Details

Time bar (total: 7.8s)

sample33.0ms

Algorithm
intervals
Results
16.0ms257×body80valid

simplify44.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
06211
115411
250311
3184011
4500311

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.1b
(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)))
23.4b
(/ (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:
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)
10.0ms
(/ (- 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))

series554.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
33.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
299.0ms
(/ (- 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)))
185.0ms
(/ (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))

simplify96.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06742773
126182640
250012638

prune985.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

7.9b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
7.9b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
14.4b
(* (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ (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)))
23.3b
(/ (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))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
40×times-frac
36×add-cube-cbrt *-un-lft-identity
35×sqrt-prod
22×associate-*r*
11×add-exp-log add-cbrt-cube
8×pow1
6×associate-*l* associate-/l* unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r*
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp prod-exp cbrt-unprod div-inv
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
4 → 121
Calls
4 calls:
2.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
2.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
11.0ms
(* (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ (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)))
4.0ms
(/ (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))

series684.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
104.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
181.0ms
(* (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ (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)))
295.0ms
(/ (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))

simplify62.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
03091938
112191710
250011649

prune572.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

7.9b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
13.6b
(sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
13.6b
(sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
20.5b
(* (pow (sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) 3) (/ (sqrt (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)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
124×add-sqr-sqrt
116×sqrt-prod
51×times-frac
35×add-cube-cbrt *-un-lft-identity
32×unswap-sqr
31×associate-*r*
24×associate-*l*
21×unpow-prod-down cube-prod
17×add-exp-log
9×pow1 sqrt-pow1 add-cbrt-cube
6×prod-exp
5×rem-sqrt-square pow1/2 sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×div-exp
2×pow-to-exp pow-exp cbrt-unprod
1×cbrt-undiv cube-mult unpow3 associate-*r/ *-commutative div-inv
Counts
4 → 163
Calls
4 calls:
2.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
2.0ms
(sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
2.0ms
(sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
22.0ms
(* (pow (sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) 3) (/ (sqrt (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)))

series606.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
157.0ms
(sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
157.0ms
(sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
184.0ms
(* (pow (sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) 3) (/ (sqrt (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)))

simplify115.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
05043318
123493143
250022702

prune690.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

13.6b
(sqrt (* (fabs (cbrt (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)))))
15.7b
(cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
15.7b
(cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
20.5b
(* (pow (sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) 3) (/ (sqrt (* (fabs (cbrt (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)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
34×sqrt-prod
24×associate-*l*
21×add-cube-cbrt *-un-lft-identity
20×times-frac
17×add-exp-log
16×associate-*r* unswap-sqr
15×unpow-prod-down cube-prod
9×add-cbrt-cube
7×pow1
6×cbrt-prod prod-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×div-exp sqr-pow
2×pow-to-exp sqrt-pow1 pow1/3 pow-exp cbrt-unprod
1×cbrt-undiv cube-mult pow1/2 unpow3 associate-*r/ pow-prod-down *-commutative div-inv
Counts
4 → 114
Calls
4 calls:
4.0ms
(sqrt (* (fabs (cbrt (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)))))
1.0ms
(cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
1.0ms
(cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
18.0ms
(* (pow (sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) 3) (/ (sqrt (* (fabs (cbrt (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)))

series1.0s

Counts
4 → 12
Calls
4 calls:
174.0ms
(sqrt (* (fabs (cbrt (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)))))
159.0ms
(cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
157.0ms
(cbrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
521.0ms
(* (pow (sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) 3) (/ (sqrt (* (fabs (cbrt (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)))

simplify105.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
05623275
122973082
250023076

prune780.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes299.0ms

Accuracy

95.7% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 25.0b

bsearch299.0ms

Steps
ItersRangePoint
11
0.0006518293038960093
5.531251689541722e+18
5.449213609141282e+18
10
-4.804704296627161e+20
-14787237.991479732
-1.367602166453584e+20

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06022
16022

end0.0ms

sample680.0ms

Algorithm
intervals
Results
497.0ms8012×body80valid