Details

Time bar (total: 4.8s)

sample27.0ms

Algorithm
intervals
Results
7.0ms237×body80valid
2.0ms18×body640valid
2.0ms13×body1280valid
1.0ms9×body320valid
0.0ms6×body160valid
0.0ms1×body2560valid

simplify73.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (13.0ms)

IterNodesCost
0226
1526
21116
32136
45175
510515
620555
732805
850025

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ y (- a t))
13.3b
(fma (/ y (- a t)) (- t z) (+ x y))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt *-un-lft-identity
15×times-frac
12×add-cube-cbrt
5×associate-/r*
4×add-exp-log add-cbrt-cube distribute-lft-out-- difference-of-squares
3×associate-/l*
2×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
1×cbrt-undiv flip3-- frac-2neg div-exp clear-num flip-- fma-udef div-inv
Counts
2 → 49
Calls
2 calls:
11.0ms
(/ y (- a t))
0.0ms
(fma (/ y (- a t)) (- t z) (+ x y))

series118.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(/ y (- a t))
87.0ms
(fma (/ y (- a t)) (- t z) (+ x y))

simplify42.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0170278
1468257
21400257
35002257

prune178.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1 (- a t))
0.2b
(* y (/ 1 (- a t)))
13.3b
(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
38×*-un-lft-identity
32×times-frac
23×add-cube-cbrt
21×associate-*r*
16×add-exp-log
10×add-cbrt-cube
7×distribute-lft-out-- difference-of-squares
6×pow1
5×associate-/r*
4×div-exp prod-exp associate-/r/
3×expm1-log1p-u associate-*l* log1p-expm1-u associate-/l* add-log-exp unswap-sqr
2×cbrt-undiv rec-exp flip3-- 1-exp flip-- cbrt-unprod div-inv
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative fma-udef inv-pow
Counts
3 → 99
Calls
3 calls:
12.0ms
(/ 1 (- a t))
31.0ms
(* y (/ 1 (- a t)))
0.0ms
(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

series159.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(/ 1 (- a t))
34.0ms
(* y (/ 1 (- a t)))
88.0ms
(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

simplify75.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 3 (69.0ms)

IterNodesCost
0288510
11143440
24305394
35001391

prune272.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ y (- a t))
3.2b
(+ (* (- t z) (/ y (- a t))) (+ x y))
11.0b
(* (- t z) (/ y (- a t)))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
39×*-un-lft-identity
31×times-frac
23×add-cube-cbrt
21×associate-*r*
10×add-exp-log frac-add add-cbrt-cube
8×flip3-- flip-- distribute-lft-out-- add-log-exp difference-of-squares
6×frac-times flip3-+ associate-*l/ flip-+
5×pow1 associate-*l* associate-/r*
4×associate-/r/
3×expm1-log1p-u associate-*r/ sum-log log1p-expm1-u associate-/l*
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×+-commutative associate-+r+ fma-def frac-2neg pow-prod-down clear-num *-commutative
Counts
3 → 113
Calls
3 calls:
11.0ms
(/ y (- a t))
33.0ms
(+ (* (- t z) (/ y (- a t))) (+ x y))
44.0ms
(* (- t z) (/ y (- a t)))

series240.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(/ y (- a t))
141.0ms
(+ (* (- t z) (/ y (- a t))) (+ x y))
67.0ms
(* (- t z) (/ y (- a t)))

simplify86.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
0639842
13106791
25001789

prune379.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt y)
0.7b
(cbrt y)
3.5b
(* (- t z) (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))))
9.3b
(+ (* (* (- t z) (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt y) (cbrt (- a t)))) (+ x y))

rewrite336.0ms

Algorithm
rewrite-expression-head
Rules
24×frac-times
22×add-exp-log associate-*l/ frac-add
16×flip3-- flip--
14×add-cbrt-cube
13×add-sqr-sqrt associate-*r*
12×cbrt-div flip3-+ flip-+
10×*-un-lft-identity
9×associate-*r/ prod-exp cbrt-unprod add-log-exp
8×add-cube-cbrt associate-/r/
6×pow1 cbrt-prod
5×associate-*l*
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×sum-log
2×times-frac pow1/3 unswap-sqr
1×+-commutative associate-+r+ fma-def pow-prod-down *-commutative div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 110
Calls
4 calls:
1.0ms
(cbrt y)
1.0ms
(cbrt y)
86.0ms
(* (- t z) (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))))
241.0ms
(+ (* (* (- t z) (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt y) (cbrt (- a t)))) (+ x y))

series863.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(cbrt y)
188.0ms
(cbrt y)
286.0ms
(* (- t z) (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t)))))
199.0ms
(+ (* (* (- t z) (/ (* (cbrt y) (cbrt y)) (* (cbrt (- a t)) (cbrt (- a t))))) (/ (cbrt y) (cbrt (- a t)))) (+ x y))

simplify56.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
011862018
150011767

prune556.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 3.5b

regimes324.0ms

Accuracy

27.5% (5.3b remaining)

Error of 8.5b against oracle of 3.2b and baseline of 10.5b

bsearch106.0ms

Steps
ItersRangePoint
10
5.918828092813435e+184
1.3751215817109247e+198
3.005206846125476e+191
9
-15126611761059.418
-1405996.5464217842
-14925789107353.797

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03220
13220

end0.0ms

sample738.0ms

Algorithm
intervals
Results
230.0ms7394×body80valid
52.0ms452×body640valid
36.0ms400×body320valid
31.0ms232×body1280valid
13.0ms244×body160valid
6.0ms16×body2560valid