Details

Time bar (total: 13.9s)

sample56.0ms

Algorithm
intervals
Results
18.0ms357×body80valid
16.0ms370×body80nan

simplify60.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (18.0ms)

IterNodesCost
04012
19212
226912
366912
4156511
5285511
6500111

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))
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)))
4.3b
(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
108×add-sqr-sqrt
106×*-un-lft-identity
75×add-cube-cbrt
74×prod-diff
64×times-frac
16×distribute-lft-out--
15×difference-of-squares
13×fma-neg
11×associate--r+
9×add-log-exp
8×add-exp-log add-cbrt-cube
7×div-inv
6×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- diff-log associate-*r* associate-*l* associate-/r* flip-- associate-/l*
2×sub-neg associate-*l/ frac-sub associate-/l/
1×cbrt-undiv frac-2neg flip3-+ div-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod flip-+ fma-udef associate--r- unswap-sqr
Counts
4 → 174
Calls
4 calls:
80.0ms
(- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))
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)))
21.0ms
(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series335.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467))
39.0ms
(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
128.0ms
(fma (log x) (- x 0.5) (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (- x 0.91893853320467)))
88.0ms
(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify89.0ms

Algorithm
egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
07373116
124312540
250022408

prune560.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.8b

localize25.0ms

Local error

Found 4 expressions with local error:

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) (* (- (sqrt x) (sqrt 0.91893853320467)) (+ (sqrt x) (sqrt 0.91893853320467)))) (* (- (sqrt x) (sqrt 0.91893853320467)) (+ (- (+ (sqrt x) (sqrt 0.91893853320467))) (+ (sqrt x) (sqrt 0.91893853320467))))))
0.3b
(* (- (sqrt x) (sqrt 0.91893853320467)) (+ (sqrt x) (sqrt 0.91893853320467)))
4.3b
(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×*-un-lft-identity
16×add-cube-cbrt
12×associate-*l*
10×add-exp-log add-cbrt-cube
9×times-frac
8×pow1 associate-*r* sqrt-prod
4×expm1-log1p-u frac-times flip3-- flip3-+ associate-*l/ flip-- flip-+ log1p-expm1-u add-log-exp difference-of-squares
3×associate-/r* associate-/l*
2×associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod associate-/l/ distribute-lft-out distribute-lft-out-- unswap-sqr
1×cbrt-undiv distribute-rgt-in frac-2neg distribute-lft-in div-exp clear-num fma-udef div-inv
Counts
4 → 101
Calls
4 calls:
20.0ms
(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
1.0ms
(fma (log x) (- x 0.5) (+ (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (* (- (sqrt x) (sqrt 0.91893853320467)) (+ (sqrt x) (sqrt 0.91893853320467)))) (* (- (sqrt x) (sqrt 0.91893853320467)) (+ (- (+ (sqrt x) (sqrt 0.91893853320467))) (+ (sqrt x) (sqrt 0.91893853320467))))))
44.0ms
(* (- (sqrt x) (sqrt 0.91893853320467)) (+ (sqrt x) (sqrt 0.91893853320467)))
21.0ms
(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series495.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
186.0ms
(fma (log x) (- x 0.5) (+ (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (* (- (sqrt x) (sqrt 0.91893853320467)) (+ (sqrt x) (sqrt 0.91893853320467)))) (* (- (sqrt x) (sqrt 0.91893853320467)) (+ (- (+ (sqrt x) (sqrt 0.91893853320467))) (+ (sqrt x) (sqrt 0.91893853320467))))))
184.0ms
(* (- (sqrt x) (sqrt 0.91893853320467)) (+ (sqrt x) (sqrt 0.91893853320467)))
86.0ms
(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify93.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
06911378
129771176
250011125

prune592.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (log x) (- x 0.5) (+ (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (expm1 (log1p (* (- (sqrt x) (sqrt 0.91893853320467)) (+ (sqrt x) (sqrt 0.91893853320467)))))) (* (- (sqrt x) (sqrt 0.91893853320467)) (+ (- (+ (sqrt x) (sqrt 0.91893853320467))) (+ (sqrt x) (sqrt 0.91893853320467))))))
0.3b
(* (- (sqrt x) (sqrt 0.91893853320467)) (+ (sqrt x) (sqrt 0.91893853320467)))
3.1b
(expm1 (log1p (* (- (sqrt x) (sqrt 0.91893853320467)) (+ (sqrt x) (sqrt 0.91893853320467)))))
4.3b
(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
22×*-un-lft-identity
14×add-cube-cbrt
9×times-frac associate-*l*
8×add-exp-log sqrt-prod add-cbrt-cube
6×pow1
5×associate-*r*
4×expm1-log1p-u frac-times flip3-+ flip-+ log1p-expm1-u add-log-exp difference-of-squares
3×flip3-- associate-/r* flip-- associate-/l*
2×associate-*r/ associate-*l/ associate-/l/ distribute-lft-out distribute-lft-out--
1×cbrt-undiv distribute-rgt-in expm1-log1p frac-2neg distribute-lft-in div-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod fma-udef div-inv expm1-udef unswap-sqr
Counts
4 → 90
Calls
4 calls:
0.0ms
(fma (log x) (- x 0.5) (+ (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (expm1 (log1p (* (- (sqrt x) (sqrt 0.91893853320467)) (+ (sqrt x) (sqrt 0.91893853320467)))))) (* (- (sqrt x) (sqrt 0.91893853320467)) (+ (- (+ (sqrt x) (sqrt 0.91893853320467))) (+ (sqrt x) (sqrt 0.91893853320467))))))
41.0ms
(* (- (sqrt x) (sqrt 0.91893853320467)) (+ (sqrt x) (sqrt 0.91893853320467)))
0.0ms
(expm1 (log1p (* (- (sqrt x) (sqrt 0.91893853320467)) (+ (sqrt x) (sqrt 0.91893853320467)))))
21.0ms
(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series5.2s

Counts
4 → 12
Calls
4 calls:
3.3s
(fma (log x) (- x 0.5) (+ (- (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x) (expm1 (log1p (* (- (sqrt x) (sqrt 0.91893853320467)) (+ (sqrt x) (sqrt 0.91893853320467)))))) (* (- (sqrt x) (sqrt 0.91893853320467)) (+ (- (+ (sqrt x) (sqrt 0.91893853320467))) (+ (sqrt x) (sqrt 0.91893853320467))))))
181.0ms
(* (- (sqrt x) (sqrt 0.91893853320467)) (+ (sqrt x) (sqrt 0.91893853320467)))
1.6s
(expm1 (log1p (* (- (sqrt x) (sqrt 0.91893853320467)) (+ (sqrt x) (sqrt 0.91893853320467)))))
85.0ms
(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify95.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
09241808
140321495
250011448

prune647.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (- (sqrt x) (sqrt 0.91893853320467)) (+ (sqrt x) (sqrt 0.91893853320467)))
0.3b
(/ 1 (/ x (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)))
3.1b
(expm1 (log1p (* (- (sqrt x) (sqrt 0.91893853320467)) (+ (sqrt x) (sqrt 0.91893853320467)))))
4.3b
(/ x (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
66×add-sqr-sqrt
64×*-un-lft-identity
56×add-cube-cbrt
19×add-exp-log
16×associate-/r*
13×add-cbrt-cube
9×associate-*l*
8×div-exp sqrt-prod
7×pow1
6×div-inv associate-/l*
5×associate-*r*
4×cbrt-undiv expm1-log1p-u frac-times log1p-expm1-u add-log-exp difference-of-squares
3×flip3-- flip3-+ flip-- flip-+
2×rec-exp frac-2neg 1-exp associate-*r/ associate-*l/ clear-num distribute-lft-out distribute-lft-out--
1×distribute-rgt-in expm1-log1p pow-flip distribute-lft-in pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod inv-pow expm1-udef unswap-sqr
Counts
4 → 156
Calls
4 calls:
42.0ms
(* (- (sqrt x) (sqrt 0.91893853320467)) (+ (sqrt x) (sqrt 0.91893853320467)))
5.0ms
(/ 1 (/ x (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)))
0.0ms
(expm1 (log1p (* (- (sqrt x) (sqrt 0.91893853320467)) (+ (sqrt x) (sqrt 0.91893853320467)))))
2.0ms
(/ x (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333))

series2.2s

Counts
4 → 12
Calls
4 calls:
184.0ms
(* (- (sqrt x) (sqrt 0.91893853320467)) (+ (sqrt x) (sqrt 0.91893853320467)))
87.0ms
(/ 1 (/ x (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)))
1.8s
(expm1 (log1p (* (- (sqrt x) (sqrt 0.91893853320467)) (+ (sqrt x) (sqrt 0.91893853320467)))))
112.0ms
(/ x (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333))

simplify49.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010732282
150012022

prune886.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.1b

regimes420.0ms

Accuracy

72.5% (1.1b remaining)

Error of 3.0b against oracle of 1.8b and baseline of 6.0b

bsearch2.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07884
17984
27984

end0.0ms

sample1.6s

Algorithm
intervals
Results
586.0ms11671×body80valid
526.0ms11895×body80nan