b against oracle of 14.7b and baseline of 21.7b

bsearch154.0ms

Steps

Iters	Range		Point
8	2.9004987402572773e-24	2.15302222000921e-20	2.0327729790594208e-23
8	-8.778595808142904e-29	-1.627781759631071e-31	-3.2842562690359854e-29

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	24
1	42	24

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.6s	3442×	body	1280	valid
1.1s	648×	body	2560	valid
731.0ms	1742×	body	640	valid
207.0ms	755×	body	320	valid
88.0ms	1081×	body	80	valid
60.0ms	332×	body	160	valid