Details

Time bar (total: 8.7s)

sample42.0ms

Algorithm
intervals
Results
21.0ms287×body80valid

simplify63.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
06211
113211
237710
3110510
4359910
5500110

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(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)
1.7b
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
21.9b
(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)

rewrite6.0ms

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 (fma z 3.13060547623 11.1667541262) z t) z a) z b)
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)

series958.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b)
29.0ms
(fma (fma z 3.13060547623 11.1667541262) z t)
117.0ms
(/ y (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
719.0ms
(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)

simplify112.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (103.0ms)

IterNodesCost
0269578
1828514
23590508
35001504

prune409.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma z 3.13060547623 11.1667541262) z t)
0.2b
(/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.9b
(* y (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
21.9b
(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)

rewrite17.0ms

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:
4.0ms
(fma (fma z 3.13060547623 11.1667541262) z t)
3.0ms
(/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
7.0ms
(* y (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
1.0ms
(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)

series936.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(fma (fma z 3.13060547623 11.1667541262) z t)
75.0ms
(/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
112.0ms
(* y (/ 1 (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
721.0ms
(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)

simplify53.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0363864
11442747
25002715

prune449.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.5b

localize32.0ms

Local error

Found 4 expressions with local error:

3.6b
(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
5.9b
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
5.9b
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
21.9b
(fma (* (/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (/ (cbrt 1) (sqrt (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)

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
6×pow1 add-exp-log associate-/r* add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv
Counts
4 → 81
Calls
4 calls:
4.0ms
(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
1.0ms
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms
(fma (* (/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (/ (cbrt 1) (sqrt (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)

series1.1s

Counts
4 → 12
Calls
4 calls:
180.0ms
(/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
108.0ms
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
102.0ms
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
728.0ms
(fma (* (/ y (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (/ (cbrt 1) (sqrt (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)

simplify123.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 3 (110.0ms)

IterNodesCost
03181011
11007921
24247898
35001896

prune537.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.5b

localize27.0ms

Local error

Found 4 expressions with local error:

2.3b
(/ (* (cbrt y) (cbrt y)) (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
5.9b
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
5.9b
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
21.9b
(fma (* (/ (* (cbrt y) (cbrt y)) (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (/ (cbrt y) (sqrt (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)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
10×add-cube-cbrt *-un-lft-identity
9×add-exp-log
7×add-cbrt-cube
6×pow1 times-frac associate-/r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp
1×frac-2neg prod-exp clear-num cbrt-unprod fma-udef div-inv associate-/l*
Counts
4 → 69
Calls
4 calls:
7.0ms
(/ (* (cbrt y) (cbrt y)) (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
1.0ms
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
1.0ms
(fma (* (/ (* (cbrt y) (cbrt y)) (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (/ (cbrt y) (sqrt (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)

series1.2s

Counts
4 → 12
Calls
4 calls:
234.0ms
(/ (* (cbrt y) (cbrt y)) (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771)))
101.0ms
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
100.0ms
(sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))
762.0ms
(fma (* (/ (* (cbrt y) (cbrt y)) (sqrt (fma (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721) z 0.607771387771))) (/ (cbrt y) (sqrt (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)

simplify45.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0380975
11456864
25002831

prune473.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0.5b

regimes777.0ms

Accuracy

97.5% (0.7b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 27.7b

bsearch217.0ms

Steps
ItersRangePoint
7
1.2637373634767756e+36
5.617561246543063e+37
2.9457931334716344e+36
8
-8.132418621279826e+53
-4.358430759579319e+50
-1.301190424057146e+53

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03814
13814

end0.0ms

sample991.0ms

Algorithm
intervals
Results
675.0ms8852×body80valid