Details

Time bar (total: 14.7s)

sample22.0ms

Algorithm
intervals
Results
7.0ms65×body1280valid
5.0ms131×body80valid
3.0ms33×body640valid
1.0ms22×body320valid
0.0ms5×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

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ x (+ x 1.0))
2.1b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
65×*-un-lft-identity
32×times-frac
23×add-sqr-sqrt
13×distribute-lft-out--
12×distribute-lft-out
11×add-cube-cbrt
4×add-exp-log associate-/r* add-cbrt-cube add-log-exp difference-of-squares
3×associate-/l*
2×pow1 associate-/r/
1×cbrt-undiv sub-neg flip3-- frac-2neg flip3-+ diff-log div-exp clear-num frac-sub flip-- flip-+ div-inv
Counts
2 → 59
Calls
2 calls:
5.0ms
(/ x (+ x 1.0))
57.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series166.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(/ x (+ x 1.0))
130.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify126.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0266459
1872434
23587429
35001429

prune121.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b
(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
2.1b
(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
347×*-un-lft-identity
204×times-frac
107×distribute-lft-out
79×add-sqr-sqrt
67×add-cube-cbrt
24×swap-sqr
20×add-exp-log add-cbrt-cube distribute-lft-out--
18×associate-*r* associate-*l* frac-sub
16×associate-/r*
14×difference-of-squares
13×frac-times associate-*r/ associate-*l/ associate-/r/
11×pow1 associate-/l/
7×associate-/l*
6×cbrt-undiv flip3-+ div-exp flip-+ div-inv add-log-exp
4×prod-exp cbrt-unprod unswap-sqr
2×flip3-- frac-2neg clear-num flip--
1×pow2 sub-neg pow-plus diff-log div-sub pow-prod-down frac-add pow-sqr *-commutative pow-prod-up
Counts
4 → 234
Calls
4 calls:
5.0ms
(/ x (+ x 1.0))
32.0ms
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
114.0ms
(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
10.0ms
(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series639.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ x (+ x 1.0))
43.0ms
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
349.0ms
(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
208.0ms
(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify153.0ms

Algorithm
egg-herbie
Counts
246 → 246
Iterations

Useful iterations: 2 (120.0ms)

IterNodesCost
09003737
147343531
250013518

prune380.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) (* (- x 1.0) (- x 1.0)))
0.1b
(* (* (+ x 1.0) (+ x 1.0)) (* (- x 1.0) (- x 1.0)))
0.1b
(* (* (+ x 1.0) (+ x 1.0)) (* (+ x 1.0) (+ x 1.0)))
26.3b
(- (* (* x x) (* (- x 1.0) (- x 1.0))) (* (* (+ x 1.0) (+ x 1.0)) (* (+ x 1.0) (+ x 1.0))))

rewrite354.0ms

Algorithm
rewrite-expression-head
Rules
1684×frac-times
1250×associate-*r/
1026×flip3-+ flip-+
640×frac-sub
602×associate-*l/
541×flip3-- flip--
171×pow1
51×pow-prod-down
44×pow-prod-up
40×add-exp-log add-cbrt-cube
32×distribute-rgt-in distribute-lft-in
26×pow-plus pow-sqr
24×prod-exp cbrt-unprod
17×pow2
13×sub-neg
8×associate--l+
6×add-log-exp
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate--r+
3×associate-*r* associate-*l* *-commutative unswap-sqr
1×diff-log swap-sqr
Counts
4 → 973
Calls
4 calls:
26.0ms
(* (* x x) (* (- x 1.0) (- x 1.0)))
46.0ms
(* (* (+ x 1.0) (+ x 1.0)) (* (- x 1.0) (- x 1.0)))
43.0ms
(* (* (+ x 1.0) (+ x 1.0)) (* (+ x 1.0) (+ x 1.0)))
79.0ms
(- (* (* x x) (* (- x 1.0) (- x 1.0))) (* (* (+ x 1.0) (+ x 1.0)) (* (+ x 1.0) (+ x 1.0))))

series190.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (* x x) (* (- x 1.0) (- x 1.0)))
87.0ms
(* (* (+ x 1.0) (+ x 1.0)) (* (- x 1.0) (- x 1.0)))
26.0ms
(* (* (+ x 1.0) (+ x 1.0)) (* (+ x 1.0) (+ x 1.0)))
36.0ms
(- (* (* x x) (* (- x 1.0) (- x 1.0))) (* (* (+ x 1.0) (+ x 1.0)) (* (+ x 1.0) (+ x 1.0))))

simplify382.0ms

Algorithm
egg-herbie
Counts
985 → 985
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
0500139198

prune4.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) (* (- x 1.0) (- x 1.0)))
0.1b
(* (* (+ x 1.0) (+ x 1.0)) (* (+ x 1.0) (+ x 1.0)))
18.1b
(/ (* (* (+ x 1.0) (+ x 1.0)) (* (- x 1.0) (- (pow x 3) (pow 1.0 3)))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))
26.3b
(- (* (* x x) (* (- x 1.0) (- x 1.0))) (* (* (+ x 1.0) (+ x 1.0)) (* (+ x 1.0) (+ x 1.0))))

rewrite405.0ms

Algorithm
rewrite-expression-head
Rules
1684×frac-times
1250×associate-*r/
1027×flip3-+ flip-+
640×frac-sub
602×associate-*l/
541×flip3-- flip--
143×pow1
80×associate-/l/
46×add-exp-log add-cbrt-cube
40×pow-prod-up
37×pow-prod-down
24×distribute-rgt-in distribute-lft-in prod-exp pow-sqr cbrt-unprod
22×pow-plus
15×pow2
9×sub-neg
8×associate--l+
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
5×cbrt-undiv div-exp
4×associate--r+
3×times-frac associate-/r*
2×associate-*r* associate-*l* associate-/r/ *-commutative unswap-sqr
1×frac-2neg diff-log swap-sqr clear-num div-inv associate-/l*
Counts
4 → 965
Calls
4 calls:
26.0ms
(* (* x x) (* (- x 1.0) (- x 1.0)))
45.0ms
(* (* (+ x 1.0) (+ x 1.0)) (* (+ x 1.0) (+ x 1.0)))
97.0ms
(/ (* (* (+ x 1.0) (+ x 1.0)) (* (- x 1.0) (- (pow x 3) (pow 1.0 3)))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))
79.0ms
(- (* (* x x) (* (- x 1.0) (- x 1.0))) (* (* (+ x 1.0) (+ x 1.0)) (* (+ x 1.0) (+ x 1.0))))

series312.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (* x x) (* (- x 1.0) (- x 1.0)))
26.0ms
(* (* (+ x 1.0) (+ x 1.0)) (* (+ x 1.0) (+ x 1.0)))
216.0ms
(/ (* (* (+ x 1.0) (+ x 1.0)) (* (- x 1.0) (- (pow x 3) (pow 1.0 3)))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))
36.0ms
(- (* (* x x) (* (- x 1.0) (- x 1.0))) (* (* (+ x 1.0) (+ x 1.0)) (* (+ x 1.0) (+ x 1.0))))

simplify582.0ms

Algorithm
egg-herbie
Counts
977 → 977
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
0500239253

prune5.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes33.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.1b

bsearch82.0ms

Steps
ItersRangePoint
10
13.582308112339199
112933556595576.11
11108.96456866358
8
-3802813.1226859456
-118.89002763209811
-10757.158233025622

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03528
13528

end0.0ms

sample529.0ms

Algorithm
intervals
Results
187.0ms1729×body1280valid
104.0ms1200×body640valid
96.0ms4137×body80valid
38.0ms613×body320valid
14.0ms321×body160valid