Details

Time bar (total: 22.8s)

sample184.0ms

Algorithm
intervals
Results
28.0ms314×body80valid
28.0ms42×body10240exit
24.0ms43×body1280valid
19.0ms46×body640valid
4.0ms16×body320valid
2.0ms14×body160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 4 (279.0ms)

IterNodesCost
01929
14729
212429
339527
4235626
done500126

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.4b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 eps) x)
0.0b
(* x (- eps 1.0))
0.0b
(/ (- 1.0 (/ 1.0 eps)) (exp (* (+ 1.0 eps) x)))
5.0b
(fma (exp (* x (- eps 1.0))) (+ 1.0 (/ 1.0 eps)) (/ (- 1.0 (/ 1.0 eps)) (exp (* (+ 1.0 eps) x))))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
43×*-un-lft-identity
31×add-cube-cbrt
22×times-frac
18×prod-diff
11×distribute-rgt-in distribute-lft-in
10×add-cbrt-cube
9×add-exp-log difference-of-squares
8×pow1 associate-*r*
7×associate-*l*
6×associate-/l*
5×distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r*
2×sub-neg flip3-- pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod flip-- unswap-sqr associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-+ div-sub div-exp flip-+ fma-udef div-inv distribute-lft-out
Counts
4 → 123
Calls
4 calls:
17.0ms
(* (+ 1.0 eps) x)
33.0ms
(* x (- eps 1.0))
42.0ms
(/ (- 1.0 (/ 1.0 eps)) (exp (* (+ 1.0 eps) x)))
1.0ms
(fma (exp (* x (- eps 1.0))) (+ 1.0 (/ 1.0 eps)) (/ (- 1.0 (/ 1.0 eps)) (exp (* (+ 1.0 eps) x))))

series260.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (+ 1.0 eps) x)
37.0ms
(* x (- eps 1.0))
56.0ms
(/ (- 1.0 (/ 1.0 eps)) (exp (* (+ 1.0 eps) x)))
118.0ms
(fma (exp (* x (- eps 1.0))) (+ 1.0 (/ 1.0 eps)) (/ (- 1.0 (/ 1.0 eps)) (exp (* (+ 1.0 eps) x))))

simplify2.6s

Counts
135 → 135
Iterations

Useful iterations: done (2.6s)

IterNodesCost
02652319
16672109
228641877
done50001823

prune756.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.6b

localize20.0ms

Local error

Found 2 expressions with local error:

5.3b
(fma 1.0 (* x x) (* 2.7755575615628914e-17 (/ (pow x 3) eps)))
5.6b
(/ (pow x 3) eps)

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
27×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×unpow-prod-down cube-prod associate-/l*
7×add-exp-log
4×cube-mult add-cbrt-cube unpow3 sqr-pow
3×associate-/r* div-exp
2×expm1-log1p-u pow1 log1p-expm1-u add-log-exp
1×pow-to-exp cbrt-undiv clear-num frac-2neg pow-exp fma-udef div-inv
Counts
2 → 77
Calls
2 calls:
1.0ms
(fma 1.0 (* x x) (* 2.7755575615628914e-17 (/ (pow x 3) eps)))
15.0ms
(/ (pow x 3) eps)

series110.0ms

Counts
2 → 6
Calls
2 calls:
85.0ms
(fma 1.0 (* x x) (* 2.7755575615628914e-17 (/ (pow x 3) eps)))
25.0ms
(/ (pow x 3) eps)

simplify581.0ms

Counts
83 → 83
Iterations

Useful iterations: 2 (149.0ms)

IterNodesCost
0118932
1233792
2939752
done5000752

prune454.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt x)
0.5b
(cbrt x)
1.9b
(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
5.3b
(fma 1.0 (* x x) (* 2.7755575615628914e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
185×times-frac
83×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
24×add-exp-log
14×cube-mult unpow-prod-down unpow3 cube-prod sqr-pow
13×associate-/r*
12×div-exp
10×div-inv
9×add-cbrt-cube
8×associate-/l*
6×cbrt-prod
4×expm1-log1p-u pow1 pow-exp log1p-expm1-u add-log-exp
3×cbrt-undiv
2×pow-to-exp pow1/3 prod-exp
1×clear-num frac-2neg associate-/r/ fma-udef
Counts
4 → 184
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
12.0ms
(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
0.0ms
(fma 1.0 (* x x) (* 2.7755575615628914e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))))

series714.0ms

Counts
4 → 12
Calls
4 calls:
250.0ms
(cbrt x)
258.0ms
(cbrt x)
68.0ms
(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
137.0ms
(fma 1.0 (* x x) (* 2.7755575615628914e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))))

simplify630.0ms

Counts
196 → 196
Iterations

Useful iterations: done (623.0ms)

IterNodesCost
03003757
18693268
done50002376

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt x)
0.5b
(cbrt x)
5.3b
(fma 1.0 (* x x) (* 2.7755575615628914e-17 (/ (pow (* (cbrt x) (log (exp (cbrt x)))) 3) (/ eps x))))
12.8b
(log (exp (cbrt x)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×log-pow
6×exp-prod
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×log-prod
2×pow1/3
1×rem-log-exp fma-udef
Counts
4 → 56
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
0.0ms
(fma 1.0 (* x x) (* 2.7755575615628914e-17 (/ (pow (* (cbrt x) (log (exp (cbrt x)))) 3) (/ eps x))))
3.0ms
(log (exp (cbrt x)))

series934.0ms

Counts
4 → 12
Calls
4 calls:
253.0ms
(cbrt x)
263.0ms
(cbrt x)
100.0ms
(fma 1.0 (* x x) (* 2.7755575615628914e-17 (/ (pow (* (cbrt x) (log (exp (cbrt x)))) 3) (/ eps x))))
317.0ms
(log (exp (cbrt x)))

simplify2.6s

Counts
68 → 68
Iterations

Useful iterations: 3 (929.0ms)

IterNodesCost
083583
1147506
2584397
34234377
done5000377

prune434.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.8b

regimes337.0ms

Accuracy

96.2% (0.6b remaining)

Error of 4.3b against oracle of 3.7b and baseline of 19.5b

bsearch216.0ms

Steps
ItersRangePoint
6
1.583250720483607e-07
7.294142785006675e-07
4.5959997329341335e-07

simplify10.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
04395
15295
done5295

end0.0ms

sample9.0s

Algorithm
intervals
Results
3.3s1938×body10240exit
1.6s1764×body1280valid
1.4s9917×body80valid
1.2s1287×body640valid
485.0ms299×body160valid
395.0ms673×body320valid