Details

Time bar (total: 6.7s)

sample20.0ms

Algorithm
intervals
Results
4.0ms42×body1280valid
3.0ms42×body640valid
3.0ms140×body80valid
1.0ms17×body320valid
1.0ms15×body160valid

simplify22.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
4.7b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite207.0ms

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:
10.0ms
(/ x (+ x 1.0))
24.0ms
(/ (+ x 1.0) (- x 1.0))
120.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series199.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(/ x (+ x 1.0))
37.0ms
(/ (+ x 1.0) (- x 1.0))
129.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify191.0ms

Algorithm
egg-herbie
Counts
605 → 605
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
0120818366
1368713388
2500113292

prune737.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b
(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
4.7b
(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite258.0ms

Algorithm
rewrite-expression-head
Rules
356×*-un-lft-identity
220×times-frac
160×add-sqr-sqrt
96×add-cube-cbrt
76×distribute-lft-out
72×swap-sqr
44×associate-*r* associate-*l*
36×distribute-lft-out--
28×add-exp-log add-cbrt-cube
21×difference-of-squares
18×pow1 fma-def associate-/r/
9×frac-sub div-inv
8×cbrt-undiv frac-times associate-*r/ div-exp associate-*l/ prod-exp cbrt-unprod add-log-exp unswap-sqr
6×flip3-+ flip-+
5×flip3-- flip--
4×expm1-log1p-u log1p-expm1-u
2×pow2 pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up
1×+-commutative sub-neg fma-neg diff-log prod-diff frac-add sum-log
Counts
4 → 287
Calls
4 calls:
84.0ms
(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
83.0ms
(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
53.0ms
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
22.0ms
(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series407.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
49.0ms
(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
45.0ms
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
218.0ms
(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify56.0ms

Algorithm
egg-herbie
Counts
299 → 299
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
011922826
150012626

prune475.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
4.7b
(log (exp (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))))
4.7b
(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite238.0ms

Algorithm
rewrite-expression-head
Rules
298×*-un-lft-identity
192×times-frac
154×add-sqr-sqrt
90×add-cube-cbrt
72×swap-sqr
56×distribute-lft-out
44×associate-*r* associate-*l*
32×distribute-lft-out--
28×add-exp-log add-cbrt-cube
22×difference-of-squares
19×pow1
16×associate-/r/
9×frac-sub
8×cbrt-undiv frac-times associate-*r/ div-exp associate-*l/ prod-exp cbrt-unprod div-inv unswap-sqr
6×log-prod add-log-exp
5×flip3-- log-pow flip--
4×expm1-log1p-u exp-prod flip3-+ flip-+ log1p-expm1-u
3×exp-sum
2×pow2 sub-neg pow-plus prod-diff pow-prod-down pow-sqr *-commutative pow-prod-up
1×log-div exp-diff fma-neg diff-log rem-log-exp
Counts
4 → 268
Calls
4 calls:
83.0ms
(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
52.0ms
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
63.0ms
(log (exp (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))))
22.0ms
(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series499.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
45.0ms
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
201.0ms
(log (exp (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))))
202.0ms
(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify56.0ms

Algorithm
egg-herbie
Counts
280 → 280
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
011633075
150012811

prune530.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

5.1b
(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
12.8b
(+ (- (+ (pow x 2) (fma 1.0 1.0 (* x 1.0)))) (fma x x (fma 1.0 1.0 (* x 1.0))))
17.8b
(/ (* (fma x x (fma 1.0 1.0 (* x 1.0))) (+ x 1.0)) (- (pow x 3) (pow 1.0 3)))
20.0b
(- (* (/ 1 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ x (cbrt (+ x 1.0)))) (/ (* (fma x x (fma 1.0 1.0 (* x 1.0))) (+ x 1.0)) (- (pow x 3) (pow 1.0 3))))

rewrite398.0ms

Algorithm
rewrite-expression-head
Rules
234×add-sqr-sqrt
185×*-un-lft-identity
150×times-frac
128×difference-of-squares
96×unpow-prod-down cube-prod
64×sqr-pow
50×associate-/r*
42×add-cube-cbrt
40×distribute-lft-out--
32×distribute-lft-out
31×prod-diff
13×add-log-exp
12×fma-def
11×add-exp-log add-cbrt-cube
8×difference-cubes
6×distribute-rgt-neg-in associate-/r/
5×associate-/l*
4×pow1 distribute-lft-neg-in expm1-log1p-u flip3-- sum-log flip-- log1p-expm1-u associate-/l/
3×cbrt-undiv flip3-+ associate-*r/ div-exp frac-sub flip-+ div-inv
2×frac-2neg neg-log clear-num
1×+-commutative neg-sub0 frac-times associate-+l- neg-mul-1 sub-neg associate-+l+ associate-+r+ distribute-neg-in fma-neg diff-log associate-*l/ prod-exp cbrt-unprod fma-udef
Counts
4 → 300
Calls
4 calls:
53.0ms
(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
123.0ms
(+ (- (+ (pow x 2) (fma 1.0 1.0 (* x 1.0)))) (fma x x (fma 1.0 1.0 (* x 1.0))))
47.0ms
(/ (* (fma x x (fma 1.0 1.0 (* x 1.0))) (+ x 1.0)) (- (pow x 3) (pow 1.0 3)))
159.0ms
(- (* (/ 1 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ x (cbrt (+ x 1.0)))) (/ (* (fma x x (fma 1.0 1.0 (* x 1.0))) (+ x 1.0)) (- (pow x 3) (pow 1.0 3))))

series438.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
102.0ms
(+ (- (+ (pow x 2) (fma 1.0 1.0 (* x 1.0)))) (fma x x (fma 1.0 1.0 (* x 1.0))))
74.0ms
(/ (* (fma x x (fma 1.0 1.0 (* x 1.0))) (+ x 1.0)) (- (pow x 3) (pow 1.0 3)))
205.0ms
(- (* (/ 1 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ x (cbrt (+ x 1.0)))) (/ (* (fma x x (fma 1.0 1.0 (* x 1.0))) (+ x 1.0)) (- (pow x 3) (pow 1.0 3))))

simplify68.0ms

Algorithm
egg-herbie
Counts
312 → 312
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011494959
150014330

prune1.1s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

regimes38.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 29.3b

bsearch94.0ms

Steps
ItersRangePoint
10
0.43775957865898985
3845520655822.575
10654.135862899073
7
-245561.44084452273
-3096.4512561506854
-15340.90493740389

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06049
17149
28549
38749
48749

end0.0ms

sample546.0ms

Algorithm
intervals
Results
182.0ms1703×body1280valid
102.0ms1237×body640valid
89.0ms4103×body80valid
41.0ms642×body320valid
13.0ms315×body160valid