Details

Time bar (total: 32.6s)

sample37.0ms

Algorithm
intervals
Results
20.0ms256×body80valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
06211
115411
250311
3184011
4500311

prune13.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 23.7b

Counts
2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.1b
(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
0.4b
(/ (- x 2.0) (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
22.9b
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
128×times-frac
98×add-sqr-sqrt *-un-lft-identity
70×add-cube-cbrt
19×associate-/r*
14×distribute-lft-out-- difference-of-squares
11×add-exp-log add-cbrt-cube associate-/l*
9×associate-/r/
8×div-inv
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×fma-udef associate-/l/
1×flip3-- div-sub flip--
Counts
4 → 160
Calls
4 calls:
1.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
1.0ms
(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
10.0ms
(/ (- x 2.0) (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
3.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

series543.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
58.0ms
(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
282.0ms
(/ (- x 2.0) (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
176.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

simplify102.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
06962853
127022718
250012716

prune841.0ms

Filtered
172 candidates to 132 candidates (76.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1657172
Fresh011
Picked101
Done000
Total1668174

Merged error: 0b

Counts
174 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
0.2b
(* (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (+ x 2.0))
15.7b
(/ (- (* x x) (* 2.0 2.0)) (* (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (+ x 2.0)))
22.9b
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
1788×add-sqr-sqrt
1151×times-frac
733×*-un-lft-identity
625×difference-of-squares
555×associate-*l*
363×add-cube-cbrt
320×unswap-sqr
300×swap-sqr
285×*-commutative
140×associate-*r*
125×distribute-lft-out--
54×associate-/l*
45×associate-/r*
37×div-inv
36×frac-times
35×distribute-lft-out
29×associate-/r/
20×add-exp-log flip3-+ add-cbrt-cube flip-+
18×associate-*l/
8×frac-2neg clear-num
6×pow1 cbrt-undiv div-exp
4×expm1-log1p-u associate-*r/ prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×+-commutative distribute-rgt-in distribute-lft-in associate-/l/
1×flip3-- div-sub pow-prod-down flip-- fma-udef
Counts
4 → 1005
Calls
4 calls:
1.0ms
(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
16.0ms
(* (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (+ x 2.0))
64.0ms
(/ (- (* x x) (* 2.0 2.0)) (* (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (+ x 2.0)))
3.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

series780.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
203.0ms
(* (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (+ x 2.0))
336.0ms
(/ (- (* x x) (* 2.0 2.0)) (* (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (+ x 2.0)))
183.0ms
(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

simplify333.0ms

Algorithm
egg-herbie
Counts
1017 → 1017
Iterations

Useful iterations: 1 (48.0ms)

IterNodesCost
0262323758
1500123474

prune2.0s

Filtered
1017 candidates to 301 candidates (29.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New101341017
Fresh527
Picked101
Done000
Total101961025

Merged error: 0b

Counts
1025 → 6

localize35.0ms

Local error

Found 4 expressions with local error:

6.1b
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
14.5b
(* (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (+ x 2.0))
20.6b
(* (/ 1 (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (- (* x x) (* 2.0 2.0)) (* (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (+ x 2.0))))
23.0b
(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

rewrite816.0ms

Algorithm
rewrite-expression-head
Rules
3854×add-sqr-sqrt
2148×times-frac
1699×*-un-lft-identity
1352×associate-*r*
1248×associate-*l*
1175×difference-of-squares
1022×add-cube-cbrt
912×frac-times
901×associate-/r*
746×sqrt-prod
695×associate-/l*
651×unswap-sqr
564×swap-sqr
518×*-commutative
239×distribute-lft-out--
94×clear-num
93×frac-2neg
76×associate-*r/
71×add-exp-log
50×div-inv
47×distribute-lft-out
43×add-cbrt-cube
38×associate-/r/
36×associate-*l/
26×flip3-+ div-exp prod-exp flip-+ associate-/l/
14×cbrt-undiv cbrt-unprod
13×flip3-- flip--
9×pow1
6×un-div-inv
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
2×+-commutative distribute-rgt-in distribute-lft-in pow-prod-down
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 2342
Calls
4 calls:
2.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
13.0ms
(* (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (+ x 2.0))
515.0ms
(* (/ 1 (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (- (* x x) (* 2.0 2.0)) (* (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (+ x 2.0))))
4.0ms
(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

series1.1s

Counts
4 → 12
Calls
4 calls:
110.0ms
(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
316.0ms
(* (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (+ x 2.0))
340.0ms
(* (/ 1 (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (- (* x x) (* 2.0 2.0)) (* (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (+ x 2.0))))
293.0ms
(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

simplify955.0ms

Algorithm
egg-herbie
Counts
2354 → 2354
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
0500259087

prune6.4s

Filtered
2354 candidates to 846 candidates (35.9%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New235222354
Fresh235
Picked011
Done000
Total235462360

Merged error: 0b

Counts
2360 → 6

localize34.0ms

Local error

Found 4 expressions with local error:

14.5b
(* (/ 1 (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (- (* x x) (* 2.0 2.0)) (+ x 2.0)))
14.6b
(/ (* (/ 1 (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (- (* x x) (* 2.0 2.0)) (+ x 2.0))) (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
15.5b
(/ (- (* x x) (* 2.0 2.0)) (+ x 2.0))
23.0b
(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
11080×times-frac
10952×add-sqr-sqrt
7248×*-un-lft-identity
3906×add-cube-cbrt
3312×associate-*r*
3175×difference-of-squares
2169×sqrt-prod
1524×swap-sqr
1510×unswap-sqr
1346×associate-/l*
1294×*-commutative
1044×associate-*l*
1008×frac-times
852×distribute-lft-out
652×associate-/r*
643×distribute-lft-out--
618×associate-/l/
227×div-inv
118×clear-num
116×frac-2neg
103×add-exp-log
84×associate-*r/
62×associate-/r/
61×add-cbrt-cube
53×div-exp
29×cbrt-undiv
27×flip3-- flip--
25×flip3-+ flip-+
24×associate-*l/ prod-exp
12×un-div-inv cbrt-unprod
6×pow1 rec-exp 1-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
1×div-sub pow-prod-down
Counts
4 → 5649
Calls
4 calls:
105.0ms
(* (/ 1 (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (- (* x x) (* 2.0 2.0)) (+ x 2.0)))
238.0ms
(/ (* (/ 1 (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (- (* x x) (* 2.0 2.0)) (+ x 2.0))) (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
40.0ms
(/ (- (* x x) (* 2.0 2.0)) (+ x 2.0))
4.0ms
(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

series903.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(* (/ 1 (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (- (* x x) (* 2.0 2.0)) (+ x 2.0)))
340.0ms
(/ (* (/ 1 (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (- (* x x) (* 2.0 2.0)) (+ x 2.0))) (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
85.0ms
(/ (- (* x x) (* 2.0 2.0)) (+ x 2.0))
292.0ms
(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

simplify2.5s

Algorithm
egg-herbie
Counts
5661 → 5661
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
05001194486

prune12.4s

Filtered
5661 candidates to 1562 candidates (27.6%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New566105661
Fresh044
Picked011
Done011
Total566165667

Merged error: 0b

Counts
5667 → 6

regimes291.0ms

Accuracy

96.7% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 24.5b

bsearch4.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07645
17645

end0.0ms

sample931.0ms

Algorithm
intervals
Results
752.0ms8005×body80valid