Details

Time bar (total: 10.8s)

sample467.0ms

Algorithm
intervals
Results
100.0ms45×body2560valid
62.0ms85×body1280valid
26.0ms61×body640valid
10.0ms37×body320valid
3.0ms16×body160valid
1.0ms12×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: 31.3b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
1.0b
(- x (tan x))
1.0b
(- x (sin x))

rewrite29.0ms

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)))
4.0ms
(- x (tan x))
7.0ms
(- x (sin x))

series176.0ms

Counts
3 → 9
Calls
3 calls:
76.0ms
(/ (- x (sin x)) (- x (tan x)))
60.0ms
(- x (tan x))
40.0ms
(- x (sin x))

simplify54.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
04721059
11737854
25001854

prune242.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sin x) (- x (tan x)))
0.7b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.0b
(- x (tan x))
1.0b
(- x (tan x))

rewrite140.0ms

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)))
72.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
3.0ms
(- x (tan x))
3.0ms
(- x (tan x))

series354.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(/ (sin x) (- x (tan x)))
180.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
55.0ms
(- x (tan x))
57.0ms
(- x (tan x))

simplify201.0ms

Algorithm
egg-herbie
Counts
600 → 600
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
0135922035
1388315840
2500115776

prune979.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b
(- x (tan x))
1.0b
(- x (sin x))
1.0b
(- x (sin x))
1.0b
(- x (sin x))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt *-un-lft-identity
36×prod-diff
32×add-cube-cbrt
12×fma-neg add-log-exp
4×pow1 add-exp-log expm1-log1p-u sub-neg flip3-- diff-log add-cbrt-cube flip-- log1p-expm1-u distribute-lft-out-- difference-of-squares
Counts
4 → 112
Calls
4 calls:
3.0ms
(- x (tan x))
3.0ms
(- x (sin x))
3.0ms
(- x (sin x))
4.0ms
(- x (sin x))

series150.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- x (tan x))
36.0ms
(- x (sin x))
30.0ms
(- x (sin x))
35.0ms
(- x (sin x))

simplify93.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0258969
1749605
23295569
35001401

prune246.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma 27/2800 (pow x 4) 1/2)
16.1b
(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
2 → 20
Calls
2 calls:
0.0ms
(fma 27/2800 (pow x 4) 1/2)
0.0ms
(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

series131.0ms

Counts
2 → 6
Calls
2 calls:
83.0ms
(fma 27/2800 (pow x 4) 1/2)
48.0ms
(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify144.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
051133
1162117
2626117
33552117
45001117

prune66.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes29.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.7b

bsearch79.0ms

Steps
ItersRangePoint
8
0.003211336228265424
0.8894813891870064
0.031197100678935472
8
-1.3862719480695398
-4.2961337728369966e-05
-0.029017087826586654

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02613
12613

end0.0ms

sample7.1s

Algorithm
intervals
Results
3.8s1663×body2560valid
2.0s2781×body1280valid
757.0ms1871×body640valid
236.0ms878×body320valid
93.0ms464×body160valid
43.0ms343×body80valid