Details

Time bar (total: 9.1s)

sample470.0ms

Algorithm
intervals
Results
137.0ms62×body2560valid
53.0ms77×body1280valid
14.0ms55×body640valid
4.0ms25×body320valid
3.0ms19×body80valid
2.0ms18×body160valid

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: 32.5b

Counts
2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
1.6b
(- x (sin x))
1.6b
(- x (tan 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 (sin x))
6.0ms
(- x (tan x))

series173.0ms

Counts
3 → 9
Calls
3 calls:
75.0ms
(/ (- x (sin x)) (- x (tan x)))
36.0ms
(- x (sin x))
61.0ms
(- x (tan x))

simplify56.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
04721059
11737854
25001854

prune219.0ms

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:

0.1b
(fma 27/2800 (pow x 4) 1/2)
14.1b
(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)))

series126.0ms

Counts
2 → 6
Calls
2 calls:
82.0ms
(fma 27/2800 (pow x 4) 1/2)
44.0ms
(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify146.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
051133
1162117
2626117
33552117
45001117

prune67.0ms

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

localize16.0ms

Local error

Found 4 expressions with local error:

1.6b
(- x (sin x))
1.6b
(- x (tan x))
1.6b
(- x (tan x))
1.6b
(- x (tan x))

rewrite19.0ms

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

series179.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(- x (sin x))
51.0ms
(- x (tan x))
48.0ms
(- x (tan x))
51.0ms
(- x (tan x))

simplify94.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 3 (85.0ms)

IterNodesCost
0258979
1749615
23295579
35001411

prune279.0ms

Filtered
124 candidates to 75 candidates (60.5%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1240124
Fresh022
Picked011
Done011
Total1244128

Merged error: 0.0b

Counts
128 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan x) (tan x))
1.6b
(- x (sin x))
1.6b
(- (* x x) (* (tan x) (tan x)))
13.0b
(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
29×add-sqr-sqrt
25×add-cube-cbrt
16×times-frac
11×pow1
10×prod-diff
8×add-exp-log add-cbrt-cube add-log-exp
7×difference-of-squares
5×distribute-lft-out
4×tan-quot expm1-log1p-u fma-neg associate-/r* log1p-expm1-u associate-/l*
3×flip3-- swap-sqr associate-*r* associate-*l* flip--
2×sub-neg diff-log associate-/r/ associate-/l/
1×cbrt-undiv pow2 frac-times frac-2neg flip3-+ pow-plus div-sub associate-*r/ div-exp pow-prod-down associate-*l/ prod-exp clear-num pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ div-inv distribute-lft-out-- unswap-sqr
Counts
4 → 118
Calls
4 calls:
5.0ms
(* (tan x) (tan x))
6.0ms
(- x (sin x))
4.0ms
(- (* x x) (* (tan x) (tan x)))
8.0ms
(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))

series287.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (tan x) (tan x))
33.0ms
(- x (sin x))
82.0ms
(- (* x x) (* (tan x) (tan x)))
139.0ms
(/ (- (* x x) (* (tan x) (tan x))) (+ x (tan x)))

simplify70.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
04971072
12197909
25001904

prune242.0ms

Filtered
130 candidates to 89 candidates (68.5%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1300130
Fresh011
Picked011
Done022
Total1304134

Merged error: 0.0b

Counts
134 → 4

regimes33.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.8b

bsearch80.0ms

Steps
ItersRangePoint
9
0.006602375602419948
2408.9151023461654
0.03184416870118442
10
-7888799.454350161
-0.0014566459989916651
-0.028761646689302346

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03228
13228

end0.0ms

sample6.5s

Algorithm
intervals
Results
4.1s1635×body2560valid
1.5s2712×body1280valid
480.0ms1897×body640valid
147.0ms922×body320valid
63.0ms494×body160valid
24.0ms340×body80valid

Profiling

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