Details

Time bar (total: 4.3s)

sample308.0ms

Algorithm
intervals
Results
27.0ms61×body1280valid
9.0ms136×body80valid
9.0ms32×body640valid
3.0ms18×body320valid
1.0ms9×body160valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0139
1229
2299
3379
4439
5459
6459

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 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))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
23×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×expm1-log1p-u log1p-expm1-u associate-/l*
3×fma-neg prod-diff 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 → 119
Calls
4 calls:
8.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
2.0ms
(- 1.0 (* (tan x) (tan x)))
5.0ms
(* (tan x) (tan x))
8.0ms
(* (tan x) (tan x))

series222.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
38.0ms
(- 1.0 (* (tan x) (tan x)))
32.0ms
(* (tan x) (tan x))
59.0ms
(* (tan x) (tan x))

simplify47.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03381007
11243918
25001882

prune292.0ms

Filtered
131 candidates to 91 candidates (69.5%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
28×*-un-lft-identity
26×add-cube-cbrt
21×prod-diff
13×pow1 add-exp-log add-cbrt-cube
12×times-frac
6×tan-quot associate-*r* associate-*l* add-log-exp
4×expm1-log1p-u log1p-expm1-u div-inv
3×fma-neg swap-sqr associate-*l/ prod-exp associate-/r* cbrt-unprod
2×cbrt-undiv div-exp pow-prod-down *-commutative unswap-sqr
1×pow2 frac-times sub-neg flip3-- frac-2neg pow-plus diff-log associate-*r/ clear-num pow-sqr pow-prod-up flip-- associate-/l/ associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 115
Calls
4 calls:
8.0ms
(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
4.0ms
(* (tan x) (sin x))
5.0ms
(/ (* (tan x) (sin x)) (cos x))
5.0ms
(* (tan x) (tan x))

series184.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
41.0ms
(* (tan x) (sin x))
59.0ms
(/ (* (tan x) (sin x)) (cos x))
32.0ms
(* (tan x) (tan x))

simplify70.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
04321314
11872967
25001929

prune307.0ms

Filtered
127 candidates to 77 candidates (60.6%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

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))

rewrite22.0ms

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 expm1-log1p-u div-exp associate-*l/ prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×frac-2neg pow-prod-down clear-num *-commutative div-inv associate-/l/ associate-/l* unswap-sqr
Counts
4 → 90
Calls
4 calls:
4.0ms
(* (tan x) (sin x))
7.0ms
(* (tan x) (sin x))
5.0ms
(/ (* (tan x) (sin x)) (cos x))
5.0ms
(/ (* (tan x) (sin x)) (cos x))

series202.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (tan x) (sin x))
44.0ms
(* (tan x) (sin x))
59.0ms
(/ (* (tan x) (sin x)) (cos x))
57.0ms
(/ (* (tan x) (sin x)) (cos x))

simplify35.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0193604
1897518
25002518

prune302.0ms

Filtered
102 candidates to 76 candidates (74.5%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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)

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×expm1-log1p-u pow-to-exp pow-pow pow-exp add-cbrt-cube log1p-expm1-u unpow2 add-log-exp sqr-pow
Counts
4 → 80
Calls
4 calls:
1.0ms
(pow (cos x) 2)
1.0ms
(pow (cos x) 2)
1.0ms
(pow (sin x) 2)
2.0ms
(pow (sin x) 2)

series73.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(pow (cos x) 2)
16.0ms
(pow (cos x) 2)
18.0ms
(pow (sin x) 2)
19.0ms
(pow (sin x) 2)

simplify63.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 3 (57.0ms)

IterNodesCost
0146308
1487260
21671260
35001256

prune224.0ms

Filtered
92 candidates to 56 candidates (60.9%)
Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes199.0ms

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
01213
11213

end0.0ms

sample1.6s

Algorithm
intervals
Results
709.0ms1515×body1280valid
355.0ms1216×body640valid
247.0ms4300×body80valid
123.0ms630×body320valid
46.0ms339×body160valid