Details

Time bar (total: 8.7s)

sample37.0ms

Algorithm
intervals
Results
17.0ms388×body80valid

simplify61.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0328
1698
21348
32258
43788
55988
68158
710358
811438
912118
1012118

prune3.0ms

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: 0.0b

Counts
2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (* a b) 4.0)
0.0b
(- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))
0.0b
(+ (* x y) (/ (* z t) 16.0))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
8×add-exp-log add-cbrt-cube
7×add-sqr-sqrt *-un-lft-identity
5×add-cube-cbrt
3×pow1 times-frac associate-/r*
2×cbrt-undiv flip3-+ diff-log div-exp sum-log frac-sub flip-+
1×+-commutative sub-neg flip3-- frac-2neg prod-exp associate--l+ clear-num flip-- cbrt-unprod div-inv associate-/l* distribute-lft-out-- difference-of-squares
Counts
3 → 50
Calls
3 calls:
4.0ms
(/ (* a b) 4.0)
9.0ms
(- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))
8.0ms
(+ (* x y) (/ (* z t) 16.0))

series164.0ms

Counts
3 → 9
Calls
3 calls:
22.0ms
(/ (* a b) 4.0)
94.0ms
(- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))
48.0ms
(+ (* x y) (/ (* z t) 16.0))

simplify42.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0301419
11260392
25002385

prune169.0ms

Filtered
59 candidates to 45 candidates (76.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New57259
Fresh000
Picked011
Done000
Total57360

Merged error: 0.0b

Counts
60 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x y) (/ (* z t) 16.0))
0.3b
(* (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))) (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))
0.5b
(sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))
0.5b
(sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
48×sqrt-div
40×add-sqr-sqrt sqrt-prod
32×*-un-lft-identity
24×frac-sub
21×pow1
16×frac-times
14×add-cube-cbrt
13×flip3-+ flip-+
12×flip3-- swap-sqr flip--
10×sqrt-pow1 pow1/2
8×associate-*r* associate-*l* distribute-lft-out--
6×add-exp-log add-cbrt-cube add-log-exp difference-of-squares
5×pow-prod-up
4×associate-*r/ associate-*l/ unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 130
Calls
4 calls:
5.0ms
(+ (* x y) (/ (* z t) 16.0))
25.0ms
(* (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))) (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))
8.0ms
(sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))
8.0ms
(sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
45.0ms
(+ (* x y) (/ (* z t) 16.0))
97.0ms
(* (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))) (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))
497.0ms
(sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))
487.0ms
(sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))

simplify79.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
04082527
116832381
250032345

prune425.0ms

Filtered
142 candidates to 84 candidates (59.2%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1411142
Fresh011
Picked011
Done011
Total1414145

Merged error: 0b

Counts
145 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (pow (sqrt (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))) 3) (sqrt (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))))
0.4b
(pow (sqrt (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))) 3)
0.5b
(sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))
0.5b
(sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
117×sqrt-prod
96×sqrt-div
84×add-sqr-sqrt
37×*-un-lft-identity
31×unpow-prod-down cube-prod
28×associate-*l*
26×frac-sub
24×cube-div unswap-sqr
23×add-cube-cbrt
16×frac-times
13×flip3-- flip3-+ flip-- flip-+
11×associate-*r*
10×pow1 add-exp-log
7×add-cbrt-cube distribute-lft-out-- difference-of-squares
6×sqrt-pow1
5×pow-pow sqr-pow
4×pow1/2 associate-*r/ associate-*l/ add-log-exp
3×pow-unpow prod-exp
2×cube-mult pow-to-exp rem-sqrt-square unpow3 pow-exp
1×pow-plus *-commutative pow-prod-up sqrt-pow2 cbrt-unprod rem-cube-cbrt
Counts
4 → 187
Calls
4 calls:
36.0ms
(* (pow (sqrt (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))) 3) (sqrt (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))))
13.0ms
(pow (sqrt (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))) 3)
9.0ms
(sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))
9.0ms
(sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))

series1.4s

Counts
4 → 12
Calls
4 calls:
96.0ms
(* (pow (sqrt (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))) 3) (sqrt (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))))
259.0ms
(pow (sqrt (sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))) 3)
500.0ms
(sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))
495.0ms
(sqrt (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)))

simplify137.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
07224211
133183807
250013582

prune698.0ms

Filtered
199 candidates to 110 candidates (55.3%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1990199
Fresh011
Picked011
Done022
Total1994203

Merged error: 0b

Counts
203 → 4

localize29.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (/ (* z t) 16.0) (- (/ (* z t) 16.0) (* x y)))
5.5b
(+ (* (- (+ (* (/ (* z t) 16.0) (- (/ (* z t) 16.0) (* x y))) (* (* x y) (* x y)))) (* a b)) (* (+ (pow (* x y) 3) (pow (/ (* z t) 16.0) 3)) 4.0))
9.7b
(* (- (+ (* (/ (* z t) 16.0) (- (/ (* z t) 16.0) (* x y))) (* (* x y) (* x y)))) (* a b))
38.3b
(/ (+ (* (- (+ (* (/ (* z t) 16.0) (- (/ (* z t) 16.0) (* x y))) (* (* x y) (* x y)))) (* a b)) (* (+ (pow (* x y) 3) (pow (/ (* z t) 16.0) 3)) 4.0)) (* 4.0 (+ (* (/ (* z t) 16.0) (- (/ (* z t) 16.0) (* x y))) (* (* x y) (* x y)))))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log add-cbrt-cube
19×associate-*l/
17×associate-*l*
14×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity flip3-+ flip-+
11×pow1
10×distribute-neg-frac
8×frac-add prod-exp cbrt-unprod
6×times-frac associate-/l/ add-log-exp
4×cbrt-undiv associate-*r/ div-exp associate-*r* pow-prod-down
3×distribute-lft-neg-in distribute-rgt-neg-in associate-/l*
2×distribute-rgt-in frac-times sub-neg flip3-- distribute-lft-in associate-/r/ *-commutative flip-- div-inv
1×+-commutative distribute-lft-neg-out neg-mul-1 frac-2neg clear-num associate-/r* sum-log unswap-sqr
Counts
4 → 107
Calls
4 calls:
13.0ms
(* (/ (* z t) 16.0) (- (/ (* z t) 16.0) (* x y)))
22.0ms
(+ (* (- (+ (* (/ (* z t) 16.0) (- (/ (* z t) 16.0) (* x y))) (* (* x y) (* x y)))) (* a b)) (* (+ (pow (* x y) 3) (pow (/ (* z t) 16.0) 3)) 4.0))
23.0ms
(* (- (+ (* (/ (* z t) 16.0) (- (/ (* z t) 16.0) (* x y))) (* (* x y) (* x y)))) (* a b))
37.0ms
(/ (+ (* (- (+ (* (/ (* z t) 16.0) (- (/ (* z t) 16.0) (* x y))) (* (* x y) (* x y)))) (* a b)) (* (+ (pow (* x y) 3) (pow (/ (* z t) 16.0) 3)) 4.0)) (* 4.0 (+ (* (/ (* z t) 16.0) (- (/ (* z t) 16.0) (* x y))) (* (* x y) (* x y)))))

series1.7s

Counts
4 → 12
Calls
4 calls:
106.0ms
(* (/ (* z t) 16.0) (- (/ (* z t) 16.0) (* x y)))
885.0ms
(+ (* (- (+ (* (/ (* z t) 16.0) (- (/ (* z t) 16.0) (* x y))) (* (* x y) (* x y)))) (* a b)) (* (+ (pow (* x y) 3) (pow (/ (* z t) 16.0) 3)) 4.0))
214.0ms
(* (- (+ (* (/ (* z t) 16.0) (- (/ (* z t) 16.0) (* x y))) (* (* x y) (* x y)))) (* a b))
456.0ms
(/ (+ (* (- (+ (* (/ (* z t) 16.0) (- (/ (* z t) 16.0) (* x y))) (* (* x y) (* x y)))) (* a b)) (* (+ (pow (* x y) 3) (pow (/ (* z t) 16.0) 3)) 4.0)) (* 4.0 (+ (* (/ (* z t) 16.0) (- (/ (* z t) 16.0) (* x y))) (* (* x y) (* x y)))))

simplify195.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
09003139
149902771
250022771

prune613.0ms

Filtered
119 candidates to 89 candidates (74.8%)
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New1190119
Fresh000
Picked011
Done033
Total1194123

Merged error: 0b

Counts
123 → 4

regimes533.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0228
1228

end0.0ms

sample1.0s

Algorithm
intervals
Results
564.0ms11945×body80valid