Details

Time bar (total: 9.8s)

sample478.0ms

Algorithm
intervals
Results
139.0ms50×body2560valid
59.0ms95×body1280valid
14.0ms54×body640valid
5.0ms33×body320valid
1.0ms12×body160valid
1.0ms12×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: 31.4b

Counts
2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
1.9b
(- x (tan x))
1.9b
(- 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:
9.0ms
(/ (- x (sin x)) (- x (tan x)))
4.0ms
(- x (tan x))
7.0ms
(- x (sin x))

series179.0ms

Counts
3 → 9
Calls
3 calls:
77.0ms
(/ (- x (sin x)) (- x (tan x)))
59.0ms
(- x (tan x))
41.0ms
(- x (sin x))

simplify57.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
04721059
11737854
25001854

prune224.0ms

Filtered
119 candidates to 79 candidates (66.4%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1136119
Fresh000
Picked101
Done000
Total1146120

Merged error: 0.0b

Counts
120 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
1.9b
(- x (sin x))
2.7b
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
28.5b
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt *-un-lft-identity
22×add-cube-cbrt
15×times-frac
9×prod-diff
6×add-exp-log add-cbrt-cube add-log-exp
5×associate-/l* distribute-lft-out-- difference-of-squares
4×pow1 expm1-log1p-u log1p-expm1-u
3×cbrt-prod fma-neg associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg pow1/3 diff-log div-sub div-exp clear-num fma-udef div-inv
Counts
4 → 91
Calls
4 calls:
1.0ms
(cbrt x)
4.0ms
(- x (sin x))
7.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
1.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series1.0s

Counts
4 → 12
Calls
4 calls:
181.0ms
(cbrt x)
31.0ms
(- x (sin x))
508.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
328.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

simplify45.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03421106
11185942
25001904

prune239.0ms

Filtered
103 candidates to 79 candidates (76.7%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1030103
Fresh055
Picked011
Done000
Total1036109

Merged error: 0.0b

Counts
109 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (- x (tan x)))
0.1b
(* (- x (sin x)) (/ 1 (- x (tan x))))
1.9b
(- x (tan x))
1.9b
(- x (sin x))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
65×add-sqr-sqrt
59×*-un-lft-identity
38×add-cube-cbrt
32×times-frac
21×associate-*r*
18×prod-diff
17×add-exp-log
11×add-cbrt-cube
10×distribute-lft-out-- difference-of-squares
8×add-log-exp
7×pow1
6×flip3-- fma-neg flip--
5×associate-*l* associate-/r*
4×expm1-log1p-u div-exp prod-exp associate-/r/ log1p-expm1-u
3×associate-/l* unswap-sqr
2×cbrt-undiv frac-times sub-neg rec-exp diff-log 1-exp associate-*l/ cbrt-unprod div-inv
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
4 → 151
Calls
4 calls:
6.0ms
(/ 1 (- x (tan x)))
17.0ms
(* (- x (sin x)) (/ 1 (- x (tan x))))
4.0ms
(- x (tan x))
4.0ms
(- x (sin x))

series214.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ 1 (- x (tan x)))
79.0ms
(* (- x (sin x)) (/ 1 (- x (tan x))))
54.0ms
(- x (tan x))
31.0ms
(- x (sin x))

simplify73.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
05731256
12566990
25001948

prune263.0ms

Filtered
163 candidates to 100 candidates (61.3%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1630163
Fresh044
Picked011
Done011
Total1636169

Merged error: 0.0b

Counts
169 → 6

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 27/2800 (pow x 4) 1/2)
16.1b
(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:
85.0ms
(fma 27/2800 (pow x 4) 1/2)
49.0ms
(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify144.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
051133
1162117
2626117
33552117
45001117

prune61.0ms

Filtered
26 candidates to 20 candidates (76.9%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New26026
Fresh033
Picked011
Done022
Total26632

Merged error: 0.0b

Counts
32 → 6

regimes40.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.3b

bsearch77.0ms

Steps
ItersRangePoint
9
0.0002199982819353488
137964.03928948785
0.02902705871059986
9
-0.41295360884021565
-1.1902930357079885e-07
-0.02453727723232867

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03011
13011

end0.0ms

sample6.4s

Algorithm
intervals
Results
4.0s1645×body2560valid
1.6s2727×body1280valid
470.0ms1858×body640valid
153.0ms928×body320valid
56.0ms477×body160valid
26.0ms365×body80valid