Details

Time bar (total: 3.2s)

sample46.0ms

Algorithm
intervals
Results
15.0ms56×body1280valid
9.0ms48×body640valid
7.0ms126×body80valid
2.0ms18×body320valid
1.0ms8×body160valid

simplify740.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (105.0ms)

IterNodesCost
0528415

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.4b

Counts
2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

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:
6.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
3.0ms
(- 1.0 (* (tan x) (tan x)))
5.0ms
(* (tan x) (tan x))
7.0ms
(* (tan x) (tan x))

series84.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
9.0ms
(- 1.0 (* (tan x) (tan x)))
26.0ms
(* (tan x) (tan x))
18.0ms
(* (tan x) (tan x))

simplify56.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
049511210
149511210

prune223.0ms

Filtered
82 candidates to 117 candidates (-42.7%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New10512117
Fresh000
Picked101
Done000
Total10612118

Merged error: 0.0b

Counts
118 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
18×*-un-lft-identity
13×pow1
10×add-cube-cbrt
9×associate-*r*
8×add-exp-log add-cbrt-cube add-log-exp
7×associate-*l*
5×frac-times
4×tan-quot flip3-- flip3-+ flip-- flip-+ difference-of-squares
3×sub-neg associate-*r/ swap-sqr associate-*l/
2×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp sqrt-prod *-commutative cbrt-unprod distribute-lft-out distribute-lft-out-- unswap-sqr
1×+-commutative pow2 pow-plus diff-log sum-log pow-sqr pow-prod-up
Counts
4 → 89
Calls
4 calls:
4.0ms
(- (sqrt 1.0) (tan x))
5.0ms
(+ (tan x) (sqrt 1.0))
12.0ms
(* (+ (tan x) (sqrt 1.0)) (- (sqrt 1.0) (tan x)))
5.0ms
(* (tan x) (tan x))

series39.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(- (sqrt 1.0) (tan x))
7.0ms
(+ (tan x) (sqrt 1.0))
17.0ms
(* (+ (tan x) (sqrt 1.0)) (- (sqrt 1.0) (tan x)))
8.0ms
(* (tan x) (tan x))

simplify43.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
05017914

prune173.0ms

Filtered
68 candidates to 101 candidates (-48.5%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New992101
Fresh01111
Picked011
Done000
Total9914113

Merged error: 0.0b

Counts
113 → 14

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (tan x) 2)
0.3b
(pow (tan x) 2)
0.3b
(pow (tan x) 2)
0.4b
(- (/ 1.0 (+ (pow (tan x) 2) 1.0)) (/ (pow (tan x) 2) (+ (pow (tan x) 2) 1.0)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
36×*-un-lft-identity
25×times-frac
12×add-cube-cbrt
11×unpow-prod-down
10×difference-of-squares
9×pow-unpow
7×pow1 add-exp-log distribute-lft-out--
6×add-log-exp
5×unpow2 sqr-pow
4×associate-/r/ add-cbrt-cube distribute-lft-out
3×pow-to-exp distribute-rgt-out-- pow-pow pow-exp
2×flip3-+ flip-+ div-inv
1×sub-neg flip3-- diff-log frac-sub flip-- sub-div
Counts
4 → 88
Calls
4 calls:
3.0ms
(pow (tan x) 2)
3.0ms
(pow (tan x) 2)
3.0ms
(pow (tan x) 2)
39.0ms
(- (/ 1.0 (+ (pow (tan x) 2) 1.0)) (/ (pow (tan x) 2) (+ (pow (tan x) 2) 1.0)))

series77.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(pow (tan x) 2)
8.0ms
(pow (tan x) 2)
8.0ms
(pow (tan x) 2)
52.0ms
(- (/ 1.0 (+ (pow (tan x) 2) 1.0)) (/ (pow (tan x) 2) (+ (pow (tan x) 2) 1.0)))

simplify36.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
051941420

prune200.0ms

Filtered
66 candidates to 100 candidates (-51.5%)
Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New991100
Fresh11112
Picked011
Done011
Total10014114

Merged error: 0.0b

Counts
114 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite11.0ms

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:
2.0ms
(pow (sin x) 2)
2.0ms
(pow (sin x) 2)
2.0ms
(pow (cos x) 2)
2.0ms
(pow (cos x) 2)

series13.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(pow (sin x) 2)
3.0ms
(pow (sin x) 2)
3.0ms
(pow (cos x) 2)
3.0ms
(pow (cos x) 2)

simplify43.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
05266424

prune112.0ms

Filtered
48 candidates to 84 candidates (-75.0%)
Pruning

14 alts after pruning (11 fresh and 3 done)

PrunedKeptTotal
New84084
Fresh01111
Picked011
Done022
Total841498

Merged error: 0.0b

Counts
98 → 14

regimes149.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02319
12319

end0.0ms

sample1.0s

Algorithm
intervals
Results
385.0ms1461×body1280valid
213.0ms1203×body640valid
173.0ms4393×body80valid
80.0ms629×body320valid
27.0ms314×body160valid

Profiling

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