Details

Time bar (total: 6.5s)

sample51.0ms

Algorithm
intervals
Results
23.0ms294×body80valid

simplify79.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
06211
113211
237710
3110510
4359910
5500110

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
0.1b
(fma (fma z 3.13060547623 11.1667541262) z t)
3.5b
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
28.5b
(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) x)

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* fma-udef associate-/l*
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 59
Calls
4 calls:
0.0ms
(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
0.0ms
(fma (fma z 3.13060547623 11.1667541262) z t)
5.0ms
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
0.0ms
(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) x)

series945.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
37.0ms
(fma (fma z 3.13060547623 11.1667541262) z t)
122.0ms
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
749.0ms
(fma (/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)) (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) x)

simplify127.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (118.0ms)

IterNodesCost
0270563
1830501
23551493
35002491

prune439.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 3.13060547623 (/ t (pow z 2)))
4.3b
(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
8.2b
(/ t (pow z 2))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×*-un-lft-identity
21×add-sqr-sqrt add-cube-cbrt
12×unpow-prod-down
8×add-exp-log associate-/r*
5×add-cbrt-cube add-log-exp
4×unpow2 sqr-pow
3×pow1 expm1-log1p-u fma-def div-exp log1p-expm1-u associate-/l*
1×cbrt-undiv +-commutative pow-to-exp frac-2neg flip3-+ pow-exp clear-num sum-log flip-+ fma-udef div-inv distribute-lft-out
Counts
3 → 78
Calls
3 calls:
24.0ms
(+ 3.13060547623 (/ t (pow z 2)))
0.0ms
(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
8.0ms
(/ t (pow z 2))

series114.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(+ 3.13060547623 (/ t (pow z 2)))
60.0ms
(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
25.0ms
(/ t (pow z 2))

simplify157.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 3 (150.0ms)

IterNodesCost
0255414
1847369
24454360
35001359

prune266.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 3.13060547623 (/ (/ t z) (pow z (/ 2 2))))
0.1b
(/ (/ t z) (pow z (/ 2 2)))
4.3b
(fma y (+ 3.13060547623 (/ (/ t z) (pow z (/ 2 2)))) x)

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
163×times-frac
90×*-un-lft-identity
88×add-sqr-sqrt add-cube-cbrt
42×unpow-prod-down
16×add-exp-log
14×sqr-pow
13×associate-/l*
9×div-exp div-inv
8×add-cbrt-cube
7×associate-/r*
5×add-log-exp
3×pow1 cbrt-undiv expm1-log1p-u fma-def log1p-expm1-u
2×pow-to-exp pow-exp
1×+-commutative frac-2neg flip3-+ clear-num sum-log flip-+ fma-udef associate-/l/ distribute-lft-out
Counts
3 → 159
Calls
3 calls:
43.0ms
(+ 3.13060547623 (/ (/ t z) (pow z (/ 2 2))))
20.0ms
(/ (/ t z) (pow z (/ 2 2)))
0.0ms
(fma y (+ 3.13060547623 (/ (/ t z) (pow z (/ 2 2)))) x)

series108.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(+ 3.13060547623 (/ (/ t z) (pow z (/ 2 2))))
23.0ms
(/ (/ t z) (pow z (/ 2 2)))
52.0ms
(fma y (+ 3.13060547623 (/ (/ t z) (pow z (/ 2 2)))) x)

simplify71.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
06551109
12543970
25002964

prune357.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma z 3.13060547623 11.1667541262) z t)
0.3b
(/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
3.4b
(* y (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
28.5b
(fma (* y (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) x)

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×*-un-lft-identity
20×add-cube-cbrt times-frac
17×add-exp-log
13×associate-*r*
11×add-cbrt-cube
7×pow1
4×expm1-log1p-u div-exp prod-exp log1p-expm1-u add-log-exp
3×associate-*l* associate-/r* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp 1-exp cbrt-unprod fma-udef div-inv
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
4 → 91
Calls
4 calls:
0.0ms
(fma (fma z 3.13060547623 11.1667541262) z t)
5.0ms
(/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
16.0ms
(* y (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
0.0ms
(fma (* y (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) x)

series980.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(fma (fma z 3.13060547623 11.1667541262) z t)
78.0ms
(/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
124.0ms
(* y (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
748.0ms
(fma (* y (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b) x)

simplify65.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0363864
11442747
25002715

prune462.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes732.0ms

Accuracy

97.3% (0.7b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 27.0b

bsearch313.0ms

Steps
ItersRangePoint
11
1401814831439.3975
4.1904334431414967e+49
1.5893385567973325e+36
9
-7.775203197540148e+52
-2.2962984177568013e+43
-3.1260025612841044e+45

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04016
14016

end0.0ms

sample1.0s

Algorithm
intervals
Results
606.0ms8844×body80valid