Details

Time bar (total: 6.0s)

sample23.0ms

Algorithm
intervals
Results
7.0ms60×body640valid
4.0ms136×body80valid
3.0ms33×body320valid
2.0ms15×body1280valid
1.0ms12×body160valid

simplify18.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1317
2437
3577
4737
5927
61267
71587
82077
92097
102097

prune2.0ms

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: 12.3b

Counts
2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (- x 1.0))
0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.0b
(/ 1.0 (+ x 1.0))
3.5b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite321.0ms

Algorithm
rewrite-expression-head
Rules
725×*-un-lft-identity
703×times-frac
524×add-sqr-sqrt
492×add-cube-cbrt
468×prod-diff
236×associate-+l+
95×distribute-lft-out
65×div-inv
58×associate-/r/
29×flip3-+ flip-+
18×fma-neg
17×distribute-lft-out--
12×difference-of-squares
11×add-log-exp
10×fma-def
9×associate-/r*
8×add-exp-log add-cbrt-cube
6×associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u
3×flip3-- frac-add flip--
2×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num sum-log frac-sub
1×+-commutative associate-+l-
Counts
4 → 618
Calls
4 calls:
5.0ms
(/ 1.0 (- x 1.0))
23.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
5.0ms
(/ 1.0 (+ x 1.0))
54.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series308.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(/ 1.0 (- x 1.0))
43.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
24.0ms
(/ 1.0 (+ x 1.0))
215.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify160.0ms

Algorithm
egg-herbie
Counts
630 → 630
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
0115610955
136078288
250017670

prune1.2s

Filtered
630 candidates to 390 candidates (61.9%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New6264630
Fresh000
Picked101
Done000
Total6274631

Merged error: 0.1b

Counts
631 → 4

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (+ x 1.0))
0.2b
(cbrt (+ x 1.0))
0.2b
(cbrt (+ x 1.0))
18.1b
(+ (fma (/ 1 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ 1.0 (cbrt (+ x 1.0))) (- (* (/ 2.0 x) 1))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 add-exp-log expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out
3×fma-def pow1/3
2×fma-udef
1×+-commutative associate-+l+ associate-+r+ sum-log
Counts
4 → 67
Calls
4 calls:
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))
3.0ms
(+ (fma (/ 1 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ 1.0 (cbrt (+ x 1.0))) (- (* (/ 2.0 x) 1))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))

series493.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(cbrt (+ x 1.0))
84.0ms
(cbrt (+ x 1.0))
85.0ms
(cbrt (+ x 1.0))
239.0ms
(+ (fma (/ 1 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ 1.0 (cbrt (+ x 1.0))) (- (* (/ 2.0 x) 1))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))

simplify45.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0386892
11320809
25002766

prune279.0ms

Filtered
79 candidates to 72 candidates (91.1%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New79079
Fresh033
Picked011
Done000
Total79483

Merged error: 0.1b

Counts
83 → 4

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (/ 2.0 x))
0.5b
(cbrt (/ 2.0 x))
0.6b
(* (cbrt (/ 2.0 x)) (cbrt (/ 2.0 x)))
23.7b
(+ (fma (* (cbrt (/ 1.0 (+ x 1.0))) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt (/ 1.0 (+ x 1.0))) (- (* (cbrt (/ 2.0 x)) (* (cbrt (/ 2.0 x)) (cbrt (/ 2.0 x)))))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
90×cbrt-prod
75×add-sqr-sqrt
60×times-frac
53×*-un-lft-identity
51×add-cube-cbrt
16×swap-sqr associate-*r* associate-*l*
11×pow1
9×unswap-sqr
8×pow1/3
6×add-exp-log cbrt-div div-inv add-log-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×fma-def
2×pow-prod-down pow-sqr pow-prod-up fma-udef
1×+-commutative pow2 frac-times associate-+l+ associate-+r+ flip3-+ pow-plus associate-*r/ associate-*l/ prod-exp sum-log *-commutative cbrt-unprod flip-+ distribute-lft-out
Counts
4 → 147
Calls
4 calls:
2.0ms
(cbrt (/ 2.0 x))
2.0ms
(cbrt (/ 2.0 x))
12.0ms
(* (cbrt (/ 2.0 x)) (cbrt (/ 2.0 x)))
3.0ms
(+ (fma (* (cbrt (/ 1.0 (+ x 1.0))) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt (/ 1.0 (+ x 1.0))) (- (* (cbrt (/ 2.0 x)) (* (cbrt (/ 2.0 x)) (cbrt (/ 2.0 x)))))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))

series965.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(cbrt (/ 2.0 x))
196.0ms
(cbrt (/ 2.0 x))
235.0ms
(* (cbrt (/ 2.0 x)) (cbrt (/ 2.0 x)))
333.0ms
(+ (fma (* (cbrt (/ 1.0 (+ x 1.0))) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt (/ 1.0 (+ x 1.0))) (- (* (cbrt (/ 2.0 x)) (* (cbrt (/ 2.0 x)) (cbrt (/ 2.0 x)))))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))

simplify61.0ms

Algorithm
egg-herbie
Counts
159 → 159
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04611626
116411495
250021378

prune554.0ms

Filtered
159 candidates to 126 candidates (79.2%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1590159
Fresh022
Picked011
Done011
Total1594163

Merged error: 0.1b

Counts
163 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3)))
0.1b
(/ 2.0 (pow x 3))
0.3b
(/ 1 (pow x 5))
0.5b
(/ 1 (pow x 7))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
61×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
36×unpow-prod-down
27×add-exp-log
26×associate-/r*
15×div-exp
12×cube-prod sqr-pow
10×add-cbrt-cube
9×associate-/l*
7×pow-to-exp pow-exp
6×rec-exp 1-exp
4×pow1 expm1-log1p-u cube-mult unpow3 log1p-expm1-u add-log-exp
3×cbrt-undiv frac-2neg clear-num div-inv
2×pow-flip inv-pow
1×fma-udef
Counts
4 → 187
Calls
4 calls:
1.0ms
(fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3)))
5.0ms
(/ 2.0 (pow x 3))
9.0ms
(/ 1 (pow x 5))
5.0ms
(/ 1 (pow x 7))

series269.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3)))
36.0ms
(/ 2.0 (pow x 3))
50.0ms
(/ 1 (pow x 5))
54.0ms
(/ 1 (pow x 7))

simplify54.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0450904
12278777
25001777

prune354.0ms

Filtered
199 candidates to 96 candidates (48.2%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New1963199
Fresh011
Picked011
Done022
Total1967203

Merged error: 0.0b

Counts
203 → 7

regimes46.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 25.4b

bsearch123.0ms

Steps
ItersRangePoint
9
2.1846438371975785e-05
719.5386143167987
99.32272563333868
10
-43540924890.08803
-0.0051836583041924315
-89.33119125302649

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04937
15837
25837

end0.0ms

sample633.0ms

Algorithm
intervals
Results
218.0ms1894×body640valid
127.0ms4157×body80valid
83.0ms544×body1280valid
81.0ms951×body320valid
26.0ms458×body160valid