Details

Time bar (total: 5.6s)

sample27.0ms

Algorithm
intervals
Results
8.0ms242×body80valid
2.0ms16×body640valid
1.0ms8×body1280valid
1.0ms13×body320valid
1.0ms17×body160valid
0.0ms2×body2560valid

simplify83.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
0206
1456
21165
33245
48615
519125
645815
750015

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- y z) (- a z))
5.8b
(fma (/ (- y z) (- a z)) (- t x) x)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt *-un-lft-identity
25×times-frac
14×add-cube-cbrt
12×distribute-lft-out-- difference-of-squares
5×associate-/r* associate-/l*
4×add-exp-log add-cbrt-cube
2×pow1 expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u associate-/l/ add-log-exp
1×cbrt-undiv frac-2neg div-sub div-exp clear-num fma-udef div-inv
Counts
2 → 64
Calls
2 calls:
12.0ms
(/ (- y z) (- a z))
0.0ms
(fma (/ (- y z) (- a z)) (- t x) x)

series173.0ms

Counts
2 → 6
Calls
2 calls:
47.0ms
(/ (- y z) (- a z))
125.0ms
(fma (/ (- y z) (- a z)) (- t x) x)

simplify65.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (58.0ms)

IterNodesCost
0265450
1729425
22562423
35002421

prune219.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1 (- a z))
0.2b
(* (- y z) (/ 1 (- a z)))
6.5b
(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
40×*-un-lft-identity
32×times-frac
23×add-cube-cbrt
21×associate-*r*
16×add-exp-log
10×add-cbrt-cube
8×distribute-lft-out-- difference-of-squares
6×pow1
5×associate-*l* associate-/r*
4×flip3-- div-exp prod-exp associate-/r/ flip--
3×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp unswap-sqr
2×cbrt-undiv frac-times rec-exp 1-exp associate-*l/ 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 → 105
Calls
3 calls:
9.0ms
(/ 1 (- a z))
25.0ms
(* (- y z) (/ 1 (- a z)))
0.0ms
(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

series206.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(/ 1 (- a z))
48.0ms
(* (- y z) (/ 1 (- a z)))
118.0ms
(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

simplify46.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0340602
11472525
25002481

prune277.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- y z) (- a z))
2.9b
(* (- t x) (/ (- y z) (- a z)))
4.2b
(+ (* (- t x) (/ (- y z) (- a z))) x)

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
73×*-un-lft-identity
51×times-frac
31×associate-*r*
27×add-cube-cbrt
23×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
5×pow1 flip3-- associate-*l* associate-/r* flip-- associate-/l* add-log-exp
4×associate-/r/
3×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-times div-exp associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×+-commutative fma-def frac-2neg flip3-+ div-sub associate-*r/ pow-prod-down clear-num sum-log *-commutative flip-+
Counts
3 → 126
Calls
3 calls:
15.0ms
(/ (- y z) (- a z))
32.0ms
(* (- t x) (/ (- y z) (- a z)))
11.0ms
(+ (* (- t x) (/ (- y z) (- a z))) x)

series341.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(/ (- y z) (- a z))
127.0ms
(* (- t x) (/ (- y z) (- a z)))
163.0ms
(+ (* (- t x) (/ (- y z) (- a z))) x)

simplify63.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0490904
12053854
25003852

prune370.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.2b

localize18.0ms

Local error

Found 4 expressions with local error:

4.2b
(+ (* (* (- t x) (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z))))) (cbrt (/ (- y z) (- a z)))) x)
4.3b
(cbrt (/ (- y z) (- a z)))
4.3b
(cbrt (/ (- y z) (- a z)))
4.3b
(cbrt (/ (- y z) (- a z)))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
97×add-sqr-sqrt *-un-lft-identity
93×cbrt-prod
75×times-frac
37×add-cube-cbrt
30×distribute-lft-out-- difference-of-squares
6×associate-/r/ add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×cbrt-div flip3-- pow1/3 flip-- div-inv
1×+-commutative fma-def flip3-+ sum-log flip-+
Counts
4 → 140
Calls
4 calls:
198.0ms
(+ (* (* (- t x) (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z))))) (cbrt (/ (- y z) (- a z)))) x)
5.0ms
(cbrt (/ (- y z) (- a z)))
6.0ms
(cbrt (/ (- y z) (- a z)))
6.0ms
(cbrt (/ (- y z) (- a z)))

series1.2s

Counts
4 → 12
Calls
4 calls:
165.0ms
(+ (* (* (- t x) (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z))))) (cbrt (/ (- y z) (- a z)))) x)
334.0ms
(cbrt (/ (- y z) (- a z)))
335.0ms
(cbrt (/ (- y z) (- a z)))
333.0ms
(cbrt (/ (- y z) (- a z)))

simplify135.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 3 (113.0ms)

IterNodesCost
04061726
110391607
243091566
350011559

prune820.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 4.2b

regimes421.0ms

Accuracy

12.4% (6.9b remaining)

Error of 10.4b against oracle of 3.6b and baseline of 11.4b

bsearch87.0ms

Steps
ItersRangePoint
9
6.522375164349517e+192
2.9199773884888967e+201
1.782566557548187e+198
4
-1.4642350205978134e+49
-9.535067694878189e+48
-1.441534308363848e+49

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02610
12610

end0.0ms

sample729.0ms

Algorithm
intervals
Results
273.0ms7862×body80valid
61.0ms471×body640valid
45.0ms268×body1280valid
38.0ms379×body320valid
17.0ms275×body160valid
4.0ms19×body2560valid