Details

Time bar (total: 10.7s)

sample440.0ms

Algorithm
intervals
Results
101.0ms41×body2560valid
61.0ms90×body1280valid
15.0ms53×body640valid
6.0ms31×body320valid
3.0ms24×body160valid
1.0ms17×body80valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0135
1175
2195
3195

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.4b

Counts
2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
2.4b
(- x (tan x))
2.5b
(- x (sin x))

rewrite40.0ms

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:
23.0ms
(/ (- x (sin x)) (- x (tan x)))
4.0ms
(- x (tan x))
6.0ms
(- x (sin x))

series173.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(/ (- x (sin x)) (- x (tan x)))
58.0ms
(- x (tan x))
41.0ms
(- x (sin x))

simplify56.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
04721059
11737854
25001854

prune212.0ms

Filtered
119 candidates to 79 candidates (66.4%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1163119
Fresh000
Picked101
Done000
Total1173120

Merged error: 0b

Counts
120 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sin x) (- x (tan x)))
2.1b
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
2.4b
(- x (tan x))
2.4b
(- x (tan x))

rewrite112.0ms

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)))
41.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
4.0ms
(- x (tan x))
4.0ms
(- x (tan x))

series329.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(/ (sin x) (- x (tan x)))
170.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
52.0ms
(- x (tan x))
49.0ms
(- x (tan x))

simplify217.0ms

Algorithm
egg-herbie
Counts
600 → 600
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
0135922035
1388315840
2500115776

prune843.0ms

Filtered
600 candidates to 256 candidates (42.7%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New6000600
Fresh022
Picked011
Done000
Total6003603

Merged error: 0b

Counts
603 → 3

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma 27/2800 (pow x 4) 1/2)
16.6b
(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)))

series129.0ms

Counts
2 → 6
Calls
2 calls:
85.0ms
(fma 27/2800 (pow x 4) 1/2)
44.0ms
(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify148.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
051133
1162117
2626117
33552117
45001117

prune59.0ms

Filtered
26 candidates to 20 candidates (76.9%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New26026
Fresh011
Picked011
Done011
Total26329

Merged error: 0b

Counts
29 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (tan x) 3)
2.4b
(- (pow x 3) (pow (tan x) 3))
2.5b
(- x (sin x))
33.7b
(/ (- (pow x 3) (pow (tan x) 3)) (fma (tan x) (+ x (tan x)) (pow x 2)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
241×add-sqr-sqrt
171×*-un-lft-identity
153×prod-diff
138×unpow-prod-down cube-prod
119×add-cube-cbrt
81×difference-of-squares
75×times-frac
66×sqr-pow
26×cube-mult unpow3 distribute-lft-out--
25×associate-/l*
15×fma-neg
8×add-log-exp
7×add-exp-log add-cbrt-cube
5×pow1 difference-cubes
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow flip3-- associate-/r* flip--
2×sub-neg diff-log associate-/l/
1×tan-quot cbrt-undiv cube-div pow-to-exp pow-pow frac-2neg div-sub div-exp pow-exp clear-num div-inv rem-cube-cbrt
Counts
4 → 366
Calls
4 calls:
3.0ms
(pow (tan x) 3)
16.0ms
(- (pow x 3) (pow (tan x) 3))
4.0ms
(- x (sin x))
26.0ms
(/ (- (pow x 3) (pow (tan x) 3)) (fma (tan x) (+ x (tan x)) (pow x 2)))

series444.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(pow (tan x) 3)
127.0ms
(- (pow x 3) (pow (tan x) 3))
31.0ms
(- x (sin x))
239.0ms
(/ (- (pow x 3) (pow (tan x) 3)) (fma (tan x) (+ x (tan x)) (pow x 2)))

simplify165.0ms

Algorithm
egg-herbie
Counts
378 → 378
Iterations

Useful iterations: 2 (113.0ms)

IterNodesCost
08915123
133284115
250014098

prune562.0ms

Filtered
378 candidates to 139 candidates (36.8%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New3780378
Fresh000
Picked011
Done022
Total3783381

Merged error: 0b

Counts
381 → 3

regimes27.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch82.0ms

Steps
ItersRangePoint
10
0.00022027325057658872
62623256.830634765
0.027715773861404648
9
-17.831791951177678
-3.7534567552478157e-06
-0.027340075628349603

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02613
12613

end0.0ms

sample6.5s

Algorithm
intervals
Results
3.9s1626×body2560valid
1.7s2738×body1280valid
525.0ms1868×body640valid
182.0ms980×body320valid
60.0ms471×body160valid
25.0ms317×body80valid

Profiling

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