Details

Time bar (total: 10.0s)

sample454.0ms

Algorithm
intervals
Results
113.0ms51×body2560valid
55.0ms84×body1280valid
21.0ms60×body640valid
7.0ms29×body320valid
3.0ms21×body160valid
1.0ms11×body80valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0135
1175
2195
3195

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
2.0b
(- x (tan x))
2.0b
(- x (sin x))

rewrite43.0ms

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:
14.0ms
(/ (- x (sin x)) (- x (tan x)))
3.0ms
(- x (tan x))
21.0ms
(- x (sin x))

series175.0ms

Counts
3 → 9
Calls
3 calls:
77.0ms
(/ (- x (sin x)) (- x (tan x)))
57.0ms
(- 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

prune233.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sin x) (- x (tan x)))
1.6b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
2.0b
(- x (tan x))
2.0b
(- 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))

series343.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ (sin x) (- x (tan x)))
176.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
54.0ms
(- x (tan x))
57.0ms
(- x (tan x))

simplify207.0ms

Algorithm
egg-herbie
Counts
600 → 600
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
0135922035
1388315840
2500115776

prune965.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
2.0b
(- x (tan x))
2.0b
(- x (sin x))

rewrite23.0ms

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))
4.0ms
(- x (sin x))

series161.0ms

Counts
3 → 9
Calls
3 calls:
78.0ms
(/ (- x (sin x)) (- x (tan x)))
48.0ms
(- x (tan x))
35.0ms
(- x (sin x))

simplify56.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
04721059
11737854
25001854

prune209.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma 27/2800 (pow x 4) 1/2)
15.3b
(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)))

series132.0ms

Counts
2 → 6
Calls
2 calls:
84.0ms
(fma 27/2800 (pow x 4) 1/2)
49.0ms
(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify145.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
051133
1162117
2626117
33552117
45001117

prune65.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes55.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.8b

bsearch79.0ms

Steps
ItersRangePoint
9
0.004380743253548005
488.5072251079851
0.031971504814548905
9
-3.9934486818618
-6.3299436832828755e-06
-0.028744253704368783

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02518

end0.0ms

sample6.4s

Algorithm
intervals
Results
3.4s1558×body2560valid
1.9s2693×body1280valid
644.0ms1933×body640valid
217.0ms948×body320valid
80.0ms513×body160valid
32.0ms355×body80valid