Details

Time bar (total: 8.8s)Debug log

sample32.0ms

Algorithm
intervals
Results
17.0ms256×body80valid
6.0ms256×pre80true

simplify247.0ms

Calls
1 calls:
Slowest
247.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.8b

localize23.0ms

Local error

Found 2 expressions with local error:

8.8b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b
(* (/ b a) (/ b a))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
6×add-sqr-sqrt
5×add-cube-cbrt
5×*-un-lft-identity
4×add-exp-log
4×associate-*l*
4×associate-*r*
4×add-cbrt-cube
3×sqrt-prod
2×add-log-exp
2×div-inv
2×log1p-expm1-u
2×expm1-log1p-u
1×cbrt-unprod
1×pow-prod-up
1×*-commutative
1×associate-*r/
1×prod-exp
1×associate-*l/
1×pow-prod-down
1×pow1/2
1×pow-plus
1×rem-sqrt-square
1×frac-times
1×pow2
Calls
2 calls:
Slowest
3.0ms
(* (/ b a) (/ b a))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series32.0ms

Calls
2 calls:
Slowest
20.0ms
(* (/ b a) (/ b a))
12.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify1.2s

Calls
25 calls:
Slowest
838.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
60.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))
59.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))
47.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
45.0ms
(sqrt (* (cbrt (fabs (- 1 (* (/ b a) (/ b a))))) (cbrt (fabs (- 1 (* (/ b a) (/ b a)))))))

prune442.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 8.7b

localize31.0ms

Local error

Found 3 expressions with local error:

8.8b
(sqrt (fabs (- 1 (* (* (/ b a) b) (/ 1 a)))))
6.2b
(* (* (/ b a) b) (/ 1 a))
0.2b
(* (/ b a) b)

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
6×add-cube-cbrt
6×*-un-lft-identity
5×add-exp-log
5×associate-*l*
5×add-cbrt-cube
5×pow1
4×associate-*l/
4×associate-*r*
3×add-log-exp
3×log1p-expm1-u
3×sqrt-prod
3×expm1-log1p-u
2×div-inv
2×*-commutative
1×cbrt-unprod
1×un-div-inv
1×associate-*r/
1×prod-exp
1×pow-prod-down
1×pow1/2
1×rem-sqrt-square
1×frac-times
Calls
3 calls:
Slowest
13.0ms
(* (* (/ b a) b) (/ 1 a))
3.0ms
(* (/ b a) b)
2.0ms
(sqrt (fabs (- 1 (* (* (/ b a) b) (/ 1 a)))))

series36.0ms

Calls
3 calls:
Slowest
14.0ms
(* (* (/ b a) b) (/ 1 a))
12.0ms
(sqrt (fabs (- 1 (* (* (/ b a) b) (/ 1 a)))))
10.0ms
(* (/ b a) b)

simplify2.4s

Calls
27 calls:
Slowest
769.0ms
(* (* (* (* (/ b a) b) (* (/ b a) b)) (* (/ b a) b)) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
480.0ms
(sqrt (sqrt (fabs (- 1 (* (* (/ b a) b) (/ 1 a))))))
327.0ms
(sqrt (* (cbrt (fabs (- 1 (* (* (/ b a) b) (/ 1 a))))) (cbrt (fabs (- 1 (* (* (/ b a) b) (/ 1 a)))))))
310.0ms
(sqrt (fabs (- 1 (* (* (/ b a) b) (/ 1 a)))))
244.0ms
(+ (log (* (/ b a) b)) (log (/ 1 a)))

prune574.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 8.7b

localize14.0ms

Local error

Found 4 expressions with local error:

13.2b
(cbrt (* (* (sqrt (fabs (- 1 (* (/ b a) (/ b a))))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))
8.8b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
8.8b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
8.8b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×add-cube-cbrt
7×*-un-lft-identity
4×add-log-exp
4×log1p-expm1-u
4×add-exp-log
4×add-cbrt-cube
4×pow1
4×expm1-log1p-u
3×pow1/2
3×rem-sqrt-square
1×rem-cbrt-cube
1×pow3
1×pow1/3
1×cbrt-prod
Calls
4 calls:
Slowest
8.0ms
(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)))))

series67.0ms

Calls
4 calls:
Slowest
21.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
18.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
15.0ms
(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)))))))

simplify1.1s

Calls
26 calls:
Slowest
67.0ms
(sqrt (* (cbrt (fabs (- 1 (* (/ b a) (/ b a))))) (cbrt (fabs (- 1 (* (/ b a) (/ b a)))))))
63.0ms
(sqrt (* (cbrt (fabs (- 1 (* (/ b a) (/ b a))))) (cbrt (fabs (- 1 (* (/ b a) (/ b a)))))))
60.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))
54.0ms
(sqrt (sqrt (fabs (- 1 (* (/ b a) (/ b a))))))
52.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))

prune770.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 8.7b

regimes86.0ms

Accuracy

0% (0.0b remaining)

Error of 7.9b against oracle of 7.9b and baseline of 7.9b

bsearch1.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.3s8000×body80valid
271.0ms8000×pre80true