Details

Time bar (total: 13.4s)

sample122.0ms

Algorithm
intervals
Results
46.0ms741×body80nan
12.0ms15×body1280valid
12.0ms183×body80valid
7.0ms20×body640valid
7.0ms29×body320valid
1.0ms9×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: 7.6b

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))
3.8b
(log (- 1.0 y))

rewrite21.0ms

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:
16.0ms
(* (- 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))

series285.0ms

Counts
3 → 9
Calls
3 calls:
45.0ms
(* (- z 1.0) (log (- 1.0 y)))
198.0ms
(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
42.0ms
(log (- 1.0 y))

simplify35.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0364521
11204461
25001449

prune237.0ms

Pruning

7 alts after pruning (7 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))

rewrite101.0ms

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:
22.0ms
(- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
28.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
38.0ms
(* (- 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))

series481.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)
52.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
64.0ms
(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
219.0ms
(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))

simplify59.0ms

Algorithm
egg-herbie
Counts
253 → 253
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010533803
150012532

prune889.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.1b
(fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))
0.2b
(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.4b
(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
139×add-sqr-sqrt
105×*-un-lft-identity
102×sqrt-prod
93×add-cube-cbrt
84×associate-*r* prod-diff
80×times-frac
56×unpow-prod-down
45×distribute-rgt-in distribute-lft-in
34×add-exp-log
32×frac-times
27×pow1
24×unpow2 sqr-pow
21×flip3-- flip--
18×unswap-sqr
16×associate-*l/ add-cbrt-cube
14×prod-exp log-pow
12×flip3-+ flip-+
11×associate-*r/
9×div-exp associate-*l*
6×pow-to-exp pow-exp cbrt-unprod
5×pow-prod-down difference-of-squares
4×expm1-log1p-u log1p-expm1-u distribute-lft-out-- add-log-exp
3×*-commutative distribute-lft-out
2×sub-neg
1×cbrt-undiv fma-udef div-inv
Counts
4 → 298
Calls
4 calls:
25.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0ms
(fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))
44.0ms
(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
86.0ms
(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
48.0ms
(* 1/2 (/ (pow y 2) (pow 1.0 2)))
689.0ms
(fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))
144.0ms
(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
257.0ms
(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify115.0ms

Algorithm
egg-herbie
Counts
310 → 310
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0155410307
150018413

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

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

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:
5.0ms
(* (cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))) (cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))))
0.0ms
(cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)))
0.0ms
(cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)))
1.0ms
(cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)))

series4.2s

Counts
4 → 12
Calls
4 calls:
1.6s
(* (cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))) (cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t))))
883.0ms
(cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)))
860.0ms
(cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)))
840.0ms
(cbrt (fma (log y) (- x 1.0) (- (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)))

simplify88.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04734647
116474219
250023829

prune535.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

regimes463.0ms

Accuracy

0% (0.3b 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

sample3.0s

Algorithm
intervals
Results
1.2s24280×body80nan
335.0ms5876×body80valid
251.0ms781×body640valid
154.0ms245×body1280valid
134.0ms690×body320valid
54.0ms448×body160valid