Details

Time bar (total: 11.4s)

sample169.0ms

Algorithm
intervals
Results
91.0ms103×body1280valid
30.0ms66×body640valid
24.0ms13×body2560valid
7.0ms22×body320valid
5.0ms44×body80valid
2.0ms8×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize8.0ms

Local error

Found 2 expressions with local error:

1.1b
(- (tan (+ x eps)) (tan x))
3.0b
(tan (+ x eps))

rewrite12.0ms

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:
8.0ms
(- (tan (+ x eps)) (tan x))
4.0ms
(tan (+ x eps))

series144.0ms

Counts
2 → 6
Calls
2 calls:
90.0ms
(- (tan (+ x eps)) (tan x))
54.0ms
(tan (+ x eps))

simplify77.0ms

Algorithm
egg-herbie
Counts
31 → 31
Iterations

Useful iterations: 3 (22.0ms)

IterNodesCost
0134211
1295202
2757200
32482199
45001199

prune81.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 12.2b

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))
2.4b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite64.0ms

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))
12.0ms
(/ (+ (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))

series754.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(+ (tan x) (tan eps))
212.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
93.0ms
(* (tan x) (tan eps))
358.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify44.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03971050
114321005
25001995

prune267.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.0b

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)))
2.4b
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite49.0ms

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)))
14.0ms
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.4s

Counts
4 → 12
Calls
4 calls:
91.0ms
(* (tan x) (tan eps))
93.0ms
(* (tan x) (tan eps))
113.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.1s
(- (* (/ (+ (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)

IterNodesCost
05991352
130211220
250011220

prune333.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b
(* (tan eps) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))))
2.4b
(+ (* 1 (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (* (tan x) (- (* (tan eps) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) 1)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
84×pow1
69×tan-quot
37×frac-times
35×pow-prod-down
33×add-exp-log add-cbrt-cube
30×associate-*r/
29×*-un-lft-identity
28×associate-*r*
24×add-sqr-sqrt associate-*l/
21×times-frac
18×prod-exp cbrt-unprod
15×add-cube-cbrt
8×pow-sqr pow-prod-up difference-of-squares
6×add-log-exp
5×associate-*l* frac-add distribute-lft-out
4×associate-+r+ pow-plus
3×flip3-- *-commutative flip--
2×pow2 distribute-rgt-in sub-neg distribute-lft-in swap-sqr associate-/r/ unswap-sqr
1×cbrt-undiv +-commutative flip3-+ div-exp sum-log flip-+ div-inv
Counts
4 → 165
Calls
4 calls:
21.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
23.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
22.0ms
(* (tan eps) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))))
15.0ms
(+ (* 1 (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (* (tan x) (- (* (tan eps) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) 1)))

series1.4s

Counts
4 → 12
Calls
4 calls:
111.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
117.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
279.0ms
(* (tan eps) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))))
891.0ms
(+ (* 1 (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (* (tan x) (- (* (tan eps) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) 1)))

simplify117.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08302854
144452509
250012509

prune414.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.0b

regimes192.0ms

Accuracy

87.4% (0.9b remaining)

Error of 15.7b against oracle of 14.8b and baseline of 22.0b

bsearch166.0ms

Steps
ItersRangePoint
6
4.762716230442895e-61
3.0568216683503453e-60
2.3271445956212298e-60
9
-8.523099056980236e-58
-9.844649097147547e-64
-5.913949303197823e-58

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05482
15482

end0.0ms

sample5.5s

Algorithm
intervals
Results
2.8s3310×body1280valid
1.2s663×body2560valid
905.0ms1817×body640valid
256.0ms748×body320valid
125.0ms1133×body80valid
73.0ms329×body160valid