Details

Time bar (total: 13.9s)

sample21.0ms

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

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
947×*-un-lft-identity
716×times-frac
563×add-sqr-sqrt
468×prod-diff
407×add-cube-cbrt
183×distribute-lft-out
92×associate-/r/
85×distribute-lft-out--
76×difference-of-squares
46×div-inv
28×flip3-+ flip-+
19×flip3-- flip--
18×fma-neg
4×add-exp-log associate-/r* add-cbrt-cube add-log-exp
3×associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num frac-sub
Counts
2 → 549
Calls
2 calls:
5.0ms
(/ x (+ x 1.0))
76.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series166.0ms

Counts
2 → 6
Calls
2 calls:
33.0ms
(/ x (+ x 1.0))
132.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify201.0ms

Algorithm
egg-herbie
Counts
555 → 555
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
0113418061
1329513091
2500112855

prune636.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

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))))

rewrite174.0ms

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×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u unswap-sqr
2×flip3-- frac-2neg clear-num flip--
1×pow2 sub-neg pow-plus fma-neg diff-log div-sub prod-diff pow-prod-down frac-add pow-sqr *-commutative pow-prod-up
Counts
4 → 244
Calls
4 calls:
5.0ms
(/ x (+ x 1.0))
31.0ms
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
110.0ms
(/ (- (* (/ 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))))
13.0ms
(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series615.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(/ x (+ x 1.0))
44.0ms
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
337.0ms
(/ (- (* (/ 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))))
202.0ms
(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify162.0ms

Algorithm
egg-herbie
Counts
256 → 256
Iterations

Useful iterations: 2 (123.0ms)

IterNodesCost
09413870
148973641
250013640

prune413.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 2 expressions with local error:

17.1b
(/ x (- (* x x) (* 1.0 1.0)))
29.9b
(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ (+ x 1.0) (- x 1.0))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×times-frac
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×add-exp-log associate-/r* add-cbrt-cube difference-of-squares
3×associate-/l*
2×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
1×cbrt-undiv flip3-- frac-2neg div-exp clear-num flip-- fma-udef div-inv
Counts
2 → 45
Calls
2 calls:
5.0ms
(/ x (- (* x x) (* 1.0 1.0)))
0.0ms
(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ (+ x 1.0) (- x 1.0))))

series230.0ms

Counts
2 → 6
Calls
2 calls:
70.0ms
(/ x (- (* x x) (* 1.0 1.0)))
159.0ms
(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ (+ x 1.0) (- x 1.0))))

simplify36.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0258444
1979400
25001391

prune141.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
0.2b
(/ (- 1.0) (pow x 2))
0.4b
(/ 3.0 (pow x 3))
6.8b
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
5088×times-frac
4093×add-sqr-sqrt
3299×*-un-lft-identity
2862×add-cube-cbrt
2824×prod-diff
1094×associate--l+
1084×unpow-prod-down
718×distribute-rgt-neg-in
675×distribute-lft-neg-in
425×difference-of-squares
418×sqr-pow
365×unpow2
225×neg-mul-1
213×div-inv
157×cube-prod
133×distribute-lft-out--
100×fma-neg
52×cube-mult unpow3
20×associate-/r*
14×add-exp-log
13×associate-/l*
11×add-log-exp
8×add-cbrt-cube
6×div-exp
5×frac-sub
4×pow1 expm1-log1p-u diff-log log1p-expm1-u
3×sub-neg flip3-- flip--
2×cbrt-undiv associate--l- neg-sub0 pow-to-exp frac-2neg div-sub pow-exp clear-num
1×distribute-frac-neg
Counts
4 → 3166
Calls
4 calls:
118.0ms
(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
12.0ms
(/ (- 1.0) (pow x 2))
4.0ms
(/ 3.0 (pow x 3))
835.0ms
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series169.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
25.0ms
(/ (- 1.0) (pow x 2))
41.0ms
(/ 3.0 (pow x 3))
32.0ms
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify659.0ms

Algorithm
egg-herbie
Counts
3178 → 3178
Iterations

Useful iterations: 1 (57.0ms)

IterNodesCost
0426673838
1500164326

prune8.0s

Pruning

4 alts after pruning (1 fresh and 3 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

bsearch83.0ms

Steps
ItersRangePoint
10
13.582308112339199
112933556595576.11
8706.16731299591
8
-3802813.1226859456
-118.89002763209811
-11235.739542492744

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03618
13918
23918

end0.0ms

sample536.0ms

Algorithm
intervals
Results
189.0ms1729×body1280valid
102.0ms1200×body640valid
97.0ms4137×body80valid
41.0ms613×body320valid
14.0ms321×body160valid