Details

Time bar (total: 10.2s)

sample32.0ms

Algorithm
intervals
Results
16.0ms256×body80valid

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06211
115411
250311
3184011
4500311

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
0.1b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.5b
(/ (- 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)))
25.6b
(/ (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
96×add-sqr-sqrt *-un-lft-identity
68×add-cube-cbrt
16×associate-/r*
14×distribute-lft-out-- difference-of-squares
11×add-exp-log add-cbrt-cube
8×div-inv associate-/l*
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×frac-2neg clear-num fma-udef associate-/l/
1×flip3-- div-sub associate-/r/ flip--
Counts
4 → 152
Calls
4 calls:
0.0ms
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
0.0ms
(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)))
2.0ms
(/ (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))

series557.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
26.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
290.0ms
(/ (- 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)))
181.0ms
(/ (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))

simplify88.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
06772773
126212640
250012638

prune863.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

8.8b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
8.8b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
22.8b
(* (/ 1 (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (- 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))))
25.5b
(/ (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))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
277×times-frac
241×add-sqr-sqrt
174×*-un-lft-identity
122×add-cube-cbrt
115×associate-*r*
85×sqrt-prod
45×add-exp-log
27×add-cbrt-cube
22×associate-*l* distribute-lft-out-- difference-of-squares
20×unswap-sqr
19×div-exp
12×prod-exp
10×cbrt-undiv
8×pow1 div-inv
6×cbrt-unprod associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rec-exp 1-exp associate-/r*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num associate-/r/ *-commutative
Counts
4 → 260
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))
74.0ms
(* (/ 1 (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (- 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))))
3.0ms
(/ (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))

series771.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
100.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
283.0ms
(* (/ 1 (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (- 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))))
288.0ms
(/ (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))

simplify91.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011315460
150014977

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

8.8b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
8.8b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
16.3b
(/ (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))))
22.4b
(/ (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)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
160×add-sqr-sqrt
158×add-cube-cbrt *-un-lft-identity
150×sqrt-prod
28×associate-/r*
11×add-exp-log add-cbrt-cube
9×div-inv associate-/l*
6×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/r/
Counts
4 → 248
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))
8.0ms
(/ (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))))
6.0ms
(/ (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)))

series753.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
107.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
177.0ms
(/ (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))))
366.0ms
(/ (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)))

simplify134.0ms

Algorithm
egg-herbie
Counts
260 → 260
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06606379
131455897
250025794

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

15.4b
(sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
17.2b
(cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
17.2b
(cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
19.5b
(* (* (fabs (cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))) (/ (sqrt (cbrt (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 (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
522×times-frac
439×sqrt-prod
284×associate-*r*
275×add-sqr-sqrt
273×add-cube-cbrt *-un-lft-identity
99×cbrt-prod
25×add-exp-log add-cbrt-cube
11×pow1
10×div-inv
9×prod-exp cbrt-unprod
6×cbrt-undiv div-exp
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp
3×pow-prod-down
2×rem-sqrt-square pow1/2 pow1/3
1×associate-*r/ associate-*l* associate-/r/ *-commutative
Counts
4 → 357
Calls
4 calls:
1.0ms
(sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
0.0ms
(cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
0.0ms
(cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
75.0ms
(* (* (fabs (cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))) (/ (sqrt (cbrt (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 (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))))

series869.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
148.0ms
(cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
140.0ms
(cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
432.0ms
(* (* (fabs (cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))) (/ (sqrt (cbrt (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 (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))))

simplify156.0ms

Algorithm
egg-herbie
Counts
369 → 369
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0196111171
1500110644

prune1.9s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes387.0ms

Accuracy

96.5% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 24.8b

bsearch214.0ms

Steps
ItersRangePoint
8
1.927335547477129e+23
1.8902799733008505e+27
1.3882080819333125e+24
7
-1.8697329502856167e+43
-6.559069104573772e+41
-1.3588681134848813e+42

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06123
16323
26323

end0.0ms

sample661.0ms

Algorithm
intervals
Results
492.0ms8013×body80valid