Details

Time bar (total: 9.4s)

sample130.0ms

Algorithm
intervals
Results
56.0ms819×body80nan
15.0ms189×body80valid
10.0ms25×body640valid
8.0ms11×body1280valid
4.0ms14×body320valid
3.0ms18×body160valid

simplify27.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0227
1386
2536
3616
4786
51106
61756
72846
83636
93926
104766
114766

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(* z (log (- 1.0 y)))
0.2b
(fma (log y) x (- (* z (log (- 1.0 y))) t))
5.6b
(log (- 1.0 y))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
15×log-prod
14×*-un-lft-identity
8×add-cube-cbrt
7×pow1
6×add-exp-log
5×distribute-rgt-in distribute-lft-in add-cbrt-cube
4×associate-*r*
3×expm1-log1p-u associate-*l* log1p-expm1-u distribute-lft-out-- add-log-exp difference-of-squares
2×log-div log-pow
1×flip3-- rem-log-exp pow-prod-down prod-exp *-commutative flip-- cbrt-unprod fma-udef unswap-sqr
Counts
3 → 59
Calls
3 calls:
7.0ms
(* z (log (- 1.0 y)))
0.0ms
(fma (log y) x (- (* z (log (- 1.0 y))) t))
3.0ms
(log (- 1.0 y))

series236.0ms

Counts
3 → 9
Calls
3 calls:
71.0ms
(* z (log (- 1.0 y)))
117.0ms
(fma (log y) x (- (* z (log (- 1.0 y))) t))
49.0ms
(log (- 1.0 y))

simplify110.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (104.0ms)

IterNodesCost
0332427
11128376
24553369
35001366

prune218.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0b
(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0b
(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
0.1b
(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
111×add-sqr-sqrt
80×times-frac
76×*-un-lft-identity
74×associate-*r*
73×add-cube-cbrt
56×unpow-prod-down
51×prod-diff
46×associate--l+
34×distribute-rgt-in distribute-lft-in
29×add-exp-log
24×unpow2 sqr-pow
21×pow1
18×unswap-sqr
13×log-pow
12×log-prod
11×prod-exp add-cbrt-cube
9×div-exp
6×pow-to-exp associate-*l* pow-exp add-log-exp
5×sub-neg
4×expm1-log1p-u log1p-expm1-u
3×associate-*r/ cbrt-unprod
2×flip3-- pow-prod-down *-commutative flip-- distribute-lft-out--
1×cbrt-undiv fma-neg diff-log fma-udef div-inv difference-of-squares
Counts
4 → 233
Calls
4 calls:
27.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
35.0ms
(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
18.0ms
(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
0.0ms
(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

series457.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
106.0ms
(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
130.0ms
(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
171.0ms
(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

simplify125.0ms

Algorithm
egg-herbie
Counts
245 → 245
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
09363375
138932186
250012179

prune994.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))
0.0b
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.1b
(fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
80×times-frac
71×add-sqr-sqrt
68×associate-*r*
56×unpow-prod-down
37×add-cube-cbrt *-un-lft-identity
26×add-exp-log
24×unpow2 sqr-pow
17×unswap-sqr
10×prod-exp
9×div-exp
8×add-cbrt-cube
6×pow-to-exp pow-exp
5×pow1 add-log-exp
3×expm1-log1p-u associate-*l* log1p-expm1-u
2×cbrt-unprod
1×cbrt-undiv +-commutative fma-def flip3-+ associate-*r/ pow-prod-down sum-log *-commutative flip-+ fma-udef div-inv
Counts
3 → 136
Calls
3 calls:
3.0ms
(+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))
26.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0ms
(fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))

series317.0ms

Counts
3 → 9
Calls
3 calls:
96.0ms
(+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))
49.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
172.0ms
(fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))

simplify77.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
0677960
12897813
25001810

prune528.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))) (cbrt (fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))))
0.5b
(cbrt (fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))))
0.5b
(cbrt (fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))))
0.5b
(cbrt (fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
6.0ms
(* (cbrt (fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))) (cbrt (fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))))
0.0ms
(cbrt (fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))))
1.0ms
(cbrt (fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))))
1.0ms
(cbrt (fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))))

series1.4s

Counts
4 → 12
Calls
4 calls:
367.0ms
(* (cbrt (fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))) (cbrt (fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))))
339.0ms
(cbrt (fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))))
327.0ms
(cbrt (fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))))
331.0ms
(cbrt (fma (log y) x (fma z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t))))

simplify60.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04192516
115362319
250012069

prune462.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

regimes274.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02212
12212

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.6s24353×body80nan
442.0ms5492×body80valid
394.0ms958×body640valid
282.0ms385×body1280valid
183.0ms702×body320valid
82.0ms502×body160valid