Details

Time bar (total: 7.7s)

sample103.0ms

Algorithm
intervals
Results
40.0ms826×body80nan
10.0ms188×body80valid
7.0ms22×body640valid
6.0ms11×body1280valid
4.0ms23×body320valid
2.0ms15×body160valid

simplify29.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

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

prune8.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.1b

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))
5.5b
(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))

series221.0ms

Counts
3 → 9
Calls
3 calls:
64.0ms
(* z (log (- 1.0 y)))
112.0ms
(fma (log y) x (- (* z (log (- 1.0 y))) t))
45.0ms
(log (- 1.0 y))

simplify104.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (98.0ms)

IterNodesCost
0332427
11128376
24553369
35001366

prune210.0ms

Filtered
68 candidates to 52 candidates (76.5%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 3 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
(* 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))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
51×prod-diff
46×associate--l+
42×add-sqr-sqrt
41×*-un-lft-identity
38×add-cube-cbrt
34×distribute-rgt-in distribute-lft-in
18×pow1
13×log-pow
12×log-prod
6×associate-*r*
5×add-exp-log sub-neg add-cbrt-cube add-log-exp
3×expm1-log1p-u associate-*l* log1p-expm1-u
2×flip3-- associate-*r/ flip-- distribute-lft-out--
1×fma-neg diff-log pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef difference-of-squares unswap-sqr
Counts
3 → 121
Calls
3 calls:
18.0ms
(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
34.0ms
(* 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))

series412.0ms

Counts
3 → 9
Calls
3 calls:
120.0ms
(- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
103.0ms
(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
188.0ms
(fma (log y) x (- (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

simplify73.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04282727
116201650
250011591

prune443.0ms

Filtered
130 candidates to 79 candidates (60.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (* 1.0 y) (* 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)
0.1b
(fma (log y) x (+ (* (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) (- (* (* (* (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))))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
22×pow1
21×sqrt-prod
15×add-cube-cbrt *-un-lft-identity
14×sqrt-div
9×sqrt-pow1 pow1/2 associate-*r* associate-*l*
8×add-exp-log swap-sqr add-cbrt-cube
7×flip3-+ flip-+
5×pow-prod-up unswap-sqr
4×expm1-log1p-u frac-times pow-prod-down log1p-expm1-u add-log-exp
3×pow-sqr
2×associate-*r/ associate-*l/ prod-exp *-commutative cbrt-unprod
1×pow2 rem-sqrt-square pow-plus sqrt-unprod rem-square-sqrt fma-udef
Counts
4 → 106
Calls
4 calls:
3.0ms
(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
3.0ms
(* (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)
0.0ms
(fma (log y) x (+ (* (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) (- (* (* (* (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (+ (- 1) 1)) 1) z) t)))
19.0ms
(* (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))))))

series772.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
217.0ms
(* (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)
387.0ms
(fma (log y) x (+ (* (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) (- (* (* (* (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))) (+ (- 1) 1)) 1) z) t)))
102.0ms
(* (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))))))

simplify81.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
04162164
118381842
250011732

prune622.0ms

Filtered
118 candidates to 78 candidates (66.1%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (cbrt z) (cbrt z))
0.6b
(cbrt z)
0.6b
(cbrt z)
0.6b
(cbrt z)

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 z) (cbrt z))
0.0ms
(cbrt z)
0.0ms
(cbrt z)
1.0ms
(cbrt z)

series732.0ms

Counts
4 → 12
Calls
4 calls:
194.0ms
(* (cbrt z) (cbrt z))
188.0ms
(cbrt z)
175.0ms
(cbrt z)
174.0ms
(cbrt z)

simplify95.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 3 (89.0ms)

IterNodesCost
0119308
1477281
22972258
35001256

prune434.0ms

Filtered
93 candidates to 72 candidates (77.4%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

regimes189.0ms

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

sample3.0s

Algorithm
intervals
Results
1.1s24591×body80nan
285.0ms5529×body80valid
265.0ms437×body1280valid
263.0ms887×body640valid
131.0ms749×body320valid
47.0ms432×body160valid