Details

Time bar (total: 5.4s)

sample45.0ms

Algorithm
intervals
Results
24.0ms286×body80valid

simplify61.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
06211
113211
237710
3110510
4359910
5500110

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b)
0.1b
(fma (fma z 3.13060547623 11.1667541262) z t)
3.6b
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
29.7b
(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)

rewrite4.0ms

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 (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b)
0.0ms
(fma (fma z 3.13060547623 11.1667541262) z t)
2.0ms
(/ 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)

series968.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b)
34.0ms
(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))
730.0ms
(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)

simplify114.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (105.0ms)

IterNodesCost
0269578
1828514
23590508
35001504

prune413.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 3.13060547623 (/ t (pow z 2)))
1.9b
(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
7.4b
(/ t (pow z 2))

rewrite22.0ms

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:
12.0ms
(+ 3.13060547623 (/ t (pow z 2)))
0.0ms
(fma y (+ 3.13060547623 (/ t (pow z 2))) x)
4.0ms
(/ t (pow z 2))

series109.0ms

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

simplify137.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 3 (131.0ms)

IterNodesCost
0255414
1847369
24454360
35001359

prune268.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 3.13060547623 (* (/ 1 (fabs z)) (/ t (fabs z))))
0.2b
(* (/ 1 (fabs z)) (/ t (fabs z)))
1.9b
(fma y (+ 3.13060547623 (* (/ 1 (fabs z)) (/ t (fabs z)))) x)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
25×add-exp-log times-frac
20×*-un-lft-identity
18×add-cube-cbrt
15×add-cbrt-cube
13×associate-*r* associate-*l*
8×div-exp prod-exp
6×unswap-sqr
5×pow1 add-log-exp
4×cbrt-undiv cbrt-unprod
3×expm1-log1p-u fma-def log1p-expm1-u
2×rec-exp 1-exp div-inv
1×+-commutative frac-times flip3-+ associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative flip-+ fma-udef
Counts
3 → 84
Calls
3 calls:
3.0ms
(+ 3.13060547623 (* (/ 1 (fabs z)) (/ t (fabs z))))
14.0ms
(* (/ 1 (fabs z)) (/ t (fabs z)))
0.0ms
(fma y (+ 3.13060547623 (* (/ 1 (fabs z)) (/ t (fabs z)))) x)

series121.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(+ 3.13060547623 (* (/ 1 (fabs z)) (/ t (fabs z))))
32.0ms
(* (/ 1 (fabs z)) (/ t (fabs z)))
50.0ms
(fma y (+ 3.13060547623 (* (/ 1 (fabs z)) (/ t (fabs z)))) x)

simplify57.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0428701
11970607
25002539

prune294.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 3.13060547623 (/ 1 (/ (pow z 2) t)))
0.6b
(/ 1 (/ (pow z 2) t))
1.9b
(fma y (+ 3.13060547623 (/ 1 (/ (pow z 2) t))) x)
7.2b
(/ (pow z 2) t)

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
204×times-frac
114×*-un-lft-identity
111×add-sqr-sqrt add-cube-cbrt
48×unpow-prod-down
31×add-exp-log associate-/r*
20×div-exp
16×unpow2 sqr-pow
11×add-cbrt-cube associate-/l*
7×div-inv
6×add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u pow-to-exp rec-exp 1-exp pow-exp log1p-expm1-u
3×fma-def
2×frac-2neg clear-num distribute-lft-out
1×+-commutative pow-flip flip3-+ sum-log associate-/r/ flip-+ fma-udef inv-pow
Counts
4 → 223
Calls
4 calls:
34.0ms
(+ 3.13060547623 (/ 1 (/ (pow z 2) t)))
10.0ms
(/ 1 (/ (pow z 2) t))
0.0ms
(fma y (+ 3.13060547623 (/ 1 (/ (pow z 2) t))) x)
5.0ms
(/ (pow z 2) t)

series105.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(+ 3.13060547623 (/ 1 (/ (pow z 2) t)))
17.0ms
(/ 1 (/ (pow z 2) t))
46.0ms
(fma y (+ 3.13060547623 (/ 1 (/ (pow z 2) t))) x)
20.0ms
(/ (pow z 2) t)

simplify65.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
06941540
129351097
250031087

prune446.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes766.0ms

Accuracy

96.6% (0.9b remaining)

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

bsearch246.0ms

Steps
ItersRangePoint
10
167712351607.73917
1.2721151610724408e+24
1.0256103088739618e+24
6
-8.124975001743472e+25
-1.3796619314999023e+25
-3.0056051312042543e+25

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04823
14823

end0.0ms

sample978.0ms

Algorithm
intervals
Results
660.0ms8907×body80valid