Details

Time bar (total: 4.1s)

sample299.0ms

Algorithm
intervals
Results
26.0ms57×body1280valid
10.0ms36×body640valid
8.0ms137×body80valid
3.0ms13×body160valid
3.0ms13×body320valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0139
1219
2269
3349
4379
5379

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(- 1.0 (* (tan x) (tan x)))
0.2b
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×pow1
12×times-frac
10×add-exp-log add-cbrt-cube
8×tan-quot
6×swap-sqr associate-*r* associate-*l* add-log-exp
5×difference-of-squares
4×associate-/l*
3×associate-/r*
2×pow2 frac-times flip3-- pow-plus associate-*r/ pow-prod-down associate-*l/ prod-exp associate-/r/ pow-sqr *-commutative pow-prod-up flip-- cbrt-unprod associate-/l/ unswap-sqr
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-sub div-exp clear-num flip-+ div-inv
Counts
4 → 105
Calls
4 calls:
2.0ms
(- 1.0 (* (tan x) (tan x)))
8.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms
(* (tan x) (tan x))
7.0ms
(* (tan x) (tan x))

series214.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- 1.0 (* (tan x) (tan x)))
95.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
33.0ms
(* (tan x) (tan x))
54.0ms
(* (tan x) (tan x))

simplify45.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0314909
11157838
25001824

prune246.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (+ 1.0 (* (tan x) (tan x))))
0.2b
(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
29×*-un-lft-identity
28×add-cube-cbrt
21×pow1 add-exp-log associate-*r*
20×times-frac
15×add-cbrt-cube
10×associate-*l*
8×tan-quot
6×swap-sqr prod-exp
5×unswap-sqr
4×frac-times div-exp associate-*l/ associate-/r/ cbrt-unprod add-log-exp
3×associate-*r/ pow-prod-down associate-/r* *-commutative associate-/l*
2×cbrt-undiv pow2 rec-exp flip3-- flip3-+ pow-plus 1-exp pow-sqr pow-prod-up flip-- flip-+ div-inv
1×pow-flip frac-2neg clear-num un-div-inv inv-pow difference-of-squares
Counts
4 → 132
Calls
4 calls:
4.0ms
(/ 1 (+ 1.0 (* (tan x) (tan x))))
19.0ms
(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
5.0ms
(* (tan x) (tan x))
5.0ms
(* (tan x) (tan x))

series211.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ 1 (+ 1.0 (* (tan x) (tan x))))
93.0ms
(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
32.0ms
(* (tan x) (tan x))
32.0ms
(* (tan x) (tan x))

simplify56.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
03921134
118131007
25002951

prune251.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (sqrt 1.0) (tan x))
0.2b
(- (sqrt 1.0) (tan x))
0.2b
(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
0.3b
(* (tan x) (tan x))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
31×*-un-lft-identity
19×add-cube-cbrt
18×times-frac
11×pow1
10×difference-of-squares
8×add-exp-log add-cbrt-cube add-log-exp
6×associate-/r*
5×sqrt-prod distribute-lft-out--
4×tan-quot
3×swap-sqr associate-*r* associate-*l* associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative pow2 frac-times sub-neg frac-2neg pow-plus diff-log associate-*r/ div-exp pow-prod-down associate-*l/ prod-exp clear-num sum-log pow-sqr *-commutative pow-prod-up cbrt-unprod div-inv distribute-lft-out unswap-sqr
Counts
4 → 98
Calls
4 calls:
4.0ms
(+ (sqrt 1.0) (tan x))
5.0ms
(- (sqrt 1.0) (tan x))
14.0ms
(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
5.0ms
(* (tan x) (tan x))

series223.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ (sqrt 1.0) (tan x))
37.0ms
(- (sqrt 1.0) (tan x))
113.0ms
(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
36.0ms
(* (tan x) (tan x))

simplify49.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0368955
11554891
25002879

prune254.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin x) 2)
0.2b
(pow (sin x) 2)
0.3b
(pow (cos x) 2)
0.3b
(pow (cos x) 2)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt unpow-prod-down pow-unpow *-un-lft-identity
8×pow1 add-exp-log
4×pow-to-exp pow-pow pow-exp add-cbrt-cube unpow2 add-log-exp sqr-pow
Counts
4 → 72
Calls
4 calls:
1.0ms
(pow (sin x) 2)
1.0ms
(pow (sin x) 2)
1.0ms
(pow (cos x) 2)
2.0ms
(pow (cos x) 2)

series72.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(pow (sin x) 2)
19.0ms
(pow (sin x) 2)
17.0ms
(pow (cos x) 2)
17.0ms
(pow (cos x) 2)

simplify62.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (53.0ms)

IterNodesCost
0141284
1469240
21588240
35001236

prune191.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes140.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01212
11212

end0.0ms

sample1.6s

Algorithm
intervals
Results
721.0ms1539×body1280valid
349.0ms1235×body640valid
251.0ms4302×body80valid
130.0ms616×body320valid
42.0ms308×body160valid