Details

Time bar (total: 4.7s)

sample44.0ms

Algorithm
intervals
Results
22.0ms285×body80valid

simplify59.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
06211
113211
237710
3110510
4359910
5500110

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)
0.1b
(fma (fma z 3.13060547623 11.1667541262) z t)
2.3b
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
30.2b
(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)

rewrite7.0ms

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:
1.0ms
(fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)
1.0ms
(fma (fma z 3.13060547623 11.1667541262) z t)
3.0ms
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms
(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)

series926.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)
31.0ms
(fma (fma z 3.13060547623 11.1667541262) z t)
109.0ms
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
735.0ms
(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)

simplify109.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (100.0ms)

IterNodesCost
0265578
1824514
23565508
35001506

prune400.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 2 expressions with local error:

2.2b
(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
6.8b
(/ t (pow z 2))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
19×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
8×associate-/r*
7×add-exp-log
4×add-cbrt-cube unpow2 sqr-pow
3×div-exp associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num fma-udef div-inv
Counts
2 → 61
Calls
2 calls:
1.0ms
(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
5.0ms
(/ t (pow z 2))

series72.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
22.0ms
(/ t (pow z 2))

simplify118.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0191332
1664290
23660281
35001281

prune192.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (/ t z) z)
2.2b
(fma y (+ 3.13060547623 (/ (/ t z) z)) x)

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
44×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×associate-/l*
7×add-exp-log add-cbrt-cube
5×div-inv
3×cbrt-undiv div-exp associate-/r*
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
1×frac-2neg clear-num fma-udef associate-/l/
Counts
2 → 82
Calls
2 calls:
7.0ms
(/ (/ t z) z)
1.0ms
(fma y (+ 3.13060547623 (/ (/ t z) z)) x)

series78.0ms

Counts
2 → 6
Calls
2 calls:
22.0ms
(/ (/ t z) z)
56.0ms
(fma y (+ 3.13060547623 (/ (/ t z) z)) x)

simplify40.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0349537
11283488
25001480

prune247.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b
(* (/ 1 (fabs z)) (/ t (fabs z)))
2.2b
(fma y (+ 3.13060547623 (* (/ 1 (fabs z)) (/ t (fabs z)))) x)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
25×times-frac
24×add-exp-log
18×*-un-lft-identity
16×add-cube-cbrt
14×add-cbrt-cube
13×associate-*r* associate-*l*
8×div-exp prod-exp
6×unswap-sqr
4×pow1 cbrt-undiv cbrt-unprod
2×expm1-log1p-u rec-exp 1-exp log1p-expm1-u div-inv add-log-exp
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative fma-udef
Counts
2 → 68
Calls
2 calls:
12.0ms
(* (/ 1 (fabs z)) (/ t (fabs z)))
1.0ms
(fma y (+ 3.13060547623 (* (/ 1 (fabs z)) (/ t (fabs z)))) x)

series80.0ms

Counts
2 → 6
Calls
2 calls:
27.0ms
(* (/ 1 (fabs z)) (/ t (fabs z)))
53.0ms
(fma y (+ 3.13060547623 (* (/ 1 (fabs z)) (/ t (fabs z)))) x)

simplify50.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0362568
11722480
25001438

prune182.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.5b

regimes738.0ms

Accuracy

96.7% (0.9b remaining)

Error of 1.2b against oracle of 0.3b and baseline of 27.0b

bsearch278.0ms

Steps
ItersRangePoint
10
4.0884001115827195e+20
2.4120748872659345e+35
1.5461650747710398e+25
9
-4.83088891996885e+34
-6.974363134443104e+27
-9.136478076128219e+32

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04521
14521

end0.0ms

sample935.0ms

Algorithm
intervals
Results
604.0ms8872×body80valid