Details

Time bar (total: 4.4s)

sample67.0ms

Algorithm
intervals
Results
27.0ms64×body1280valid
14.0ms54×body640valid
8.0ms23×body2560valid
4.0ms25×body320valid
3.0ms71×body80valid
2.0ms19×body160valid

simplify2.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
099
199

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 52.8b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.9b
(+ x (sqrt (+ (* x x) 1.0)))
5.1b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.7b
(sqrt (+ (* x x) 1.0))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×add-exp-log log-prod
3×flip3-+ sqrt-prod add-cbrt-cube flip-+
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow
Counts
3 → 42
Calls
3 calls:
6.0ms
(+ x (sqrt (+ (* x x) 1.0)))
6.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series19.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ x (sqrt (+ (* x x) 1.0)))
10.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

simplify33.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
05105591

prune137.0ms

Filtered
42 candidates to 51 candidates (-21.4%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New44751
Fresh000
Picked101
Done000
Total45752

Merged error: 0.1b

Counts
52 → 7

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) -1/6))
0.3b
(* (pow (/ x (sqrt 1.0)) 3) -1/6)

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
50×associate-*l*
49×add-sqr-sqrt
40×times-frac
30×add-cube-cbrt *-un-lft-identity
25×unpow-prod-down cube-prod
20×sqrt-prod
10×add-exp-log
8×unswap-sqr
4×prod-exp add-cbrt-cube add-log-exp
3×associate-*r*
2×pow1 cube-div associate-*l/ pow-exp div-inv sqr-pow
1×+-commutative cube-mult pow-to-exp flip3-+ unpow3 div-exp frac-add sum-log *-commutative cbrt-unprod flip-+
Counts
2 → 87
Calls
2 calls:
9.0ms
(+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) -1/6))
15.0ms
(* (pow (/ x (sqrt 1.0)) 3) -1/6)

series50.0ms

Counts
2 → 6
Calls
2 calls:
33.0ms
(+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) -1/6))
17.0ms
(* (pow (/ x (sqrt 1.0)) 3) -1/6)

simplify24.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 0 (16.0ms)

IterNodesCost
051291007

prune194.0ms

Filtered
51 candidates to 93 candidates (-82.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New91293
Fresh066
Picked101
Done000
Total928100

Merged error: 0.1b

Counts
100 → 8

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (/ x (sqrt 1.0)) (log (pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6)))
1.5b
(log (pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
14×log-prod
8×*-un-lft-identity
7×associate-+r+
6×add-sqr-sqrt add-cube-cbrt unpow-prod-down
3×add-exp-log rem-log-exp add-log-exp
2×pow1 add-cbrt-cube sqr-pow
1×+-commutative pow-to-exp flip3-+ pow-exp sum-log log-pow flip-+ distribute-lft-out
Counts
2 → 37
Calls
2 calls:
19.0ms
(+ (/ x (sqrt 1.0)) (log (pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6)))
9.0ms
(log (pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6))

series147.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(+ (/ x (sqrt 1.0)) (log (pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6)))
98.0ms
(log (pow (exp (pow (/ x (sqrt 1.0)) 3)) -1/6))

simplify32.0ms

Algorithm
egg-herbie
Counts
43 → 43
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
05103580

prune142.0ms

Filtered
32 candidates to 43 candidates (-34.4%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New43043
Fresh077
Picked011
Done000
Total43851

Merged error: 0.1b

Counts
51 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ x (/ 1.0 x))
0.3b
(* (pow (/ x (sqrt 1.0)) 3) 1/6)
15.8b
(+ (/ x (/ 1.0 x)) (* (pow (/ x (sqrt 1.0)) 6) -1/36))
37.0b
(/ (+ (/ x (/ 1.0 x)) (* (pow (/ x (sqrt 1.0)) 6) -1/36)) (+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) 1/6)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
124×times-frac
101×add-sqr-sqrt
82×add-cube-cbrt *-un-lft-identity
50×associate-*l*
25×unpow-prod-down cube-prod
20×sqrt-prod
19×add-exp-log
16×associate-/r*
13×add-cbrt-cube
8×div-inv unswap-sqr
6×associate-/l* add-log-exp
5×div-exp
4×pow1 cbrt-undiv prod-exp associate-/r/
3×flip3-+ associate-*r* flip-+
2×cube-div frac-2neg associate-*l/ pow-exp clear-num associate-/l/ sqr-pow
1×+-commutative cube-mult pow-to-exp unpow3 frac-add sum-log *-commutative cbrt-unprod
Counts
4 → 188
Calls
4 calls:
6.0ms
(/ x (/ 1.0 x))
14.0ms
(* (pow (/ x (sqrt 1.0)) 3) 1/6)
17.0ms
(+ (/ x (/ 1.0 x)) (* (pow (/ x (sqrt 1.0)) 6) -1/36))
25.0ms
(/ (+ (/ x (/ 1.0 x)) (* (pow (/ x (sqrt 1.0)) 6) -1/36)) (+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) 1/6)))

series96.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(/ x (/ 1.0 x))
17.0ms
(* (pow (/ x (sqrt 1.0)) 3) 1/6)
44.0ms
(+ (/ x (/ 1.0 x)) (* (pow (/ x (sqrt 1.0)) 6) -1/36))
33.0ms
(/ (+ (/ x (/ 1.0 x)) (* (pow (/ x (sqrt 1.0)) 6) -1/36)) (+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) 1/6)))

simplify63.0ms

Algorithm
egg-herbie
Counts
200 → 200
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
049893075
149893075

prune643.0ms

Filtered
134 candidates to 200 candidates (-49.3%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1991200
Fresh066
Picked011
Done011
Total1999208

Merged error: 0.1b

Counts
208 → 9

regimes140.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.7b

bsearch34.0ms

Steps
ItersRangePoint
9
0.009971872296741319
901.3230478674768
0.9623652222862653
9
-174458.2165831976
-0.46594774775336223
-0.9999789100910194

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04960
14960

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.0s2379×body1280valid
469.0ms798×body2560valid
414.0ms1562×body640valid
125.0ms770×body320valid
93.0ms2070×body80valid
42.0ms421×body160valid

Profiling

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