Details

Time bar (total: 11.2s)

sample100.0ms

Algorithm
intervals
Results
40.0ms772×body80nan
10.0ms183×body80valid
8.0ms27×body640valid
4.0ms24×body320valid
3.0ms4×body1280valid
2.0ms18×body160valid

simplify131.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0269
1499
21189
32569
45339
512509
626379
742979
845739
945889
1045889

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- z 1.0) (log (- 1.0 y)))
0.0b
(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
0.1b
(* (- x 1.0) (log y))
4.8b
(log (- 1.0 y))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
25×*-un-lft-identity
21×log-prod
13×add-cube-cbrt
11×pow1
10×associate-*l*
9×add-exp-log add-log-exp
8×distribute-rgt-in distribute-lft-in associate-*r* add-cbrt-cube
6×distribute-lft-out-- difference-of-squares
4×flip3-- associate-*l/ flip--
3×log-pow
2×log-div diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg rem-log-exp associate--l+ sum-log
Counts
4 → 94
Calls
4 calls:
16.0ms
(* (- z 1.0) (log (- 1.0 y)))
35.0ms
(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
11.0ms
(* (- x 1.0) (log y))
2.0ms
(log (- 1.0 y))

series299.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (- z 1.0) (log (- 1.0 y)))
157.0ms
(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
58.0ms
(* (- x 1.0) (log y))
42.0ms
(log (- 1.0 y))

simplify50.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0498803
11805714
25001701

prune330.0ms

Filtered
106 candidates to 75 candidates (70.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
0.0b
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0b
(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.1b
(* (- x 1.0) (log y))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
92×add-sqr-sqrt
80×times-frac
78×associate-*r*
56×unpow-prod-down
55×*-un-lft-identity
46×add-cube-cbrt
31×add-exp-log
24×unpow2 sqr-pow
19×unswap-sqr
13×associate-*l* add-cbrt-cube
12×pow1 log-prod prod-exp
9×div-exp add-log-exp
8×distribute-rgt-in flip3-- distribute-lft-in flip--
7×associate--l+
6×pow-to-exp pow-exp
5×distribute-lft-out--
4×frac-times associate-*l/ cbrt-unprod difference-of-squares
3×sub-neg associate-*r/ pow-prod-down *-commutative
2×diff-log log-pow
1×cbrt-undiv sum-log div-inv
Counts
4 → 196
Calls
4 calls:
40.0ms
(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
26.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
36.0ms
(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
11.0ms
(* (- x 1.0) (log y))

series435.0ms

Counts
4 → 12
Calls
4 calls:
256.0ms
(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
54.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
63.0ms
(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
61.0ms
(* (- x 1.0) (log y))

simplify113.0ms

Algorithm
egg-herbie
Counts
208 → 208
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
010201850
145671639
250021636

prune782.0ms

Filtered
208 candidates to 134 candidates (64.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
0.1b
(* (- x 1.0) (log y))
0.1b
(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.4b
(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
32×frac-times
29×add-sqr-sqrt
26×*-un-lft-identity
22×flip3-- flip--
20×associate-*r*
18×associate-*l/
17×pow1
15×sqrt-prod
13×add-exp-log flip3-+ add-cbrt-cube flip-+
12×add-cube-cbrt
11×associate-*l*
10×associate-*r/
6×distribute-rgt-in log-prod distribute-lft-in difference-of-squares
5×pow-prod-down prod-exp cbrt-unprod distribute-lft-out--
4×add-log-exp
3×log-pow *-commutative distribute-lft-out
2×sub-neg sqrt-div unswap-sqr
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 132
Calls
4 calls:
3.0ms
(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
12.0ms
(* (- x 1.0) (log y))
44.0ms
(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
81.0ms
(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series560.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
56.0ms
(* (- x 1.0) (log y))
157.0ms
(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
278.0ms
(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify129.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09322872
149352520
250022520

prune794.0ms

Filtered
144 candidates to 109 candidates (75.7%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.5b
(pow (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) 3)
2.8b
(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (pow (sqrt (log 1.0)) 3) (pow (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) 3)))
22.2b
(/ (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (pow (sqrt (log 1.0)) 3) (pow (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) 3))) (+ (* (sqrt (log 1.0)) (sqrt (log 1.0))) (+ (* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (* (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))

rewrite334.0ms

Algorithm
rewrite-expression-head
Rules
92×add-sqr-sqrt
64×sqrt-prod
60×frac-times
59×associate-*r*
42×unpow-prod-down *-un-lft-identity cube-prod
36×flip3-- flip-- difference-of-squares
30×pow1 associate-*l/
26×flip3-+ flip-+ associate-/l/
21×add-exp-log add-cbrt-cube
20×add-cube-cbrt
18×associate-*r/
14×sqrt-div
13×distribute-lft-out-- sqr-pow
9×sqrt-pow1 pow1/2
8×swap-sqr
7×associate-*l* prod-exp cbrt-unprod
6×pow-prod-down
5×pow-prod-up
4×log-pow add-log-exp unswap-sqr
3×cbrt-undiv pow-unpow pow-pow times-frac div-exp associate-/r* pow-sqr
2×cube-div distribute-rgt-in sub-neg distribute-lft-in associate-/r/ *-commutative
1×difference-cubes pow2 cube-mult pow-to-exp frac-2neg pow-plus sqrt-unprod unpow3 pow-exp clear-num rem-square-sqrt sqrt-pow2 div-inv associate-/l* rem-cube-cbrt
Counts
4 → 240
Calls
4 calls:
19.0ms
(* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
5.0ms
(pow (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) 3)
156.0ms
(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (pow (sqrt (log 1.0)) 3) (pow (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) 3)))
138.0ms
(/ (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (pow (sqrt (log 1.0)) 3) (pow (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) 3))) (+ (* (sqrt (log 1.0)) (sqrt (log 1.0))) (+ (* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (* (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))

series1.7s

Counts
4 → 12
Calls
4 calls:
102.0ms
(* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
119.0ms
(pow (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) 3)
469.0ms
(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (pow (sqrt (log 1.0)) 3) (pow (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) 3)))
1.1s
(/ (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (pow (sqrt (log 1.0)) 3) (pow (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) 3))) (+ (* (sqrt (log 1.0)) (sqrt (log 1.0))) (+ (* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (* (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))

simplify105.0ms

Algorithm
egg-herbie
Counts
252 → 252
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
014777685
150037199

prune1.4s

Filtered
252 candidates to 148 candidates (58.7%)
Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes531.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03428
13428

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.2s23975×body80nan
328.0ms5915×body80valid
224.0ms726×body640valid
170.0ms279×body1280valid
134.0ms702×body320valid
47.0ms403×body160valid