Details

Time bar (total: 9.4s)

sample35.0ms

Algorithm
intervals
Results
17.0ms256×body80valid

simplify46.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
06211
115411
250311
3184011
4500311

prune15.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 22.7b

Counts
2 → 2

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.0b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.3b
(/ (- x 2.0) (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
22.0b
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
128×times-frac
98×add-sqr-sqrt *-un-lft-identity
70×add-cube-cbrt
19×associate-/r*
14×distribute-lft-out-- difference-of-squares
11×add-exp-log add-cbrt-cube associate-/l*
9×associate-/r/
8×div-inv
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×fma-udef associate-/l/
1×flip3-- div-sub flip--
Counts
4 → 160
Calls
4 calls:
1.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
1.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
11.0ms
(/ (- x 2.0) (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
3.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

series569.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
27.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
307.0ms
(/ (- x 2.0) (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
193.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

simplify93.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
06942838
126772705
250012703

prune699.0ms

Filtered
172 candidates to 132 candidates (76.7%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1657172
Fresh101
Picked101
Done000
Total1677174

Merged error: 0.0b

Counts
174 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- x 2.0) (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
0.0b
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.0b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
22.0b
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×*-un-lft-identity
26×add-cube-cbrt
19×times-frac
18×frac-times
13×associate-*r* associate-/l*
12×associate-/r*
11×add-exp-log add-cbrt-cube
10×flip3-- flip--
9×associate-*r/
6×pow1
5×associate-*l* clear-num
4×expm1-log1p-u frac-2neg log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp associate-*l/ prod-exp un-div-inv cbrt-unprod fma-udef div-inv unswap-sqr
1×pow-prod-down *-commutative distribute-lft-out-- difference-of-squares
Counts
4 → 115
Calls
4 calls:
11.0ms
(* (- x 2.0) (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
1.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
1.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
3.0ms
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

series632.0ms

Counts
4 → 12
Calls
4 calls:
309.0ms
(* (- x 2.0) (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
37.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
32.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
254.0ms
(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

simplify76.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
04881553
122001430
250021428

prune487.0ms

Filtered
127 candidates to 98 candidates (77.2%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1243127
Fresh426
Picked101
Done000
Total1295134

Merged error: 0.0b

Counts
134 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.0b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
2.8b
(/ (- x 2.0) (- (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
22.1b
(* (/ (- x 2.0) (- (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (- (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
115×add-sqr-sqrt
110×*-un-lft-identity
101×times-frac
66×add-cube-cbrt
54×associate-*l*
39×distribute-lft-neg-in distribute-rgt-neg-in
22×distribute-lft-out-- difference-of-squares
20×associate-*l/ associate-/r*
13×neg-mul-1
11×add-exp-log add-cbrt-cube
10×associate-*r* associate-/l*
6×pow1
4×expm1-log1p-u fma-udef log1p-expm1-u associate-/l/ add-log-exp
2×cbrt-undiv distribute-neg-in flip3-- frac-2neg div-exp prod-exp clear-num flip-- cbrt-unprod div-inv unswap-sqr
1×distribute-rgt-in distribute-lft-in div-sub pow-prod-down *-commutative distribute-rgt-neg-out
Counts
4 → 206
Calls
4 calls:
1.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
1.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
8.0ms
(/ (- x 2.0) (- (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
21.0ms
(* (/ (- x 2.0) (- (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (- (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))

series472.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
27.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
110.0ms
(/ (- x 2.0) (- (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
298.0ms
(* (/ (- x 2.0) (- (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (- (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))

simplify114.0ms

Algorithm
egg-herbie
Counts
218 → 218
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
08622733
138962613
250022611

prune798.0ms

Filtered
218 candidates to 163 candidates (74.8%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New2153218
Fresh314
Picked011
Done000
Total2185223

Merged error: 0.0b

Counts
223 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

6.3b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
6.3b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
14.6b
(/ (- x 2.0) (- (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
19.1b
(/ (* (/ (- x 2.0) (- (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))) (- (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
1253×times-frac
882×add-sqr-sqrt
845×*-un-lft-identity
588×associate-*l*
585×add-cube-cbrt
564×sqrt-prod
273×distribute-lft-neg-in distribute-rgt-neg-in
130×distribute-lft-out-- difference-of-squares
111×associate-/l*
70×associate-*r*
49×neg-mul-1
38×associate-/r*
30×associate-/l/
26×associate-*l/
15×add-exp-log add-cbrt-cube
14×unswap-sqr
9×div-inv
7×*-commutative
6×pow1
5×cbrt-undiv div-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 prod-exp flip-- cbrt-unprod
1×div-sub distribute-frac-neg distribute-rgt-neg-out
Counts
4 → 906
Calls
4 calls:
1.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
1.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
9.0ms
(/ (- x 2.0) (- (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
59.0ms
(/ (* (/ (- x 2.0) (- (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))) (- (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

series708.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
114.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
178.0ms
(/ (- x 2.0) (- (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
307.0ms
(/ (* (/ (- x 2.0) (- (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))) (- (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

simplify337.0ms

Algorithm
egg-herbie
Counts
918 → 918
Iterations

Useful iterations: 1 (50.0ms)

IterNodesCost
0252127046
1500226274

prune2.8s

Filtered
918 candidates to 449 candidates (48.9%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New9171918
Fresh123
Picked101
Done011
Total9194923

Merged error: 0.0b

Counts
923 → 4

regimes170.0ms

Accuracy

96.4% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 24.6b

bsearch226.0ms

Steps
ItersRangePoint
9
1.0815468575645218e+20
8.37173053923323e+25
8.22351433349814e+25
7
-1.8347284548271936e+73
-2.541648319617525e+71
-2.375496922690379e+72

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05636
16236
26536
36736
46736

end0.0ms

sample722.0ms

Algorithm
intervals
Results
538.0ms8009×body80valid