Details

Time bar (total: 10.0s)

sample110.0ms

Algorithm
intervals
Results
37.0ms832×body80nan
9.0ms184×body80valid
8.0ms29×body640valid
5.0ms8×body1280valid
3.0ms20×body320valid
2.0ms16×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: 7.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(* z (log (- 1.0 y)))
0.1b
(fma (log y) x (- (* z (log (- 1.0 y))) t))
7.0b
(log (- 1.0 y))

rewrite26.0ms

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:
18.0ms
(* z (log (- 1.0 y)))
0.0ms
(fma (log y) x (- (* z (log (- 1.0 y))) t))
6.0ms
(log (- 1.0 y))

series239.0ms

Counts
3 → 9
Calls
3 calls:
69.0ms
(* z (log (- 1.0 y)))
126.0ms
(fma (log y) x (- (* z (log (- 1.0 y))) t))
44.0ms
(log (- 1.0 y))

simplify103.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (97.0ms)

IterNodesCost
0332427
11128376
24553369
35001366

prune223.0ms

Pruning

7 alts after pruning (7 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)))))) t)
0.0b
(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.1b
(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

rewrite167.0ms

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:
40.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
40.0ms
(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
74.0ms
(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0ms
(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

series665.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
325.0ms
(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
104.0ms
(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
182.0ms
(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

simplify109.0ms

Algorithm
egg-herbie
Counts
245 → 245
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
09363444
143412184
250012177

prune817.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

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:
12.0ms
(* (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))) (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))
1.0ms
(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
1.0ms
(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
1.0ms
(cbrt (fma (log y) x (- (* 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:
365.0ms
(* (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))) (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))
329.0ms
(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
328.0ms
(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
340.0ms
(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))

simplify66.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04212516
115382319
250022069

prune502.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
0.6b
(cbrt (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))
0.6b
(cbrt (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))
0.6b
(cbrt (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
30×cbrt-prod
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp
Counts
4 → 61
Calls
4 calls:
1.0ms
(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
2.0ms
(cbrt (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))
2.0ms
(cbrt (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))
2.0ms
(cbrt (cbrt (fma (log y) x (- (* 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:
348.0ms
(cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
343.0ms
(cbrt (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))
332.0ms
(cbrt (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))
345.0ms
(cbrt (cbrt (fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))

simplify111.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 3 (89.0ms)

IterNodesCost
03731860
110701736
239901665
350011660

prune492.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.1b

regimes308.0ms

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
02312
12312

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.0s23996×body80nan
266.0ms5517×body80valid
249.0ms886×body640valid
246.0ms425×body1280valid
126.0ms754×body320valid
45.0ms448×body160valid