Details

Time bar (total: 11.3s)

sample549.0ms

Algorithm
intervals
Results
117.0ms54×body2560valid
55.0ms83×body1280valid
42.0ms58×body640valid
7.0ms32×body320valid
3.0ms18×body160valid
1.0ms11×body80valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0135
1175
2195
3195

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
0.8b
(- x (tan x))
0.8b
(- x (sin x))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt *-un-lft-identity
29×add-cube-cbrt
25×times-frac
18×prod-diff
14×distribute-lft-out-- difference-of-squares
7×add-log-exp
6×fma-neg
5×add-exp-log associate-/r* add-cbrt-cube associate-/l*
4×flip3-- flip--
3×pow1 expm1-log1p-u log1p-expm1-u
2×sub-neg diff-log associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-sub div-exp clear-num div-inv
Counts
3 → 110
Calls
3 calls:
33.0ms
(/ (- x (sin x)) (- x (tan x)))
7.0ms
(- x (tan x))
10.0ms
(- x (sin x))

series176.0ms

Counts
3 → 9
Calls
3 calls:
76.0ms
(/ (- x (sin x)) (- x (tan x)))
58.0ms
(- x (tan x))
42.0ms
(- x (sin x))

simplify56.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
04721059
11737854
25001854

prune229.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sin x) (- x (tan x)))
0.8b
(- x (tan x))
0.8b
(- x (tan x))
0.8b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
713×*-un-lft-identity
703×add-sqr-sqrt
678×times-frac
459×prod-diff
417×add-cube-cbrt
147×distribute-lft-out--
141×difference-of-squares
92×associate-/r/
49×flip3-- flip--
46×div-inv
27×fma-neg
10×add-log-exp
6×add-exp-log add-cbrt-cube
5×associate-/r*
4×pow1 expm1-log1p-u log1p-expm1-u
3×sub-neg distribute-rgt-out-- diff-log associate-/l*
1×cbrt-undiv frac-2neg div-exp clear-num frac-sub sub-div
Counts
4 → 588
Calls
4 calls:
16.0ms
(/ (sin x) (- x (tan x)))
7.0ms
(- x (tan x))
6.0ms
(- x (tan x))
111.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

series348.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(/ (sin x) (- x (tan x)))
50.0ms
(- x (tan x))
56.0ms
(- x (tan x))
181.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

simplify204.0ms

Algorithm
egg-herbie
Counts
600 → 600
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
0135922035
1388215840
2500115774

prune940.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b
(- x (tan x))
0.8b
(- x (tan x))
0.8b
(- x (tan x))
0.8b
(- (* (/ x (- x (tan x))) (/ x (- x (tan x)))) (* (/ (sin x) (- x (tan x))) (/ (sin x) (- x (tan x)))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt *-un-lft-identity
28×prod-diff
25×add-cube-cbrt
12×add-log-exp
10×fma-neg associate-*r/ associate-*l/
9×frac-sub
8×frac-times
5×sub-div
4×pow1 add-exp-log expm1-log1p-u sub-neg flip3-- diff-log add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
3×distribute-lft-out--
Counts
4 → 115
Calls
4 calls:
6.0ms
(- x (tan x))
6.0ms
(- x (tan x))
6.0ms
(- x (tan x))
27.0ms
(- (* (/ x (- x (tan x))) (/ x (- x (tan x)))) (* (/ (sin x) (- x (tan x))) (/ (sin x) (- x (tan x)))))

series363.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- x (tan x))
55.0ms
(- x (tan x))
56.0ms
(- x (tan x))
203.0ms
(- (* (/ x (- x (tan x))) (/ x (- x (tan x)))) (* (/ (sin x) (- x (tan x))) (/ (sin x) (- x (tan x)))))

simplify49.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04191436
114471077
250011056

prune287.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b
(- x (tan x))
0.8b
(- x (tan x))
0.8b
(fma x (/ x (- x (tan x))) (/ (- (pow (sin x) 2)) (- x (tan x))))
15.2b
(/ (- (pow (sin x) 2)) (- x (tan x)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
115×add-sqr-sqrt *-un-lft-identity
100×times-frac
69×add-cube-cbrt
48×distribute-lft-neg-in distribute-rgt-neg-in
36×unpow-prod-down
23×distribute-lft-out-- difference-of-squares
20×associate-/l*
18×prod-diff
12×unpow2 sqr-pow
8×add-log-exp
6×add-exp-log neg-mul-1 fma-neg add-cbrt-cube
5×associate-/r*
4×pow1 expm1-log1p-u log1p-expm1-u
3×flip3-- flip--
2×sub-neg diff-log associate-/r/
1×cbrt-undiv neg-sub0 frac-2neg div-sub distribute-frac-neg div-exp clear-num fma-udef div-inv
Counts
4 → 209
Calls
4 calls:
6.0ms
(- x (tan x))
6.0ms
(- x (tan x))
0.0ms
(fma x (/ x (- x (tan x))) (/ (- (pow (sin x) 2)) (- x (tan x))))
24.0ms
(/ (- (pow (sin x) 2)) (- x (tan x)))

series397.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(- x (tan x))
50.0ms
(- x (tan x))
221.0ms
(fma x (/ x (- x (tan x))) (/ (- (pow (sin x) 2)) (- x (tan x))))
71.0ms
(/ (- (pow (sin x) 2)) (- x (tan x)))

simplify66.0ms

Algorithm
egg-herbie
Counts
221 → 221
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
06582369
124192014
250012013

prune558.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes35.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.5b

bsearch93.0ms

Steps
ItersRangePoint
11
1.661404138935296e-22
2.5556453819330236
0.026711642772946572
9
-0.04331797882383785
-2.2082264187638084e-10
-0.026797644779880028

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04041
14041

end0.0ms

sample6.5s

Algorithm
intervals
Results
3.4s1576×body2560valid
1.9s2801×body1280valid
637.0ms1898×body640valid
213.0ms930×body320valid
81.0ms466×body160valid
30.0ms329×body80valid