Details

Time bar (total: 10.1s)

sample40.0ms

Algorithm
intervals
Results
20.0ms256×body80valid
9.0ms256×pre80true

simplify238.0ms

Calls
1 calls:
Slowest
238.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.2b

localize12.0ms

Local error

Found 3 expressions with local error:

6.2b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b
(* (/ b a) (/ b a))
0.0b
(- 1 (* (/ b a) (/ b a)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt
5×add-cbrt-cube add-exp-log
4×associate-*r* associate-*l*
3×sqrt-prod insert-posit16 add-log-exp
2×div-inv
1×pow2 frac-times rem-sqrt-square sub-neg pow-plus flip3-- pow1/2 pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative pow-prod-up cbrt-unprod flip--
Calls
3 calls:
Slowest
4.0ms
(* (/ b a) (/ b a))
1.0ms
(- 1 (* (/ b a) (/ b a)))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series57.0ms

Calls
3 calls:
Slowest
20.0ms
(* (/ b a) (/ b a))
19.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
17.0ms
(- 1 (* (/ b a) (/ b a)))

simplify1.1s

Calls
28 calls:
Slowest
155.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
115.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))
97.0ms
(sqrt (sqrt (fabs (- 1 (* (/ b a) (/ b a))))))
97.0ms
(sqrt (* (cbrt (fabs (- 1 (* (/ b a) (/ b a))))) (cbrt (fabs (- 1 (* (/ b a) (/ b a)))))))
89.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))

prune572.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 6.1b

localize12.0ms

Local error

Found 4 expressions with local error:

6.5b
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
6.5b
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b
(* (/ b a) (/ b a))
0.4b
(* (/ b a) (/ b a))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×add-cbrt-cube associate-*r* associate-*l* add-exp-log
6×cbrt-prod
4×insert-posit16 div-inv add-log-exp
2×pow2 frac-times pow-plus pow1/3 pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative pow-prod-up cbrt-unprod
Calls
4 calls:
Slowest
4.0ms
(* (/ b a) (/ b a))
4.0ms
(* (/ b a) (/ b a))
1.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
1.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))

series188.0ms

Calls
4 calls:
Slowest
76.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
75.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
22.0ms
(* (/ b a) (/ b a))
14.0ms
(* (/ b a) (/ b a))

simplify1.8s

Calls
48 calls:
Slowest
223.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
205.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
133.0ms
(pow (fabs (- 1 (/ (pow b 2) (pow a 2)))) 1/3)
128.0ms
(cbrt (* (cbrt (fabs (- 1 (* (/ b a) (/ b a))))) (cbrt (fabs (- 1 (* (/ b a) (/ b a)))))))
126.0ms
(cbrt (sqrt (fabs (- 1 (* (/ b a) (/ b a))))))

prune1.6s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 6.1b

localize19.0ms

Local error

Found 4 expressions with local error:

13.0b
(cbrt (* (* (sqrt (fabs (- 1 (* (/ b a) (/ b a))))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))
6.2b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
6.2b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
6.2b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×*-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×rem-sqrt-square pow1/2
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Calls
4 calls:
Slowest
17.0ms
(cbrt (* (* (sqrt (fabs (- 1 (* (/ b a) (/ b a))))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series64.0ms

Calls
4 calls:
Slowest
25.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
13.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
13.0ms
(cbrt (* (* (sqrt (fabs (- 1 (* (/ b a) (/ b a))))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))
13.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify2.3s

Calls
26 calls:
Slowest
125.0ms
(sqrt (* (cbrt (fabs (- 1 (* (/ b a) (/ b a))))) (cbrt (fabs (- 1 (* (/ b a) (/ b a)))))))
123.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))
119.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
118.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))
116.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))

prune631.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 6.1b

regimes86.0ms

Accuracy

0% (0.0b remaining)

Error of 7.7b against oracle of 7.7b and baseline of 7.7b

bsearch1.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
852.0ms8000×body80valid
305.0ms8000×pre80true