Details

Time bar (total: 9.8s)

sample97.0ms

Algorithm
intervals
Results
34.0ms681×body80nan
9.0ms15×body1280valid
9.0ms171×body80valid
8.0ms26×body640valid
6.0ms31×body320valid
2.0ms15×body160valid

simplify65.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0279
1578
21368
33128
47098
516298
635648
750018

prune6.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 9.4b

Counts
2 → 1

localize12.0ms

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))
5.0b
(log (- 1.0 y))

rewrite20.0ms

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:
12.0ms
(* (- z 1.0) (log (- 1.0 y)))
1.0ms
(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
4.0ms
(log (- 1.0 y))

series315.0ms

Counts
3 → 9
Calls
3 calls:
45.0ms
(* (- z 1.0) (log (- 1.0 y)))
215.0ms
(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
55.0ms
(log (- 1.0 y))

simplify39.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0361521
11194461
25002449

prune179.0ms

Filtered
72 candidates to 55 candidates (23.6%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New68472
Fresh000
Picked101
Done000
Total69473

Merged error: 0.1b

Counts
73 → 4

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* 1.0 y) (* 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))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
129×*-un-lft-identity
56×prod-diff
52×associate-*l*
44×distribute-lft-out
40×add-sqr-sqrt
33×distribute-rgt-in distribute-lft-in
32×add-cube-cbrt
24×pow1
19×log-pow
17×associate-*r*
12×fma-def
11×distribute-lft-out--
6×log-prod flip3-- associate--l+ flip--
5×add-exp-log add-cbrt-cube add-log-exp
4×frac-times
3×expm1-log1p-u log1p-expm1-u
2×sub-neg associate-*r/ associate-*l/ *-commutative difference-of-squares unswap-sqr
1×+-commutative flip3-+ pow-prod-down prod-exp sum-log cbrt-unprod flip-+ fma-udef
Counts
3 → 146
Calls
3 calls:
61.0ms
(+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))
74.0ms
(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
1.0ms
(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))

series411.0ms

Counts
3 → 9
Calls
3 calls:
101.0ms
(+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))
71.0ms
(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
239.0ms
(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))

simplify90.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
04943150
122652165
250012159

prune313.0ms

Filtered
155 candidates to 69 candidates (55.5%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1505155
Fresh303
Picked011
Done000
Total1536159

Merged error: 0.1b

Counts
159 → 6

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- z 1.0) (- (log 1.0) (fma (* 1.0 (sqrt y)) (sqrt y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.1b
(fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (fma (* 1.0 (sqrt y)) (sqrt y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))
0.4b
(fma (* 1.0 (sqrt y)) (sqrt y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
26×*-un-lft-identity
24×prod-diff
21×add-cube-cbrt
17×distribute-rgt-in distribute-lft-in
12×pow1
7×log-pow
6×log-prod flip3-- associate-*r* associate--l+ flip--
5×add-exp-log associate-*l* add-cbrt-cube
4×frac-times
3×expm1-log1p-u log1p-expm1-u distribute-lft-out-- add-log-exp
2×sub-neg associate-*r/ associate-*l/ fma-udef difference-of-squares
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
3 → 87
Calls
3 calls:
11.0ms
(* (- z 1.0) (- (log 1.0) (fma (* 1.0 (sqrt y)) (sqrt y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
1.0ms
(fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (fma (* 1.0 (sqrt y)) (sqrt y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))
1.0ms
(fma (* 1.0 (sqrt y)) (sqrt y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))

series766.0ms

Counts
3 → 9
Calls
3 calls:
108.0ms
(* (- z 1.0) (- (log 1.0) (fma (* 1.0 (sqrt y)) (sqrt y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
522.0ms
(fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (fma (* 1.0 (sqrt y)) (sqrt y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))
135.0ms
(fma (* 1.0 (sqrt y)) (sqrt y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))

simplify71.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04862497
120281674
250021652

prune294.0ms

Filtered
96 candidates to 58 candidates (39.6%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New95196
Fresh134
Picked011
Done011
Total966102

Merged error: 0.1b

Counts
102 → 6

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
8×add-cbrt-cube
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative
Counts
4 → 84
Calls
4 calls:
1.0ms
(cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (fma (* 1.0 (sqrt y)) (sqrt y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
1.0ms
(cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (fma (* 1.0 (sqrt y)) (sqrt y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
1.0ms
(cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (fma (* 1.0 (sqrt y)) (sqrt y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
5.0ms
(* (cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (fma (* 1.0 (sqrt y)) (sqrt y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))) (cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (fma (* 1.0 (sqrt y)) (sqrt y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))

series3.0s

Counts
4 → 12
Calls
4 calls:
668.0ms
(cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (fma (* 1.0 (sqrt y)) (sqrt y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
669.0ms
(cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (fma (* 1.0 (sqrt y)) (sqrt y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
659.0ms
(cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (fma (* 1.0 (sqrt y)) (sqrt y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
1.1s
(* (cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (fma (* 1.0 (sqrt y)) (sqrt y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))) (cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (fma (* 1.0 (sqrt y)) (sqrt y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))

simplify75.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04863411
117423036
250012730

prune435.0ms

Filtered
96 candidates to 72 candidates (25.0%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New91596
Fresh123
Picked011
Done022
Total9210102

Merged error: 0.0b

Counts
102 → 10

regimes427.0ms

Accuracy

0% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02514
12514

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.1s23956×body80nan
305.0ms5788×body80valid
237.0ms796×body640valid
170.0ms281×body1280valid
132.0ms696×body320valid
53.0ms474×body160valid