Details

Time bar (total: 7.9s)

sample98.0ms

Algorithm
intervals
Results
32.0ms741×body80nan
8.0ms180×body80valid
6.0ms23×body640valid
6.0ms10×body1280valid
5.0ms30×body320valid
2.0ms17×body160valid

simplify26.0ms

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: 9.6b

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))
5.9b
(log (- 1.0 y))

rewrite22.0ms

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:
14.0ms
(* z (log (- 1.0 y)))
0.0ms
(fma (log y) x (- (* z (log (- 1.0 y))) t))
6.0ms
(log (- 1.0 y))

series205.0ms

Counts
3 → 9
Calls
3 calls:
59.0ms
(* z (log (- 1.0 y)))
103.0ms
(fma (log y) x (- (* z (log (- 1.0 y))) t))
42.0ms
(log (- 1.0 y))

simplify101.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (95.0ms)

IterNodesCost
0332427
11128376
24553369
35001366

prune195.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite160.0ms

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:
37.0ms
(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
38.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
69.0ms
(* 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))

series394.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
47.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
89.0ms
(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
146.0ms
(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

simplify116.0ms

Algorithm
egg-herbie
Counts
245 → 245
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
09363375
138932186
250012179

prune781.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 0.5 (* z (pow y 2)))
0.0b
(fma 1.0 (* z y) (* 0.5 (* z (pow y 2))))
0.1b
(fma (log y) x (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 0.5 (* z (pow y 2)))))) t))
6.1b
(* z (pow y 2))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log
14×add-sqr-sqrt
11×add-cbrt-cube
10×prod-exp
9×associate-*r*
8×add-cube-cbrt *-un-lft-identity
6×pow1 associate-*l*
4×expm1-log1p-u unpow-prod-down cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
2×pow-to-exp pow-exp *-commutative fma-udef unpow2 sqr-pow
1×pow-prod-down
Counts
4 → 70
Calls
4 calls:
19.0ms
(* 0.5 (* z (pow y 2)))
0.0ms
(fma 1.0 (* z y) (* 0.5 (* z (pow y 2))))
0.0ms
(fma (log y) x (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 0.5 (* z (pow y 2)))))) t))
15.0ms
(* z (pow y 2))

series263.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* 0.5 (* z (pow y 2)))
77.0ms
(fma 1.0 (* z y) (* 0.5 (* z (pow y 2))))
131.0ms
(fma (log y) x (- (fma z (log 1.0) (- (fma 1.0 (* z y) (* 0.5 (* z (pow y 2)))))) t))
27.0ms
(* z (pow y 2))

simplify180.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0226473
1852402
24875402
35001402

prune302.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0b
(* (fma (sqrt (log 1.0)) (sqrt (log 1.0)) (- (* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) z)
0.1b
(fma (log y) x (+ (* (fma (sqrt (log 1.0)) (sqrt (log 1.0)) (- (* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) z) (- (* (* (* (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (+ (- 1) 1)) 1) z) t)))
0.5b
(* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt
80×times-frac
77×associate-*r*
56×unpow-prod-down
48×add-cube-cbrt *-un-lft-identity
31×add-exp-log
24×unpow2 sqr-pow
23×pow1
22×unswap-sqr
18×sqrt-prod
13×add-cbrt-cube
12×sqrt-div associate-*l* prod-exp
9×div-exp
8×sqrt-pow1 pow1/2 swap-sqr
6×pow-to-exp flip3-+ pow-exp flip-+
5×pow-prod-down pow-prod-up
4×expm1-log1p-u frac-times cbrt-unprod log1p-expm1-u add-log-exp
3×associate-*r/ pow-sqr *-commutative
2×associate-*l/
1×cbrt-undiv pow2 pow-plus sqrt-unprod rem-square-sqrt fma-udef div-inv
Counts
4 → 201
Calls
4 calls:
37.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
7.0ms
(* (fma (sqrt (log 1.0)) (sqrt (log 1.0)) (- (* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) z)
0.0ms
(fma (log y) x (+ (* (fma (sqrt (log 1.0)) (sqrt (log 1.0)) (- (* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) z) (- (* (* (* (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (+ (- 1) 1)) 1) z) t)))
46.0ms
(* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

series524.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
133.0ms
(* (fma (sqrt (log 1.0)) (sqrt (log 1.0)) (- (* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) z)
247.0ms
(fma (log y) x (+ (* (fma (sqrt (log 1.0)) (sqrt (log 1.0)) (- (* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) z) (- (* (* (* (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (+ (- 1) 1)) 1) z) t)))
99.0ms
(* (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

simplify123.0ms

Algorithm
egg-herbie
Counts
213 → 213
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
08422483
139702066
250011946

prune1.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes175.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02312
12312

end0.0ms

sample3.0s

Algorithm
intervals
Results
964.0ms23953×body80nan
268.0ms5588×body80valid
224.0ms404×body1280valid
221.0ms822×body640valid
120.0ms757×body320valid
45.0ms466×body160valid