Details

Time bar (total: 4.6s)

sample36.0ms

Algorithm
intervals
Results
7.0ms256×pre80true
6.0ms240×pre80false
5.0ms256×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0103
1123
2123

prune2.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 8.0b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.0b
(/ x0 (- 1.0 x1))
7.2b
(- (/ x0 (- 1.0 x1)) x0)

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
16×times-frac
12×add-cube-cbrt
6×difference-of-squares
5×associate-/r* distribute-lft-out--
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/l*
2×pow1 flip3-- associate-/r/ flip--
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num div-inv
Counts
2 → 52
Calls
2 calls:
5.0ms
(/ x0 (- 1.0 x1))
10.0ms
(- (/ x0 (- 1.0 x1)) x0)

series12.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(/ x0 (- 1.0 x1))
6.0ms
(- (/ x0 (- 1.0 x1)) x0)

simplify90.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0244328
1801315
23109310
35001310

prune66.0ms

Filtered
58 candidates to 44 candidates (24.1%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New56258
Fresh000
Picked101
Done000
Total57259

Merged error: 6.9b

Counts
59 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
1.0b
(/ x0 (- 1.0 x1))
1.0b
(/ x0 (- 1.0 x1))
6.7b
(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt
54×*-un-lft-identity
34×times-frac
26×add-cube-cbrt
20×sqrt-prod difference-of-squares
12×distribute-lft-out--
11×associate-*r*
10×add-exp-log associate-/r* add-cbrt-cube
6×pow1 flip3-- flip-- associate-/l* add-log-exp
5×associate-*l*
4×frac-times associate-/r/
3×sub-neg flip3-+ flip-+
2×cbrt-undiv distribute-rgt-in frac-2neg distribute-lft-in associate-*r/ div-exp associate-*l/ clear-num div-inv distribute-lft-out
1×diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 134
Calls
4 calls:
31.0ms
(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
5.0ms
(/ x0 (- 1.0 x1))
5.0ms
(/ x0 (- 1.0 x1))
16.0ms
(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

series59.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))
5.0ms
(/ x0 (- 1.0 x1))
5.0ms
(/ x0 (- 1.0 x1))
12.0ms
(- (sqrt (/ x0 (- 1.0 x1))) (sqrt x0))

simplify64.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04791254
122181139
250021119

prune220.0ms

Filtered
146 candidates to 106 candidates (27.4%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1442146
Fresh101
Picked101
Done000
Total1462148

Merged error: 5.6b

Counts
148 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ x0 (- 1.0 x1))
1.0b
(/ x0 (- 1.0 x1))
1.0b
(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (/ (- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)) (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))))
5.5b
(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
487×add-sqr-sqrt
262×times-frac
200×difference-of-squares
194×sqrt-prod
191×associate-*r*
182×*-un-lft-identity
168×unpow-prod-down cube-prod
90×add-cube-cbrt
56×sqr-pow
44×distribute-lft-out--
13×add-exp-log add-cbrt-cube
10×associate-/r*
8×associate-/r/
6×pow1 associate-/l* add-log-exp
5×associate-*l*
4×difference-cubes flip3-+ associate-*l/ flip-+
3×cbrt-undiv flip3-- div-exp flip-- div-inv
2×frac-times frac-2neg sqrt-div frac-add prod-exp clear-num cbrt-unprod distribute-lft-out unswap-sqr
1×sub-neg diff-log associate-*r/ pow-prod-down *-commutative
Counts
4 → 360
Calls
4 calls:
5.0ms
(/ x0 (- 1.0 x1))
5.0ms
(/ x0 (- 1.0 x1))
115.0ms
(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (/ (- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)) (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))))
49.0ms
(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))

series183.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ x0 (- 1.0 x1))
6.0ms
(/ x0 (- 1.0 x1))
148.0ms
(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (/ (- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)) (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))))
25.0ms
(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))

simplify91.0ms

Algorithm
egg-herbie
Counts
372 → 372
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
011287105
150016887

prune800.0ms

Filtered
372 candidates to 163 candidates (56.2%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New3702372
Fresh101
Picked101
Done000
Total3722374

Merged error: 4.7b

Counts
374 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ x0 (- 1.0 x1))
1.0b
(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (/ (- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)) (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))))
5.5b
(log (exp (* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (/ (- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)) (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))))))
5.5b
(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
470×add-sqr-sqrt
247×times-frac
196×difference-of-squares
194×sqrt-prod
191×associate-*r*
168×unpow-prod-down cube-prod
165×*-un-lft-identity
81×add-cube-cbrt
56×sqr-pow
40×distribute-lft-out--
11×add-exp-log add-cbrt-cube
9×add-log-exp
7×pow1
6×associate-/r/
5×associate-*l* associate-/r*
4×difference-cubes flip3-+ associate-*l/ log-pow flip-+
3×log-prod associate-/l*
2×cbrt-undiv frac-times flip3-- exp-to-pow sqrt-div div-exp frac-add prod-exp flip-- cbrt-unprod div-inv distribute-lft-out unswap-sqr
1×sub-neg exp-prod frac-2neg diff-log associate-*r/ rem-log-exp pow-prod-down clear-num sum-log *-commutative
Counts
4 → 338
Calls
4 calls:
5.0ms
(/ x0 (- 1.0 x1))
115.0ms
(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (/ (- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)) (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))))
14.0ms
(log (exp (* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (/ (- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)) (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))))))
49.0ms
(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))

series317.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ x0 (- 1.0 x1))
142.0ms
(* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (/ (- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)) (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))))
140.0ms
(log (exp (* (+ (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)) (/ (- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3)) (+ (+ (/ x0 (- 1.0 x1)) x0) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt x0)))))))
30.0ms
(- (pow (sqrt (/ x0 (- 1.0 x1))) 3) (pow (sqrt x0) 3))

simplify88.0ms

Algorithm
egg-herbie
Counts
350 → 350
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011547412
150017140

prune856.0ms

Filtered
350 candidates to 148 candidates (57.7%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New3500350
Fresh011
Picked011
Done000
Total3502352

Merged error: 4.7b

Counts
352 → 2

regimes93.0ms

Accuracy

100% (0.0b remaining)

Error of 5.1b against oracle of 5.1b and baseline of 7.0b

bsearch13.0ms

Steps
ItersRangePoint
7
0.000209
0.0186
0.018204597656249998

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03453
13453

end0.0ms

sample1.0s

Algorithm
intervals
Results
203.0ms7980×pre80false
202.0ms8000×pre80true
158.0ms8000×body80valid

Profiling

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