Details

Time bar (total: 4.3s)

sample21.0ms

Algorithm
intervals
Results
5.0ms52×body1280valid
4.0ms45×body640valid
3.0ms132×body80valid
1.0ms16×body320valid
0.0ms11×body160valid

simplify21.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0126
1166
2196
3216
4276
5396
6586
7796
81076
91606
102776
113036
123036

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: 29.2b

Counts
2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
3.1b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
981×*-un-lft-identity
736×times-frac
585×add-sqr-sqrt
468×prod-diff
419×add-cube-cbrt
189×distribute-lft-out
94×associate-/r/
90×distribute-lft-out--
81×difference-of-squares
47×div-inv
29×flip3-+ flip-+
20×flip3-- flip--
18×fma-neg
9×associate-/r*
7×add-exp-log add-cbrt-cube associate-/l*
5×add-log-exp
3×pow1 expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 596
Calls
3 calls:
5.0ms
(/ x (+ x 1.0))
7.0ms
(/ (+ x 1.0) (- x 1.0))
42.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series207.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(/ x (+ x 1.0))
36.0ms
(/ (+ x 1.0) (- x 1.0))
133.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify203.0ms

Algorithm
egg-herbie
Counts
605 → 605
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
0120818366
1368713388
2500113292

prune648.0ms

Filtered
605 candidates to 217 candidates (35.9%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New6014605
Fresh000
Picked101
Done000
Total6024606

Merged error: 0.2b

Counts
606 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))
5.9b
(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
9.0b
(- (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
15.6b
(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
303×add-sqr-sqrt
286×*-un-lft-identity
225×times-frac
144×difference-of-squares
108×unpow-prod-down cube-prod
106×associate-*l*
82×add-cube-cbrt
72×sqr-pow
57×distribute-lft-out
45×distribute-lft-out--
25×associate-/r*
18×fma-neg prod-diff
11×add-exp-log add-cbrt-cube add-log-exp
9×difference-cubes
8×flip3-+ associate-/r/ flip-+
6×pow1
5×frac-sub
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u div-inv associate-/l*
3×flip3-- associate-*r* sum-log flip--
2×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp associate-*l/ prod-exp cbrt-unprod associate-/l/ associate--r+ unswap-sqr
1×+-commutative sub-neg associate-+r+ fma-def frac-2neg diff-log pow-prod-down clear-num *-commutative
Counts
4 → 353
Calls
4 calls:
6.0ms
(+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))
21.0ms
(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
11.0ms
(- (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
34.0ms
(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

series309.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))
55.0ms
(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
164.0ms
(- (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
71.0ms
(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

simplify77.0ms

Algorithm
egg-herbie
Counts
365 → 365
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013134703
150024382

prune708.0ms

Filtered
365 candidates to 204 candidates (55.9%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New3641365
Fresh123
Picked011
Done000
Total3654369

Merged error: 0.2b

Counts
369 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1 (sqrt (+ x 1.0))) (/ x (sqrt (+ x 1.0))))
0.1b
(/ 1 (sqrt (+ x 1.0)))
0.1b
(/ x (sqrt (+ x 1.0)))
8.2b
(- (* (/ 1 (sqrt (+ x 1.0))) (/ x (sqrt (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
128×add-sqr-sqrt
126×*-un-lft-identity times-frac
74×add-cube-cbrt
67×sqrt-prod
32×add-exp-log
27×associate-*r* associate-*l*
26×prod-diff
20×add-cbrt-cube
19×distribute-lft-out
15×unswap-sqr
14×associate-/r*
11×div-exp
10×associate-/r/
8×pow1 sqrt-div prod-exp
6×cbrt-undiv associate-/l* add-log-exp
5×div-inv
4×expm1-log1p-u flip3-+ cbrt-unprod flip-+ log1p-expm1-u distribute-lft-out-- difference-of-squares
3×rec-exp pow-flip 1-exp frac-sub
2×frac-times flip3-- frac-2neg associate-*r/ associate-*l/ clear-num flip--
1×sub-neg sqrt-pow1 pow1/2 fma-neg diff-log pow-prod-down *-commutative inv-pow
Counts
4 → 239
Calls
4 calls:
30.0ms
(* (/ 1 (sqrt (+ x 1.0))) (/ x (sqrt (+ x 1.0))))
6.0ms
(/ 1 (sqrt (+ x 1.0)))
6.0ms
(/ x (sqrt (+ x 1.0)))
23.0ms
(- (* (/ 1 (sqrt (+ x 1.0))) (/ x (sqrt (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

series508.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (/ 1 (sqrt (+ x 1.0))) (/ x (sqrt (+ x 1.0))))
237.0ms
(/ 1 (sqrt (+ x 1.0)))
107.0ms
(/ x (sqrt (+ x 1.0)))
132.0ms
(- (* (/ 1 (sqrt (+ x 1.0))) (/ x (sqrt (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

simplify56.0ms

Algorithm
egg-herbie
Counts
251 → 251
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
011112920
150012465

prune336.0ms

Filtered
251 candidates to 140 candidates (55.8%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New2510251
Fresh022
Picked011
Done011
Total2514255

Merged error: 0.2b

Counts
255 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 1.0 (pow x 2) (fma 3.0 x 1.0))
0.1b
(fma 3.0 x 1.0)

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 1.0 (pow x 2) (fma 3.0 x 1.0))
1.0ms
(fma 3.0 x 1.0)

series52.0ms

Counts
2 → 6
Calls
2 calls:
21.0ms
(fma 1.0 (pow x 2) (fma 3.0 x 1.0))
30.0ms
(fma 3.0 x 1.0)

simplify117.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 4 (114.0ms)

IterNodesCost
04387
113777
262677
3388877
4500174

prune49.0ms

Filtered
26 candidates to 21 candidates (80.8%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New26026
Fresh011
Picked011
Done022
Total26430

Merged error: 0.2b

Counts
30 → 4

regimes30.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 30.0b

bsearch88.0ms

Steps
ItersRangePoint
9
0.06406876111163662
2027774.326345067
11213.051466178713
8
-27949.393755151574
-3.7752751361666412
-8835.708508846454

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05325
16425
27725
37925
47925

end0.0ms

sample536.0ms

Algorithm
intervals
Results
181.0ms1665×body1280valid
102.0ms1235×body640valid
101.0ms4147×body80valid
45.0ms630×body320valid
14.0ms323×body160valid