Details

sample183.0ms

Algorithm

intervals

Results

81.0ms	105×	body	1280	valid
55.0ms	30×	body	2560	valid
20.0ms	44×	body	640	valid
10.0ms	33×	body	320	valid
3.0ms	31×	body	80	valid
3.0ms	13×	body	160	valid

simplify5.0ms

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: 41.0b

localize9.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (tan (+ x eps)) (tan x))
4.4b	(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))

series143.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(- (tan (+ x eps)) (tan x))
57.0ms	(tan (+ x eps))

simplify78.0ms

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

prune83.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 15.8b

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

rewrite63.0ms

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:

3.0ms	(+ (tan x) (tan eps))
11.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
42.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series730.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(+ (tan x) (tan eps))
208.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
88.0ms	(* (tan x) (tan eps))
341.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (37.0ms)

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

prune298.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 15.7b

localize15.0ms

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

rewrite45.0ms

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))
21.0ms	(* (* (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:

92.0ms	(* (tan x) (tan eps))
91.0ms	(* (tan x) (tan eps))
113.0ms	(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
905.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify81.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	599	1352
1	3021	1220
2	5001	1220

prune361.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 15.7b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

25×	`tan-quot`
20×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt` `associate-*l/`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`frac-times`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r/` `associate-r` `associate-l*`
6×	`add-log-exp`
5×	`frac-sub`
3×	`*-commutative`
2×	`flip3-+` `associate--l+` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `flip--`

Counts

4 → 90

Calls

4 calls:

18.0ms	(* (* (tan x) (tan eps)) (* (tan x) (sin eps)))
5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
19.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (/ (* (* (tan x) (tan eps)) (* (tan x) (sin eps))) (cos eps)))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.4s

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (* (tan x) (tan eps)) (* (tan x) (sin eps)))
93.0ms	(* (tan x) (tan eps))
93.0ms	(* (tan x) (tan eps))
1.1s	(- (* (/ (+ (tan x) (tan eps)) (- 1 (/ (* (* (tan x) (tan eps)) (* (tan x) (sin eps))) (cos eps)))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify81.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	592	1377
1	2980	1234
2	5002	1234

prune327.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 15.7b

regimes162.0ms

Accuracy

84.7% (1.1b remaining)

Error of 15.3b against oracle of 14.2b and baseline of 21.7b

bsearch181.0ms

Steps

Iters	Range		Point
9	1.5258420908667198e-63	2.388651929375621e-54	1.5951375447724633e-59
6	-8.548233405337335e-107	-8.128622870315377e-108	-8.404515429597364e-107

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	39
1	50	39
2	50	39

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.7s	3337×	body	1280	valid
1.3s	627×	body	2560	valid
863.0ms	1814×	body	640	valid
244.0ms	769×	body	320	valid
123.0ms	1115×	body	80	valid
70.0ms	338×	body	160	valid