Details

Time bar (total: 10.8s)

sample451.0ms

Algorithm
intervals
Results
98.0ms48×body2560valid
70.0ms101×body1280valid
17.0ms51×body640valid
7.0ms30×body320valid
2.0ms16×body160valid
1.0ms10×body80valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0135
1175
2195
3195

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
1.7b
(- x (tan x))
1.7b
(- x (sin x))

rewrite28.0ms

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:
13.0ms
(/ (- x (sin x)) (- x (tan x)))
3.0ms
(- x (tan x))
6.0ms
(- x (sin x))

series173.0ms

Counts
3 → 9
Calls
3 calls:
75.0ms
(/ (- x (sin x)) (- x (tan x)))
58.0ms
(- x (tan x))
39.0ms
(- x (sin x))

simplify54.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
04721059
11737854
25001854

prune242.0ms

Filtered
119 candidates to 79 candidates (66.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(expm1 (log1p (/ (- x (sin x)) (- x (tan x)))))
0.0b
(/ (- x (sin x)) (- x (tan x)))
1.7b
(- x (tan x))
1.7b
(- x (sin x))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt *-un-lft-identity
30×add-cube-cbrt
25×times-frac
18×prod-diff
14×distribute-lft-out-- difference-of-squares
8×add-log-exp
6×add-exp-log fma-neg add-cbrt-cube
5×associate-/r* associate-/l*
4×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u
2×sub-neg diff-log associate-/r/ associate-/l/
1×cbrt-undiv expm1-log1p frac-2neg div-sub div-exp clear-num div-inv expm1-udef
Counts
4 → 121
Calls
4 calls:
0.0ms
(expm1 (log1p (/ (- x (sin x)) (- x (tan x)))))
13.0ms
(/ (- x (sin x)) (- x (tan x)))
3.0ms
(- x (tan x))
4.0ms
(- x (sin x))

series282.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(expm1 (log1p (/ (- x (sin x)) (- x (tan x)))))
75.0ms
(/ (- x (sin x)) (- x (tan x)))
53.0ms
(- x (tan x))
30.0ms
(- x (sin x))

simplify54.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
04841189
11751973
25001973

prune305.0ms

Filtered
133 candidates to 90 candidates (67.7%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sin x) (- x (tan x)))
1.7b
(- x (tan x))
1.7b
(- x (tan x))
1.7b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

rewrite143.0ms

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:
7.0ms
(/ (sin x) (- x (tan x)))
5.0ms
(- x (tan x))
3.0ms
(- x (tan x))
75.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

series345.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(/ (sin x) (- x (tan x)))
53.0ms
(- x (tan x))
48.0ms
(- x (tan x))
183.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

simplify203.0ms

Algorithm
egg-herbie
Counts
600 → 600
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
0135922035
1388215840
2500115774

prune968.0ms

Filtered
600 candidates to 257 candidates (42.8%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

1.7b
(- x (tan x))
1.7b
(- x (tan x))
1.7b
(- x (tan x))
1.7b
(- (* (/ x (- x (tan x))) (/ x (- x (tan x)))) (* (/ (sin x) (- x (tan x))) (/ (sin x) (- x (tan x)))))

rewrite29.0ms

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:
3.0ms
(- x (tan x))
3.0ms
(- x (tan x))
3.0ms
(- x (tan x))
16.0ms
(- (* (/ x (- x (tan x))) (/ x (- x (tan x)))) (* (/ (sin x) (- x (tan x))) (/ (sin x) (- x (tan x)))))

series349.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(- x (tan x))
48.0ms
(- x (tan x))
53.0ms
(- x (tan x))
195.0ms
(- (* (/ 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

prune288.0ms

Filtered
127 candidates to 83 candidates (65.4%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes63.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.8b

bsearch79.0ms

Steps
ItersRangePoint
9
0.0004320794088804456
4086.0217424804537
0.024272639190728022
7
-0.37949367736095085
-0.007251023403816859
-0.029200373970740375

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04054
14054

end0.0ms

sample6.5s

Algorithm
intervals
Results
3.5s1598×body2560valid
1.9s2865×body1280valid
639.0ms1818×body640valid
223.0ms925×body320valid
71.0ms452×body160valid
31.0ms342×body80valid