Details

Time bar (total: 10.1s)

sample498.0ms

Algorithm
intervals
Results
165.0ms57×body2560valid
52.0ms81×body1280valid
16.0ms58×body640valid
6.0ms31×body320valid
3.0ms19×body160valid
1.0ms10×body80valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 33.2b

Counts
2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
1.7b
(- x (tan x))
1.8b
(- x (sin x))

rewrite39.0ms

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:
24.0ms
(/ (- x (sin x)) (- x (tan x)))
4.0ms
(- x (tan x))
7.0ms
(- x (sin x))

series181.0ms

Counts
3 → 9
Calls
3 calls:
78.0ms
(/ (- x (sin x)) (- x (tan x)))
60.0ms
(- x (tan x))
42.0ms
(- x (sin x))

simplify57.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
04721059
11737854
25001854

prune220.0ms

Filtered
119 candidates to 79 candidates (66.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1154119
Fresh000
Picked101
Done000
Total1164120

Merged error: 0.0b

Counts
120 → 4

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b
(fma 27/2800 (pow x 4) 1/2)
15.1b
(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)))

series135.0ms

Counts
2 → 6
Calls
2 calls:
86.0ms
(fma 27/2800 (pow x 4) 1/2)
49.0ms
(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify146.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
051133
1162117
2626117
33552117
45001117

prune66.0ms

Filtered
26 candidates to 20 candidates (76.9%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New26026
Fresh033
Picked011
Done000
Total26430

Merged error: 0.0b

Counts
30 → 4

localize9.0ms

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))))
1.7b
(- x (tan x))
1.7b
(- x (tan x))

rewrite103.0ms

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:
10.0ms
(/ (sin x) (- x (tan x)))
38.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
4.0ms
(- x (tan x))
4.0ms
(- x (tan x))

series363.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(/ (sin x) (- x (tan x)))
185.0ms
(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
55.0ms
(- x (tan x))
58.0ms
(- x (tan x))

simplify213.0ms

Algorithm
egg-herbie
Counts
600 → 600
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
0135922035
1388315840
2500115776

prune894.0ms

Filtered
600 candidates to 256 candidates (42.7%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New6000600
Fresh022
Picked011
Done011
Total6004604

Merged error: 0.0b

Counts
604 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

1.7b
(- x (tan x))
1.8b
(- x (sin x))
1.8b
(- x (sin x))
1.8b
(- x (sin x))

rewrite20.0ms

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

series155.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(- x (tan x))
31.0ms
(- x (sin x))
36.0ms
(- x (sin x))
33.0ms
(- x (sin x))

simplify94.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 3 (85.0ms)

IterNodesCost
0258969
1749605
23295569
35001401

prune243.0ms

Filtered
124 candidates to 73 candidates (58.9%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1240124
Fresh011
Picked011
Done022
Total1244128

Merged error: 0.0b

Counts
128 → 4

regimes58.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.9b

bsearch81.0ms

Steps
ItersRangePoint
9
8.159003009805276e-07
0.06291072096871789
0.026837057201601722
9
-5.855776674212404
-7.74497267090904e-05
-0.02703430163315367

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02933
12933

end0.0ms

sample6.5s

Algorithm
intervals
Results
3.9s1552×body2560valid
1.7s2752×body1280valid
533.0ms1941×body640valid
163.0ms897×body320valid
59.0ms490×body160valid
27.0ms368×body80valid