Details

Time bar (total: 8.2s)

sample103.0ms

Algorithm
intervals
Results
38.0ms826×body80nan
13.0ms199×body80valid
6.0ms9×body1280valid
4.0ms24×body320valid
4.0ms14×body640valid
1.0ms13×body160valid

simplify69.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0279
1578
21368
33128
47098
516298
635648
750018

prune7.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.0b

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))
5.5b
(log (- 1.0 y))

rewrite23.0ms

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:
15.0ms
(* (- z 1.0) (log (- 1.0 y)))
0.0ms
(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
3.0ms
(log (- 1.0 y))

series301.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(* (- z 1.0) (log (- 1.0 y)))
210.0ms
(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
43.0ms
(log (- 1.0 y))

simplify37.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0364521
11204461
25001449

prune247.0ms

Filtered
72 candidates to 55 candidates (76.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 3 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
(* (- 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))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
51×prod-diff
46×associate--l+
44×add-sqr-sqrt
43×*-un-lft-identity
38×add-cube-cbrt
34×distribute-rgt-in distribute-lft-in
18×pow1
13×log-pow
12×log-prod
7×flip3-- flip--
6×associate-*r*
5×add-exp-log sub-neg associate-*l* add-cbrt-cube add-log-exp
4×frac-times
3×expm1-log1p-u log1p-expm1-u distribute-lft-out--
2×associate-*r/ associate-*l/ difference-of-squares
1×fma-neg diff-log pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
3 → 129
Calls
3 calls:
24.0ms
(- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
41.0ms
(* (- 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))

series588.0ms

Counts
3 → 9
Calls
3 calls:
147.0ms
(- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
69.0ms
(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
372.0ms
(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))

simplify86.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
05473086
123541998
250021990

prune542.0ms

Filtered
138 candidates to 87 candidates (63.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize30.0ms

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 1 (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 1 (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))))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
29×*-un-lft-identity
27×add-cube-cbrt
22×pow1
21×sqrt-prod
18×prod-diff
14×sqrt-div
11×distribute-rgt-in distribute-lft-in associate-*r*
9×sqrt-pow1 pow1/2 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 associate-*r/ pow-prod-down log1p-expm1-u add-log-exp
3×pow-sqr
2×sub-neg associate-*l/ prod-exp *-commutative cbrt-unprod
1×pow2 rem-sqrt-square flip3-- pow-plus sqrt-unprod rem-square-sqrt flip-- fma-udef distribute-lft-out-- difference-of-squares
Counts
4 → 132
Calls
4 calls:
3.0ms
(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
12.0ms
(* (fma 1 (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 1 (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)))
23.0ms
(* (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))))))

series498.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
62.0ms
(* (fma 1 (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))
272.0ms
(fma (log y) (- x 1.0) (+ (* (fma 1 (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)))
103.0ms
(* (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))))))

simplify110.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
05513146
126062358
250012206

prune704.0ms

Filtered
144 candidates to 85 candidates (59.0%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cbrt (- z 1.0)) (* (cbrt (- z 1.0)) (+ (* 1 (log 1.0)) (* 1 (- (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))
0.3b
(cbrt (- z 1.0))
0.3b
(cbrt (- z 1.0))
0.3b
(cbrt (- z 1.0))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
42×cbrt-div
28×frac-times
21×flip3-- flip--
20×cbrt-prod
17×add-sqr-sqrt *-un-lft-identity
14×associate-*r/
9×pow1 add-exp-log add-cube-cbrt flip3-+ flip-+
8×associate-*l* associate-*l/
6×add-cbrt-cube
4×distribute-rgt-in expm1-log1p-u distribute-lft-in log1p-expm1-u distribute-lft-out-- add-log-exp difference-of-squares
3×pow1/3 pow-prod-down prod-exp cbrt-unprod
1×associate-*r* *-commutative
Counts
4 → 106
Calls
4 calls:
34.0ms
(* (cbrt (- z 1.0)) (* (cbrt (- z 1.0)) (+ (* 1 (log 1.0)) (* 1 (- (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))
2.0ms
(cbrt (- z 1.0))
2.0ms
(cbrt (- z 1.0))
2.0ms
(cbrt (- z 1.0))

series488.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(* (cbrt (- z 1.0)) (* (cbrt (- z 1.0)) (+ (* 1 (log 1.0)) (* 1 (- (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))
106.0ms
(cbrt (- z 1.0))
99.0ms
(cbrt (- z 1.0))
103.0ms
(cbrt (- z 1.0))

simplify84.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
06871866
128551707
250011667

prune858.0ms

Filtered
118 candidates to 95 candidates (80.5%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

regimes314.0ms

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
02514
12514

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.2s24591×body80nan
311.0ms5861×body80valid
238.0ms780×body640valid
177.0ms288×body1280valid
129.0ms698×body320valid
49.0ms407×body160valid