Details

Time bar (total: 4.7s)

sample307.0ms

Algorithm
intervals
Results
24.0ms51×body1280valid
9.0ms35×body640valid
8.0ms134×body80valid
4.0ms20×body320valid
2.0ms16×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

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:
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))
8.0ms
(* (tan x) (tan x))

series214.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms
(- 1.0 (* (tan x) (tan x)))
32.0ms
(* (tan x) (tan x))
54.0ms
(* (tan x) (tan x))

simplify49.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03381007
11243918
25001882

prune302.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

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)

rewrite12.0ms

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:
2.0ms
(pow (cos x) 2)
2.0ms
(pow (cos x) 2)
3.0ms
(pow (sin x) 2)
3.0ms
(pow (sin x) 2)

series74.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(pow (cos x) 2)
16.0ms
(pow (cos x) 2)
21.0ms
(pow (sin x) 2)
19.0ms
(pow (sin x) 2)

simplify62.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 3 (56.0ms)

IterNodesCost
0146308
1487260
21671260
35001256

prune266.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(- 1.0 (/ (pow (sin x) 2) (pow (cos x) 2)))
0.3b
(pow (cos x) 2)
0.3b
(pow (sin x) 2)
0.3b
(* (tan x) (tan x))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
216×add-sqr-sqrt
208×times-frac
204×prod-diff
182×*-un-lft-identity
180×add-cube-cbrt
158×unpow-prod-down
58×unpow2 sqr-pow
17×difference-of-squares
13×pow1
8×add-exp-log
6×pow-unpow add-cbrt-cube add-log-exp
4×tan-quot expm1-log1p-u log1p-expm1-u
3×fma-neg swap-sqr associate-*r* associate-*l* div-inv
2×pow-to-exp pow-pow pow-exp
1×pow2 frac-times sub-neg flip3-- pow-plus diff-log associate-*r/ pow-prod-down associate-*l/ prod-exp pow-sqr *-commutative pow-prod-up flip-- cbrt-unprod distribute-lft-out-- unswap-sqr
Counts
4 → 309
Calls
4 calls:
26.0ms
(- 1.0 (/ (pow (sin x) 2) (pow (cos x) 2)))
2.0ms
(pow (cos x) 2)
3.0ms
(pow (sin x) 2)
5.0ms
(* (tan x) (tan x))

series118.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- 1.0 (/ (pow (sin x) 2) (pow (cos x) 2)))
17.0ms
(pow (cos x) 2)
18.0ms
(pow (sin x) 2)
32.0ms
(* (tan x) (tan x))

simplify90.0ms

Algorithm
egg-herbie
Counts
321 → 321
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
017589345
150016254

prune467.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(- 1.0 (* (tan x) (tan x)))
0.2b
(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
0.3b
(* (tan x) (tan x))
0.3b
(* (tan x) (tan x))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×pow1
14×add-cube-cbrt *-un-lft-identity
8×tan-quot add-exp-log add-cbrt-cube
6×swap-sqr associate-*r* associate-*l* add-log-exp
5×expm1-log1p-u
4×log1p-expm1-u
3×fma-neg prod-diff
2×pow2 frac-times pow-plus associate-*r/ pow-prod-down associate-*l/ prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
1×sub-neg log1p-udef flip3-- diff-log log1p-expm1 flip-- difference-of-squares
Counts
4 → 92
Calls
4 calls:
3.0ms
(- 1.0 (* (tan x) (tan x)))
1.0ms
(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
5.0ms
(* (tan x) (tan x))
5.0ms
(* (tan x) (tan x))

series324.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- 1.0 (* (tan x) (tan x)))
223.0ms
(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
32.0ms
(* (tan x) (tan x))
36.0ms
(* (tan x) (tan x))

simplify133.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 3 (126.0ms)

IterNodesCost
0246612
1827546
23958530
35002525

prune238.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

regimes252.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01411
11411

end0.0ms

sample1.6s

Algorithm
intervals
Results
713.0ms1566×body1280valid
354.0ms1246×body640valid
253.0ms4289×body80valid
114.0ms595×body320valid
41.0ms304×body160valid