Details

Time bar (total: 2.7s)

sample55.0ms

Algorithm
intervals
Results
17.0ms50×body1280valid
9.0ms133×body80valid
9.0ms38×body640valid
4.0ms21×body320valid
2.0ms14×body160valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03515
13515

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.3b

Counts
2 → 1

localize11.0ms

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))

rewrite42.0ms

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:
3.0ms
(- 1.0 (* (tan x) (tan x)))
7.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
6.0ms
(* (tan x) (tan x))
22.0ms
(* (tan x) (tan x))

series77.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(- 1.0 (* (tan x) (tan x)))
37.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
10.0ms
(* (tan x) (tan x))
20.0ms
(* (tan x) (tan x))

simplify51.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
049601331
149601331

prune204.0ms

Filtered
78 candidates to 117 candidates (-50.0%)
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:

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

rewrite15.0ms

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:
3.0ms
(pow (cos x) 2)
3.0ms
(pow (cos x) 2)
3.0ms
(pow (sin x) 2)
5.0ms
(pow (sin x) 2)

series15.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(pow (cos x) 2)
3.0ms
(pow (cos x) 2)
4.0ms
(pow (sin x) 2)
4.0ms
(pow (sin x) 2)

simplify30.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
04985424
14985424

prune171.0ms

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

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New81384
Fresh11011
Picked101
Done000
Total831396

Merged error: 0.0b

Counts
96 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
30×*-un-lft-identity
22×add-cube-cbrt
18×times-frac
15×add-exp-log add-cbrt-cube
13×pow1
6×tan-quot associate-*r* associate-*l* associate-/r* associate-/l*
4×distribute-lft-out-- add-log-exp difference-of-squares
3×cbrt-undiv swap-sqr div-exp associate-*l/ prod-exp cbrt-unprod associate-/l/
2×frac-2neg pow-prod-down clear-num associate-/r/ *-commutative div-inv unswap-sqr
1×pow2 frac-times flip3-- flip3-+ pow-plus div-sub associate-*r/ pow-sqr pow-prod-up flip-- flip-+
Counts
4 → 109
Calls
4 calls:
9.0ms
(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms
(* (tan x) (sin x))
7.0ms
(/ (* (tan x) (sin x)) (cos x))
6.0ms
(* (tan x) (tan x))

series82.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
11.0ms
(* (tan x) (sin x))
18.0ms
(/ (* (tan x) (sin x)) (cos x))
10.0ms
(* (tan x) (tan x))

simplify41.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
054061680

prune180.0ms

Filtered
84 candidates to 121 candidates (-44.0%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1183121
Fresh3912
Picked011
Done000
Total12113134

Merged error: 0.0b

Counts
134 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (sin x))
0.2b
(* (tan x) (sin x))
0.2b
(/ (* (tan x) (sin x)) (cos x))
0.2b
(/ (* (tan x) (sin x)) (cos x))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
16×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
8×pow1
6×times-frac associate-*r* associate-*l* associate-/r*
4×tan-quot cbrt-undiv div-exp associate-*l/ prod-exp cbrt-unprod add-log-exp
2×frac-2neg pow-prod-down clear-num *-commutative div-inv associate-/l/ associate-/l* unswap-sqr
Counts
4 → 82
Calls
4 calls:
5.0ms
(* (tan x) (sin x))
6.0ms
(* (tan x) (sin x))
7.0ms
(/ (* (tan x) (sin x)) (cos x))
7.0ms
(/ (* (tan x) (sin x)) (cos x))

series59.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(* (tan x) (sin x))
11.0ms
(* (tan x) (sin x))
17.0ms
(/ (* (tan x) (sin x)) (cos x))
17.0ms
(/ (* (tan x) (sin x)) (cos x))

simplify44.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
04948774
14948774

prune85.0ms

Filtered
68 candidates to 94 candidates (-38.2%)
Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New94094
Fresh01111
Picked011
Done011
Total9413107

Merged error: 0.0b

Counts
107 → 13

regimes322.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01221
11221

end0.0ms

sample1.1s

Algorithm
intervals
Results
393.0ms1509×body1280valid
220.0ms1205×body640valid
191.0ms4390×body80valid
79.0ms612×body320valid
26.0ms284×body160valid

Profiling

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