Details

Time bar (total: 11.8s)

sample524.0ms

Algorithm
intervals
Results
127.0ms60×body2560valid
62.0ms85×body1280valid
25.0ms59×body640valid
6.0ms23×body320valid
4.0ms20×body160valid
1.0ms9×body80valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0135
1175
2195
3195

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
1.1b
(- x (sin x))
1.1b
(- x (tan x))

rewrite27.0ms

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 (sin x))
6.0ms
(- x (tan x))

series175.0ms

Counts
3 → 9
Calls
3 calls:
76.0ms
(/ (- x (sin x)) (- x (tan x)))
30.0ms
(- x (sin x))
68.0ms
(- x (tan x))

simplify56.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
04721059
11737854
25001854

prune240.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
1.1b
(- x (sin x))
1.5b
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
26.8b
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

rewrite17.0ms

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))
10.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
0.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series1.1s

Counts
4 → 12
Calls
4 calls:
184.0ms
(cbrt x)
31.0ms
(- x (sin x))
521.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
331.0ms
(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

prune259.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
1.5b
(/ (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (sin x))) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
26.8b
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))
26.8b
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (sin x)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-prod associate-/r* associate-/l*
2×fma-udef
1×cbrt-undiv frac-2neg pow1/3 div-exp clear-num div-inv
Counts
4 → 62
Calls
4 calls:
0.0ms
(cbrt x)
2.0ms
(/ (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (sin x))) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
0.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))
0.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (sin x)))

series1.5s

Counts
4 → 12
Calls
4 calls:
181.0ms
(cbrt x)
711.0ms
(/ (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (sin x))) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
335.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))
322.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (sin x)))

simplify70.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 3 (62.0ms)

IterNodesCost
0177970
1484863
22298803
35001754

prune227.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma 27/2800 (pow x 4) 1/2)
18.1b
(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)))

series125.0ms

Counts
2 → 6
Calls
2 calls:
81.0ms
(fma 27/2800 (pow x 4) 1/2)
43.0ms
(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify141.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
051133
1162117
2626117
33552117
45001117

prune68.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes31.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.1b

bsearch94.0ms

Steps
ItersRangePoint
8
0.007618006570916684
21.02059315853866
0.03585824700307232
11
-7.192008941699975e+16
-0.00038629318802677867
-0.036940832627954695

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02920
12920

end0.0ms

sample7.0s

Algorithm
intervals
Results
3.7s1621×body2560valid
2.0s2706×body1280valid
752.0ms1926×body640valid
232.0ms901×body320valid
101.0ms510×body160valid
43.0ms336×body80valid