Details

Time bar (total: 8.7s)

sample102.0ms

Algorithm
intervals
Results
33.0ms741×body80nan
12.0ms194×body80valid
5.0ms18×body640valid
4.0ms25×body320valid
4.0ms5×body1280valid
2.0ms18×body160valid

simplify128.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- z 1.0) (log (- 1.0 y)))
0.1b
(* (- x 1.0) (log y))
5.9b
(log (- 1.0 y))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
22×*-un-lft-identity
21×log-prod
12×add-cube-cbrt
10×pow1 associate-*l*
8×add-exp-log distribute-rgt-in distribute-lft-in associate-*r*
7×add-cbrt-cube
5×distribute-lft-out-- difference-of-squares
4×associate-*l/
3×flip3-- log-pow flip-- add-log-exp
2×log-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-log-exp
Counts
3 → 78
Calls
3 calls:
31.0ms
(* (- z 1.0) (log (- 1.0 y)))
23.0ms
(* (- x 1.0) (log y))
5.0ms
(log (- 1.0 y))

series131.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(* (- z 1.0) (log (- 1.0 y)))
53.0ms
(* (- x 1.0) (log y))
39.0ms
(log (- 1.0 y))

simplify39.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0391550
11408490
25002469

prune247.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
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)))))))
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))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
94×add-sqr-sqrt
80×times-frac
78×associate-*r*
57×*-un-lft-identity
56×unpow-prod-down
50×add-cube-cbrt
31×add-exp-log
27×flip3-- flip--
24×log-prod associate-*l/ unpow2 sqr-pow
19×unswap-sqr
16×distribute-rgt-in distribute-lft-in frac-add
13×associate-*l* add-cbrt-cube
12×pow1 frac-times prod-exp associate--l+
10×associate-+r+
9×div-exp
7×associate-*r/
6×pow-to-exp associate-+l+ pow-exp add-log-exp
4×sub-neg cbrt-unprod distribute-lft-out--
3×pow-prod-down *-commutative difference-of-squares
2×log-pow
1×cbrt-undiv +-commutative flip3-+ sum-log flip-+ div-inv
Counts
4 → 223
Calls
4 calls:
39.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
28.0ms
(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
77.0ms
(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
25.0ms
(* (- x 1.0) (log y))

series296.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
136.0ms
(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
57.0ms
(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
54.0ms
(* (- x 1.0) (log y))

simplify55.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013322812
150012662

prune941.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt flip3-- flip--
26×associate-*r/
23×*-un-lft-identity
17×associate-*l*
16×distribute-rgt-in distribute-lft-in associate-*r* frac-add
15×pow1
14×add-cube-cbrt
12×frac-times log-prod associate--l+
10×add-exp-log sub-neg associate-+r+ add-cbrt-cube
7×log-pow
6×associate-*l/ add-log-exp
5×distribute-lft-out--
4×associate-+l+ difference-of-squares
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×sqrt-pow1 pow1/2
1×+-commutative flip3-+ sum-log flip-+
Counts
4 → 140
Calls
4 calls:
27.0ms
(+ (* (log (sqrt y)) (- x 1.0)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
78.0ms
(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
25.0ms
(* (log (sqrt y)) (- x 1.0))
23.0ms
(* (log (sqrt y)) (- x 1.0))

series364.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(+ (* (log (sqrt y)) (- x 1.0)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
58.0ms
(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
64.0ms
(* (log (sqrt y)) (- x 1.0))
63.0ms
(* (log (sqrt y)) (- x 1.0))

simplify123.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (96.0ms)

IterNodesCost
08412399
145462317
250012313

prune740.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (log (sqrt y)) (- x 1.0))
0.1b
(* (log (sqrt y)) (- x 1.0))
0.1b
(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.5b
(* (* (- 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)))))))

rewrite305.0ms

Algorithm
rewrite-expression-head
Rules
32×frac-times
31×add-sqr-sqrt
27×*-un-lft-identity
26×associate-*r*
23×flip3-- flip--
21×pow1
18×associate-*l*
16×associate-*l/
15×add-exp-log add-cbrt-cube
14×associate-*r/
12×flip3-+ sqrt-prod flip-+
11×add-cube-cbrt
8×log-pow
7×distribute-rgt-in distribute-lft-in difference-of-squares
6×sub-neg pow-prod-down prod-exp cbrt-unprod distribute-lft-out--
4×*-commutative add-log-exp
3×distribute-lft-out unswap-sqr
2×sqrt-pow1 pow1/2
Counts
4 → 146
Calls
4 calls:
23.0ms
(* (log (sqrt y)) (- x 1.0))
23.0ms
(* (log (sqrt y)) (- x 1.0))
89.0ms
(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
164.0ms
(* (* (- 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)))))))

series512.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(* (log (sqrt y)) (- x 1.0))
59.0ms
(* (log (sqrt y)) (- x 1.0))
144.0ms
(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
245.0ms
(* (* (- 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)))))))

simplify114.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
08052898
144142533
250012521

prune807.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes269.0ms

Accuracy

0% (0.4b 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
03734
13734

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.1s23953×body80nan
310.0ms5916×body80valid
209.0ms712×body640valid
152.0ms254×body1280valid
122.0ms694×body320valid
50.0ms461×body160valid