Details

Time bar (total: 8.5s)

sample26.0ms

Algorithm
intervals
Results
7.0ms53×body1280valid
6.0ms128×body80valid
4.0ms41×body640valid
2.0ms26×body320valid
0.0ms8×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: 30.3b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ x (+ x 1.0))
3.2b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite108.0ms

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))
47.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series162.0ms

Counts
2 → 6
Calls
2 calls:
32.0ms
(/ x (+ x 1.0))
130.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify203.0ms

Algorithm
egg-herbie
Counts
555 → 555
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
0113418061
1329513091
2500112855

prune570.0ms

Filtered
555 candidates to 173 candidates (31.2%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New5505555
Fresh000
Picked101
Done000
Total5515556

Merged error: 0.2b

Counts
556 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
0.0b
(/ x (+ x 1.0))
3.2b
(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
3.2b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite422.0ms

Algorithm
rewrite-expression-head
Rules
2780×*-un-lft-identity
2100×times-frac
1656×add-sqr-sqrt
1404×prod-diff
1188×add-cube-cbrt
940×exp-sum
535×distribute-lft-out
473×log-prod
268×associate-/r/
255×distribute-lft-out--
228×difference-of-squares
134×div-inv
80×flip3-+ flip-+
55×flip3-- flip--
32×exp-prod
18×fma-neg
17×log-pow
9×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u associate-/r* log1p-expm1-u
3×sub-neg associate-/l*
2×exp-diff diff-log rem-exp-log
1×cbrt-undiv log-div frac-2neg div-exp rem-log-exp clear-num frac-sub
Counts
4 → 1548
Calls
4 calls:
71.0ms
(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
5.0ms
(/ x (+ x 1.0))
88.0ms
(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
47.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series442.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
35.0ms
(/ x (+ x 1.0))
127.0ms
(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
134.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify513.0ms

Algorithm
egg-herbie
Counts
1560 → 1560
Iterations

Useful iterations: 2 (99.0ms)

IterNodesCost
0180554466
1443842811
2500142721

prune1.7s

Filtered
1560 candidates to 461 candidates (29.6%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New155911560
Fresh134
Picked011
Done000
Total156051565

Merged error: 0.2b

Counts
1565 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (/ x (+ x 1.0)))
0.3b
(cbrt (/ x (+ x 1.0)))
0.3b
(cbrt (/ x (+ x 1.0)))
3.2b
(- (* (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0)))) (pow (/ (cbrt (+ x 1.0)) (cbrt (- x 1.0))) 3))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
188×cbrt-prod
169×*-un-lft-identity
148×times-frac
130×prod-diff
119×add-sqr-sqrt
91×add-cube-cbrt
62×unpow-prod-down cube-prod
25×distribute-lft-out
19×cbrt-div
14×distribute-lft-out-- difference-of-squares
10×associate-/r/
7×cube-div frac-sub
6×add-log-exp
5×frac-times associate-*l/ div-inv
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×flip3-- flip3-+ pow1/3 associate-*r/ flip-- flip-+
1×difference-cubes cube-mult sub-neg fma-neg diff-log unpow3 pow3 sqr-pow
Counts
4 → 240
Calls
4 calls:
5.0ms
(cbrt (/ x (+ x 1.0)))
5.0ms
(cbrt (/ x (+ x 1.0)))
5.0ms
(cbrt (/ x (+ x 1.0)))
63.0ms
(- (* (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0)))) (pow (/ (cbrt (+ x 1.0)) (cbrt (- x 1.0))) 3))

series583.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(cbrt (/ x (+ x 1.0)))
151.0ms
(cbrt (/ x (+ x 1.0)))
152.0ms
(cbrt (/ x (+ x 1.0)))
133.0ms
(- (* (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0)))) (pow (/ (cbrt (+ x 1.0)) (cbrt (- x 1.0))) 3))

simplify105.0ms

Algorithm
egg-herbie
Counts
252 → 252
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
016069008
150016891

prune620.0ms

Filtered
252 candidates to 119 candidates (47.2%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2502252
Fresh123
Picked101
Done011
Total2525257

Merged error: 0.2b

Counts
257 → 5

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (/ x (+ x 1.0)))
3.2b
(- (* (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0)))) (pow (/ (cbrt (+ x 1.0)) (cbrt (- x 1.0))) 3))
3.2b
(- (* (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0)))) (pow (/ (cbrt (+ x 1.0)) (cbrt (- x 1.0))) 3))
3.2b
(- (* (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0)))) (pow (/ (cbrt (+ x 1.0)) (cbrt (- x 1.0))) 3))

rewrite246.0ms

Algorithm
rewrite-expression-head
Rules
420×cbrt-prod
390×prod-diff
387×*-un-lft-identity
348×times-frac
285×add-sqr-sqrt
201×add-cube-cbrt
186×unpow-prod-down cube-prod
51×distribute-lft-out
49×cbrt-div
42×distribute-lft-out-- difference-of-squares
21×cube-div frac-sub
15×frac-times associate-*l/
14×associate-/r/
10×add-log-exp
9×flip3-- associate-*r/ flip--
7×div-inv
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×difference-cubes cube-mult sub-neg fma-neg diff-log unpow3 pow3 sqr-pow
1×flip3-+ pow1/3 flip-+
Counts
4 → 488
Calls
4 calls:
5.0ms
(cbrt (/ x (+ x 1.0)))
66.0ms
(- (* (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0)))) (pow (/ (cbrt (+ x 1.0)) (cbrt (- x 1.0))) 3))
63.0ms
(- (* (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0)))) (pow (/ (cbrt (+ x 1.0)) (cbrt (- x 1.0))) 3))
60.0ms
(- (* (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0)))) (pow (/ (cbrt (+ x 1.0)) (cbrt (- x 1.0))) 3))

series544.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(cbrt (/ x (+ x 1.0)))
135.0ms
(- (* (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0)))) (pow (/ (cbrt (+ x 1.0)) (cbrt (- x 1.0))) 3))
132.0ms
(- (* (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0)))) (pow (/ (cbrt (+ x 1.0)) (cbrt (- x 1.0))) 3))
130.0ms
(- (* (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0)))) (pow (/ (cbrt (+ x 1.0)) (cbrt (- x 1.0))) 3))

simplify215.0ms

Algorithm
egg-herbie
Counts
500 → 500
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0160624936
1500118737

prune1.1s

Filtered
500 candidates to 149 candidates (29.8%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New4991500
Fresh033
Picked101
Done011
Total5005505

Merged error: 0.2b

Counts
505 → 5

regimes72.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 29.2b

bsearch2.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05350
16450
27750
37950
47950

end0.0ms

sample642.0ms

Algorithm
intervals
Results
233.0ms1718×body1280valid
129.0ms1226×body640valid
118.0ms4109×body80valid
50.0ms636×body320valid
17.0ms311×body160valid