Details

Time bar (total: 7.4s)

sample51.0ms

Algorithm
intervals
Results
18.0ms350×body80valid
13.0ms296×body80nan

simplify56.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (17.0ms)

IterNodesCost
04012
19212
226912
366912
4156511
5285511
6500111

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ y 0.0007936500793651) z)
0.1b
(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.1b
(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
6.4b
(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
18×*-un-lft-identity
16×add-cube-cbrt
10×add-exp-log add-cbrt-cube
9×times-frac
8×pow1
7×associate-*l*
6×associate-*r*
4×expm1-log1p-u associate-*l/ log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ associate-/l/ unswap-sqr
1×cbrt-undiv flip3-- frac-2neg div-exp clear-num flip-- fma-udef div-inv distribute-lft-out
Counts
4 → 86
Calls
4 calls:
10.0ms
(* (+ y 0.0007936500793651) z)
19.0ms
(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.0ms
(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
24.0ms
(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series271.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (+ y 0.0007936500793651) z)
42.0ms
(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
120.0ms
(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
82.0ms
(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify50.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0446778
11546696
25002694

prune387.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ y 0.0007936500793651))
0.3b
(* (* (cbrt (+ y 0.0007936500793651)) (cbrt (+ y 0.0007936500793651))) (* (cbrt (+ y 0.0007936500793651)) z))
0.3b
(* (cbrt (+ y 0.0007936500793651)) z)
6.4b
(/ (+ (* (- (* (* (cbrt (+ y 0.0007936500793651)) (cbrt (+ y 0.0007936500793651))) (* (cbrt (+ y 0.0007936500793651)) z)) 0.0027777777777778) z) 0.083333333333333) x)

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
58×cbrt-div
34×associate-*l/
30×flip3-+ flip-+
28×frac-times
20×add-exp-log add-sqr-sqrt *-un-lft-identity
18×pow1
16×add-cube-cbrt
13×add-cbrt-cube
9×cbrt-prod times-frac pow-prod-down prod-exp cbrt-unprod
8×associate-*r/ associate-*l*
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×*-commutative associate-/l/ distribute-lft-out unswap-sqr
1×cbrt-undiv frac-2neg pow1/3 div-exp clear-num div-inv
Counts
4 → 124
Calls
4 calls:
2.0ms
(cbrt (+ y 0.0007936500793651))
42.0ms
(* (* (cbrt (+ y 0.0007936500793651)) (cbrt (+ y 0.0007936500793651))) (* (cbrt (+ y 0.0007936500793651)) z))
11.0ms
(* (cbrt (+ y 0.0007936500793651)) z)
139.0ms
(/ (+ (* (- (* (* (cbrt (+ y 0.0007936500793651)) (cbrt (+ y 0.0007936500793651))) (* (cbrt (+ y 0.0007936500793651)) z)) 0.0027777777777778) z) 0.083333333333333) x)

series412.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(cbrt (+ y 0.0007936500793651))
29.0ms
(* (* (cbrt (+ y 0.0007936500793651)) (cbrt (+ y 0.0007936500793651))) (* (cbrt (+ y 0.0007936500793651)) z))
208.0ms
(* (cbrt (+ y 0.0007936500793651)) z)
85.0ms
(/ (+ (* (- (* (* (cbrt (+ y 0.0007936500793651)) (cbrt (+ y 0.0007936500793651))) (* (cbrt (+ y 0.0007936500793651)) z)) 0.0027777777777778) z) 0.083333333333333) x)

simplify83.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
07651800
125701613
250011538

prune562.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (log x) (- x 0.5) (- (/ (fma (- z) (fma (pow (cbrt (+ y 0.0007936500793651)) 3) z (- 0.0027777777777778)) (- 0.083333333333333)) (- x)) (- x 0.91893853320467)))
0.3b
(cbrt (+ y 0.0007936500793651))
0.9b
(pow (cbrt (+ y 0.0007936500793651)) 3)
6.4b
(/ (fma (- z) (fma (pow (cbrt (+ y 0.0007936500793651)) 3) z (- 0.0027777777777778)) (- 0.083333333333333)) (- x))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
33×add-sqr-sqrt add-cube-cbrt
30×times-frac
12×cbrt-prod distribute-lft-neg-in distribute-rgt-neg-in
10×associate-/r*
7×add-exp-log unpow-prod-down cube-prod
6×add-cbrt-cube
5×pow1
4×expm1-log1p-u neg-mul-1 cbrt-div log1p-expm1-u add-log-exp
3×pow-unpow distribute-lft-out associate-/l*
2×cube-div pow-pow flip3-+ pow1/3 flip-+
1×cbrt-undiv cube-mult pow-to-exp frac-2neg unpow3 div-exp pow-exp clear-num fma-udef div-inv rem-cube-cbrt sqr-pow
Counts
4 → 119
Calls
4 calls:
0.0ms
(fma (log x) (- x 0.5) (- (/ (fma (- z) (fma (pow (cbrt (+ y 0.0007936500793651)) 3) z (- 0.0027777777777778)) (- 0.083333333333333)) (- x)) (- x 0.91893853320467)))
2.0ms
(cbrt (+ y 0.0007936500793651))
5.0ms
(pow (cbrt (+ y 0.0007936500793651)) 3)
4.0ms
(/ (fma (- z) (fma (pow (cbrt (+ y 0.0007936500793651)) 3) z (- 0.0027777777777778)) (- 0.083333333333333)) (- x))

series692.0ms

Counts
4 → 12
Calls
4 calls:
334.0ms
(fma (log x) (- x 0.5) (- (/ (fma (- z) (fma (pow (cbrt (+ y 0.0007936500793651)) 3) z (- 0.0027777777777778)) (- 0.083333333333333)) (- x)) (- x 0.91893853320467)))
91.0ms
(cbrt (+ y 0.0007936500793651))
138.0ms
(pow (cbrt (+ y 0.0007936500793651)) 3)
129.0ms
(/ (fma (- z) (fma (pow (cbrt (+ y 0.0007936500793651)) 3) z (- 0.0027777777777778)) (- 0.083333333333333)) (- x))

simplify73.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
06361561
127671460
250011442

prune607.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.1b
(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
0.2b
(* (log x) (- x 0.5))
6.4b
(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
120×add-sqr-sqrt
116×*-un-lft-identity
101×prod-diff
88×add-cube-cbrt
68×associate-+r+
54×times-frac
22×distribute-rgt-in associate-+l+ distribute-lft-in
14×distribute-lft-out-- difference-of-squares
13×add-log-exp
10×add-exp-log flip3-- associate-*r/ add-cbrt-cube flip--
9×pow1
8×associate-*r* frac-add
7×associate-*l*
6×div-inv
5×sub-neg
4×expm1-log1p-u frac-sub log1p-expm1-u
3×diff-log associate-/r* sum-log associate-/l*
2×flip3-+ pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod flip-+ associate-/l/ unswap-sqr
1×cbrt-undiv +-commutative associate-+r- fma-def frac-2neg div-exp clear-num log-pow associate--r-
Counts
4 → 215
Calls
4 calls:
21.0ms
(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
136.0ms
(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
14.0ms
(* (log x) (- x 0.5))
21.0ms
(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series505.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
130.0ms
(+ (* (log x) (- x 0.5)) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
245.0ms
(* (log x) (- x 0.5))
86.0ms
(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify143.0ms

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012533523
148823081
250013081

prune787.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.0b

regimes401.0ms

Accuracy

50.6% (1.0b remaining)

Error of 4.9b against oracle of 3.9b and baseline of 6.0b

bsearch156.0ms

Steps
ItersRangePoint
5
1.3344057483475615e-15
3.162646055653571e-15
3.1271743150542163e-15
9
-1.9324167353905947e+99
-4.5938591310774295e+92
-4.6498906881920206e+92

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04928
14928

end0.0ms

sample1.6s

Algorithm
intervals
Results
598.0ms11582×body80valid
505.0ms11338×body80nan