Details

Time bar (total: 2.2m)

sample26.0ms

Algorithm
intervals
Results
11.0ms271×body80valid

simplify141.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0248
1438
2758
31208
41568
51898
62658
74518
810238
936328
1050018

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* z (- t a))
0.0b
(+ y (* z (- b y)))
0.7b
(+ (* x y) (* z (- t a)))
22.6b
(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
54×prod-diff
53×*-un-lft-identity
51×add-cube-cbrt
44×associate-+r+
33×distribute-rgt-in distribute-lft-in
9×times-frac
8×add-exp-log add-cbrt-cube add-log-exp
6×pow1 sub-neg
5×associate-*r*
4×expm1-log1p-u fma-def flip3-+ flip-+ log1p-expm1-u
3×associate-*l* associate-/r* associate-/l*
2×+-commutative associate-*r/ sum-log associate-/r/ associate-/l/
1×cbrt-undiv flip3-- frac-2neg div-exp pow-prod-down prod-exp clear-num *-commutative flip-- cbrt-unprod div-inv distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 153
Calls
4 calls:
16.0ms
(* z (- t a))
6.0ms
(+ y (* z (- b y)))
6.0ms
(+ (* x y) (* z (- t a)))
12.0ms
(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series479.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* z (- t a))
31.0ms
(+ y (* z (- b y)))
49.0ms
(+ (* x y) (* z (- t a)))
360.0ms
(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify89.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
06081288
12360956
25001942

prune558.0ms

Filtered
165 candidates to 109 candidates (66.1%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt a)
0.6b
(cbrt a)
22.6b
(/ (+ (fma x y (* z (- t a))) (* z (fma (- (cbrt a)) (* (cbrt a) (cbrt a)) (* (cbrt a) (* (cbrt a) (cbrt a)))))) (+ y (* z (- b y))))
59.9b
(fma (- (cbrt a)) (* (cbrt a) (cbrt a)) (* (cbrt a) (* (cbrt a) (cbrt a))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log cbrt-prod add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×flip3-+ pow1/3 associate-/r/ flip-+ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv
Counts
4 → 69
Calls
4 calls:
1.0ms
(cbrt a)
1.0ms
(cbrt a)
9.0ms
(/ (+ (fma x y (* z (- t a))) (* z (fma (- (cbrt a)) (* (cbrt a) (cbrt a)) (* (cbrt a) (* (cbrt a) (cbrt a)))))) (+ y (* z (- b y))))
0.0ms
(fma (- (cbrt a)) (* (cbrt a) (cbrt a)) (* (cbrt a) (* (cbrt a) (cbrt a))))

series2.1m

Counts
4 → 12
Calls
4 calls:
216.0ms
(cbrt a)
203.0ms
(cbrt a)
2.1m
(/ (+ (fma x y (* z (- t a))) (* z (fma (- (cbrt a)) (* (cbrt a) (cbrt a)) (* (cbrt a) (* (cbrt a) (cbrt a)))))) (+ y (* z (- b y))))
589.0ms
(fma (- (cbrt a)) (* (cbrt a) (cbrt a)) (* (cbrt a) (* (cbrt a) (cbrt a))))

simplify53.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
02591232
19381052
25001980

prune454.0ms

Filtered
81 candidates to 70 candidates (86.4%)
Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 22.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* z (- t a))
0.2b
(/ 1 (/ (fma (- b y) z y) (fma x y (* z (- t a)))))
0.3b
(fma x y (* z (- t a)))
22.6b
(/ (fma (- b y) z y) (fma x y (* z (- t a))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
72×add-sqr-sqrt
70×*-un-lft-identity
68×add-cube-cbrt
19×add-exp-log
18×prod-diff
16×associate-/r*
13×add-cbrt-cube
11×distribute-rgt-in distribute-lft-in
8×div-exp
7×pow1
6×div-inv associate-/l*
5×associate-*r*
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l*
2×sub-neg rec-exp frac-2neg 1-exp associate-*r/ clear-num
1×flip3-- pow-flip pow-prod-down prod-exp associate-/r/ *-commutative flip-- cbrt-unprod fma-udef distribute-lft-out-- inv-pow difference-of-squares unswap-sqr
Counts
4 → 163
Calls
4 calls:
12.0ms
(* z (- t a))
5.0ms
(/ 1 (/ (fma (- b y) z y) (fma x y (* z (- t a)))))
0.0ms
(fma x y (* z (- t a)))
2.0ms
(/ (fma (- b y) z y) (fma x y (* z (- t a))))

series1.6s

Counts
4 → 12
Calls
4 calls:
42.0ms
(* z (- t a))
1.3s
(/ 1 (/ (fma (- b y) z y) (fma x y (* z (- t a)))))
53.0ms
(fma x y (* z (- t a)))
175.0ms
(/ (fma (- b y) z y) (fma x y (* z (- t a))))

simplify66.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05201776
121461503
250011426

prune409.0ms

Filtered
175 candidates to 96 candidates (54.9%)
Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 9.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma x y (* z (- t a)))
0.7b
(/ 1 (fma x y (* z (- t a))))
0.8b
(/ 1 (fma (- b y) z y))
21.8b
(/ (/ 1 (fma (- b y) z y)) (/ 1 (fma x y (* z (- t a)))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
439×times-frac
216×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
52×add-exp-log
36×div-exp
31×div-inv
20×add-cbrt-cube
19×associate-/r* associate-/l*
10×cbrt-undiv rec-exp 1-exp
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×pow-flip inv-pow
1×associate-/r/ fma-udef associate-/l/
Counts
4 → 305
Calls
4 calls:
0.0ms
(fma x y (* z (- t a)))
2.0ms
(/ 1 (fma x y (* z (- t a))))
7.0ms
(/ 1 (fma (- b y) z y))
13.0ms
(/ (/ 1 (fma (- b y) z y)) (/ 1 (fma x y (* z (- t a)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
51.0ms
(fma x y (* z (- t a)))
70.0ms
(/ 1 (fma x y (* z (- t a))))
97.0ms
(/ 1 (fma (- b y) z y))
1.2s
(/ (/ 1 (fma (- b y) z y)) (/ 1 (fma x y (* z (- t a)))))

simplify80.0ms

Algorithm
egg-herbie
Counts
317 → 317
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
011774596
150024026

prune664.0ms

Filtered
317 candidates to 150 candidates (47.3%)
Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 9.8b

regimes469.0ms

Accuracy

30.3% (8.5b remaining)

Error of 19.2b against oracle of 10.6b and baseline of 22.8b

bsearch77.0ms

Steps
ItersRangePoint
6
4.0667917201222455e+196
3.255633477239645e+197
4.855374827111781e+196
8
-3.194939220471551e+133
-4.2310204673979254e+129
-2.105295868119687e+131

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02910
12910

end0.0ms

sample628.0ms

Algorithm
intervals
Results
344.0ms8417×body80valid