Details

Time bar (total: 10.1s)

sample103.0ms

Algorithm
intervals
Results
33.0ms741×body80nan
10.0ms194×body80valid
8.0ms18×body640valid
5.0ms25×body320valid
4.0ms5×body1280valid
2.0ms18×body160valid

simplify68.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0279
1578
21368
33128
47098
516298
635648
750018

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- z 1.0) (log (- 1.0 y)))
0.1b
(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
5.9b
(log (- 1.0 y))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×*-un-lft-identity
15×log-prod
8×add-cube-cbrt
7×pow1
6×add-exp-log
5×distribute-rgt-in distribute-lft-in associate-*l* add-cbrt-cube
4×associate-*r* distribute-lft-out-- difference-of-squares
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×log-div flip3-- associate-*l/ log-pow flip--
1×rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
3 → 63
Calls
3 calls:
28.0ms
(* (- z 1.0) (log (- 1.0 y)))
0.0ms
(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
6.0ms
(log (- 1.0 y))

series267.0ms

Counts
3 → 9
Calls
3 calls:
43.0ms
(* (- z 1.0) (log (- 1.0 y)))
185.0ms
(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
38.0ms
(log (- 1.0 y))

simplify38.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0364521
11204461
25001449

prune220.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
113×add-sqr-sqrt
80×times-frac
78×*-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
8×associate-*l*
7×flip3-- flip--
6×pow-to-exp pow-exp add-log-exp
5×sub-neg
4×expm1-log1p-u frac-times log1p-expm1-u
3×associate-*r/ cbrt-unprod distribute-lft-out--
2×pow-prod-down associate-*l/ *-commutative difference-of-squares
1×cbrt-undiv fma-neg diff-log fma-udef div-inv
Counts
4 → 241
Calls
4 calls:
48.0ms
(- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
37.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
87.0ms
(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0ms
(fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

series446.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
50.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
62.0ms
(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
201.0ms
(fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

simplify131.0ms

Algorithm
egg-herbie
Counts
253 → 253
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
010533734
146722536
250012536

prune882.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
110×add-sqr-sqrt
80×times-frac
79×associate-*r*
62×*-un-lft-identity
60×add-cube-cbrt
56×unpow-prod-down
31×add-exp-log
24×unpow2 sqr-pow
23×pow1
22×unswap-sqr
18×prod-diff sqrt-prod
13×add-cbrt-cube
12×sqrt-div associate-*l* prod-exp
11×distribute-rgt-in distribute-lft-in
9×div-exp
8×sqrt-pow1 pow1/2 swap-sqr
6×pow-to-exp flip3-+ pow-exp flip-+
5×associate-*r/ pow-prod-down pow-prod-up
4×expm1-log1p-u frac-times cbrt-unprod log1p-expm1-u add-log-exp
3×pow-sqr *-commutative
2×sub-neg associate-*l/
1×cbrt-undiv pow2 flip3-- pow-plus sqrt-unprod rem-square-sqrt flip-- fma-udef div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 227
Calls
4 calls:
38.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
22.0ms
(* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (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 1.0))
0.0ms
(fma (log y) (- x 1.0) (+ (* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (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 1.0)) (- (* (* (* (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (+ (- 1) 1)) 1) (- z 1.0)) t)))
45.0ms
(* (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))))))

series821.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
140.0ms
(* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (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 1.0))
542.0ms
(fma (log y) (- x 1.0) (+ (* (fma (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (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 1.0)) (- (* (* (* (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (+ (- 1) 1)) 1) (- z 1.0)) t)))
94.0ms
(* (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))))))

simplify69.0ms

Algorithm
egg-herbie
Counts
239 → 239
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09764122
150013227

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
160×times-frac
148×add-sqr-sqrt
146×associate-*r*
112×unpow-prod-down
78×*-un-lft-identity
76×add-cube-cbrt
52×add-exp-log
48×unpow2 sqr-pow
35×unswap-sqr
21×prod-exp
18×div-exp
16×add-cbrt-cube
12×pow-to-exp pow-exp
11×associate-*l*
10×pow1
5×cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×distribute-lft-neg-in distribute-rgt-neg-in pow-prod-down *-commutative fma-udef
2×cbrt-undiv distribute-neg-in associate-*r/ associate-*l/ div-inv
1×distribute-rgt-in neg-mul-1 flip3-- distribute-lft-in distribute-rgt-neg-out flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 268
Calls
4 calls:
38.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
37.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
28.0ms
(* (- z 1.0) (- (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0ms
(fma (log y) (- x 1.0) (+ (pow (+ (* (- z 1.0) (* (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)))) (* (- z 1.0) (- (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) 1) (- (* (* (* (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (+ (- 1) 1)) 1) (- z 1.0)) t)))

series363.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
46.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
51.0ms
(* (- z 1.0) (- (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
216.0ms
(fma (log y) (- x 1.0) (+ (pow (+ (* (- z 1.0) (* (* (cbrt (log 1.0)) (cbrt (log 1.0))) (cbrt (log 1.0)))) (* (- z 1.0) (- (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) 1) (- (* (* (* (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (+ (- 1) 1)) 1) (- z 1.0)) t)))

simplify98.0ms

Algorithm
egg-herbie
Counts
280 → 280
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
08102131
136541794
250031780

prune1.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes308.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04736
15336
25436
35436

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.1s23953×body80nan
299.0ms5916×body80valid
204.0ms712×body640valid
149.0ms254×body1280valid
118.0ms694×body320valid
48.0ms461×body160valid