Timeout in 10.0m

Use the --timeout flag to change the timeout.

Details

Time bar (total: 42.8s)Debug log

sample212.0ms

Algorithm
intervals

simplify104.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

104.0ms
(/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v))))

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ (fma (* v v) -5 1) PI) (* (sqrt (* 2 (fma (* v v) -3 1))) (* t (- 1 (* v v)))))
0.4b
(* (sqrt (* 2 (fma (* v v) -3 1))) (* t (- 1 (* v v))))
0.0b
(/ (fma (* v v) -5 1) PI)
0.0b
(fma (* v v) -5 1)

rewrite24.0ms

Algorithm
rewrite-expression-head
Counts
4 → 81
Calls

4 calls. Slowest were:

9.0ms
(* (sqrt (* 2 (fma (* v v) -3 1))) (* t (- 1 (* v v))))
8.0ms
(/ (/ (fma (* v v) -5 1) PI) (* (sqrt (* 2 (fma (* v v) -3 1))) (* t (- 1 (* v v)))))
5.0ms
(/ (fma (* v v) -5 1) PI)

series615.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

320.0ms
(/ (/ (fma (* v v) -5 1) PI) (* (sqrt (* 2 (fma (* v v) -3 1))) (* t (- 1 (* v v)))))
180.0ms
(* (sqrt (* 2 (fma (* v v) -3 1))) (* t (- 1 (* v v))))
94.0ms
(/ (fma (* v v) -5 1) PI)
21.0ms
(fma (* v v) -5 1)

simplify5.9s

Counts
50 → 93
Calls

50 calls. Slowest were:

670.0ms
(* (sqrt (* 2 (fma (* v v) -3 1))) (* t (- 1 (* v v))))
334.0ms
(- (* t (sqrt 2)) (* 5/2 (* t (* (sqrt 2) (pow v 2)))))
319.0ms
(- (/ 1 (* t (* (sqrt 2) PI))) (+ (* 53/8 (/ (pow v 4) (* t (* (sqrt 2) PI)))) (* 5/2 (/ (pow v 2) (* t (* (sqrt 2) PI))))))

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (/ (fma (* v v) -5 1) PI) (sqrt (* 2 (fma (* v v) -3 1)))) (* t (- 1 (* v v))))
0.0b
(/ (/ (fma (* v v) -5 1) PI) (sqrt (* 2 (fma (* v v) -3 1))))
0.0b
(/ (fma (* v v) -5 1) PI)
0.0b
(fma (* v v) -5 1)

rewrite40.0ms

Algorithm
rewrite-expression-head
Counts
4 → 124
Calls

4 calls. Slowest were:

21.0ms
(/ (/ (/ (fma (* v v) -5 1) PI) (sqrt (* 2 (fma (* v v) -3 1)))) (* t (- 1 (* v v))))
10.0ms
(/ (/ (fma (* v v) -5 1) PI) (sqrt (* 2 (fma (* v v) -3 1))))
5.0ms
(/ (fma (* v v) -5 1) PI)

series696.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

377.0ms
(/ (/ (/ (fma (* v v) -5 1) PI) (sqrt (* 2 (fma (* v v) -3 1)))) (* t (- 1 (* v v))))
197.0ms
(/ (/ (fma (* v v) -5 1) PI) (sqrt (* 2 (fma (* v v) -3 1))))
99.0ms
(/ (fma (* v v) -5 1) PI)
23.0ms
(fma (* v v) -5 1)

simplify8.7s

Counts
123 → 136
Calls

123 calls. Slowest were:

337.0ms
(- (/ 1 (* t (* (sqrt 2) PI))) (+ (* 53/8 (/ (pow v 4) (* t (* (sqrt 2) PI)))) (* 5/2 (/ (pow v 2) (* t (* (sqrt 2) PI))))))
300.0ms
(/ (/ (* (* (/ (fma (* v v) -5 1) PI) (/ (fma (* v v) -5 1) PI)) (/ (fma (* v v) -5 1) PI)) (* (* (sqrt (* 2 (fma (* v v) -3 1))) (sqrt (* 2 (fma (* v v) -3 1)))) (sqrt (* 2 (fma (* v v) -3 1))))) (* (* (* t (- 1 (* v v))) (* t (- 1 (* v v)))) (* t (- 1 (* v v)))))
277.0ms
(- (log (/ (/ (fma (* v v) -5 1) PI) (sqrt (* 2 (fma (* v v) -3 1))))) (log (* t (- 1 (* v v)))))

prune2.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* t (- 1 (* v v))) (/ (/ (fma (* v v) -5 1) PI) (sqrt (* 2 (fma (* v v) -3 1))))))
0.1b
(/ (* t (- 1 (* v v))) (/ (/ (fma (* v v) -5 1) PI) (sqrt (* 2 (fma (* v v) -3 1)))))
0.0b
(/ (/ (fma (* v v) -5 1) PI) (sqrt (* 2 (fma (* v v) -3 1))))
0.0b
(/ (fma (* v v) -5 1) PI)

rewrite38.0ms

Algorithm
rewrite-expression-head
Counts
4 → 157
Calls

4 calls. Slowest were:

14.0ms
(/ (* t (- 1 (* v v))) (/ (/ (fma (* v v) -5 1) PI) (sqrt (* 2 (fma (* v v) -3 1)))))
9.0ms
(/ (/ (fma (* v v) -5 1) PI) (sqrt (* 2 (fma (* v v) -3 1))))
7.0ms
(/ 1 (/ (* t (- 1 (* v v))) (/ (/ (fma (* v v) -5 1) PI) (sqrt (* 2 (fma (* v v) -3 1))))))

series1.0s

Counts
4 → 12
Calls

4 calls. Slowest were:

358.0ms
(/ (* t (- 1 (* v v))) (/ (/ (fma (* v v) -5 1) PI) (sqrt (* 2 (fma (* v v) -3 1)))))
305.0ms
(/ 1 (/ (* t (- 1 (* v v))) (/ (/ (fma (* v v) -5 1) PI) (sqrt (* 2 (fma (* v v) -3 1))))))
240.0ms
(/ (/ (fma (* v v) -5 1) PI) (sqrt (* 2 (fma (* v v) -3 1))))
124.0ms
(/ (fma (* v v) -5 1) PI)

simplify18.0s

Counts
150 → 169
Calls

150 calls. Slowest were:

649.0ms
(- (/ 1 (* t (* (sqrt 2) PI))) (* 5/2 (/ (pow v 2) (* t (* (sqrt 2) PI)))))
400.0ms
(/ (- 1 (* v v)) (/ 1 (sqrt (* 2 (fma (* v v) -3 1)))))
378.0ms
(- (log (* t (- 1 (* v v)))) (log (/ (/ (fma (* v v) -5 1) PI) (sqrt (* 2 (fma (* v v) -3 1))))))

prune2.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ (sqrt (/ (fma v (* v -5) 1) PI)) (sqrt (sqrt (fma v (* v -6) 2)))) (/ (* t (- 1 (* v v))) (/ (sqrt (/ (fma (* v v) -5 1) PI)) (sqrt (sqrt (* 2 (fma (* v v) -3 1)))))))
0.3b
(/ (* t (- 1 (* v v))) (/ (sqrt (/ (fma (* v v) -5 1) PI)) (sqrt (sqrt (* 2 (fma (* v v) -3 1))))))
0.0b
(/ (fma (* v v) -5 1) PI)
0.0b
(/ (fma v (* v -5) 1) PI)

rewrite454.0ms

Algorithm
rewrite-expression-head
Counts
4 → 4193
Calls

4 calls. Slowest were:

43.0ms
(/ (/ (sqrt (/ (fma v (* v -5) 1) PI)) (sqrt (sqrt (fma v (* v -6) 2)))) (/ (* t (- 1 (* v v))) (/ (sqrt (/ (fma (* v v) -5 1) PI)) (sqrt (sqrt (* 2 (fma (* v v) -3 1)))))))
16.0ms
(/ (* t (- 1 (* v v))) (/ (sqrt (/ (fma (* v v) -5 1) PI)) (sqrt (sqrt (* 2 (fma (* v v) -3 1))))))
5.0ms
(/ (fma v (* v -5) 1) PI)

series1.2s

Counts
4 → 12
Calls

4 calls. Slowest were:

541.0ms
(/ (/ (sqrt (/ (fma v (* v -5) 1) PI)) (sqrt (sqrt (fma v (* v -6) 2)))) (/ (* t (- 1 (* v v))) (/ (sqrt (/ (fma (* v v) -5 1) PI)) (sqrt (sqrt (* 2 (fma (* v v) -3 1)))))))
414.0ms
(/ (* t (- 1 (* v v))) (/ (sqrt (/ (fma (* v v) -5 1) PI)) (sqrt (sqrt (* 2 (fma (* v v) -3 1))))))
144.0ms
(/ (fma (* v v) -5 1) PI)
122.0ms
(/ (fma v (* v -5) 1) PI)

Reproduce

herbie shell --seed 2019007 +o rules:numerics
(FPCore (v t)
  :name "Falkner and Boettcher, Equation (20:1,3)"
  (/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v)))))