Details

Time bar (total: 10.5s)

sample449.0ms

Algorithm
intervals
Results
117.0ms58×body2560valid
55.0ms86×body1280valid
16.0ms67×body640valid
4.0ms24×body320valid
1.0ms12×body160valid
1.0ms9×body80valid

simplify11.0ms

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: 32.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
1.4b
(- x (tan x))
1.4b
(- x (sin x))

rewrite25.0ms

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:
9.0ms
(/ (- x (sin x)) (- x (tan x)))
4.0ms
(- x (tan x))
7.0ms
(- x (sin x))

series181.0ms

Counts
3 → 9
Calls
3 calls:
73.0ms
(/ (- x (sin x)) (- x (tan x)))
57.0ms
(- x (tan x))
51.0ms
(- x (sin x))

simplify57.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
04721059
11737854
25001854

prune256.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 27/2800 (pow x 4) 1/2)
17.3b
(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite2.0ms

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:
1.0ms
(fma 27/2800 (pow x 4) 1/2)
1.0ms
(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

series127.0ms

Counts
2 → 6
Calls
2 calls:
83.0ms
(fma 27/2800 (pow x 4) 1/2)
44.0ms
(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify151.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
051133
1162117
2626117
33552117
45001117

prune80.0ms

Pruning

5 alts after pruning (4 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)))
1.3b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.4b
(- x (tan x))
1.4b
(- x (tan x))

rewrite113.0ms

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)))
44.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
4.0ms
(- x (tan x))
4.0ms
(- x (tan x))

series343.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(/ (sin x) (- x (tan x)))
178.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
54.0ms
(- x (tan x))
49.0ms
(- x (tan x))

simplify201.0ms

Algorithm
egg-herbie
Counts
600 → 600
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
0135922035
1388315840
2500115776

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b
(- x (tan x))
1.4b
(- x (tan x))
1.4b
(- x (tan x))
1.4b
(- x (tan x))

rewrite23.0ms

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

series207.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(- x (tan x))
49.0ms
(- x (tan x))
54.0ms
(- x (tan x))
49.0ms
(- x (tan x))

simplify58.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 3 (50.0ms)

IterNodesCost
0150984
1409620
21744584
35001416

prune323.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes35.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.6b

bsearch82.0ms

Steps
ItersRangePoint
9
1.2358748968334836e-07
0.22405535791780642
0.03553658186569096
9
-0.11986014733990268
-1.6789357321840064e-10
-0.032711082873140764

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03124
13124

end0.0ms

sample6.7s

Algorithm
intervals
Results
4.1s1677×body2560valid
1.7s2811×body1280valid
465.0ms1827×body640valid
156.0ms856×body320valid
66.0ms478×body160valid
26.0ms351×body80valid