Timeout in 10.0m

Use the --timeout flag to change the timeout.

Details

Time bar (total: 7.8m)Debug log

sample2.2s

Algorithm
intervals
Results
524×(pre true 80)
108×(body exit 10240)
104×(body real 1280)
82×(body real 640)
70×(body nan 1280)
47×(body nan 640)
40×(body real 320)
19×(body nan 320)
19×(body real 160)
12×(body nan 80)
12×(body real 80)
11×(body nan 160)

simplify419.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
419.0ms
(* (* (* (sqrt (* PI 2)) (pow (+ (+ (- z 1) 7) 0.5) (+ (- z 1) 0.5))) (exp (- (+ (+ (- z 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- z 1) 1))) (/ -1259.1392167224028 (+ (- z 1) 2))) (/ 771.3234287776531 (+ (- z 1) 3))) (/ -176.6150291621406 (+ (- z 1) 4))) (/ 12.507343278686905 (+ (- z 1) 5))) (/ -0.13857109526572012 (+ (- z 1) 6))) (/ 9.984369578019572e-06 (+ (- z 1) 7))) (/ 1.5056327351493116e-07 (+ (- z 1) 8))))

prune37.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.3b

localize130.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt (* PI 2))
1.0b
(* (pow (+ (+ 6 0.5) z) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
1.0b
(/ (* (pow (+ (+ 6 0.5) z) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (+ 6 0.5) z)))
0.9b
(* (/ (* (pow (+ (+ 6 0.5) z) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (+ 6 0.5) z))) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -176.6150291621406 (+ z 3))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ 1 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ 7 z))))))

rewrite596.0ms

Algorithm
rewrite-expression-head
Rules
1212×frac-add
440×flip-+
440×flip3-+
156×associate-*r/
156×frac-times
142×*-un-lft-identity
105×distribute-lft-out
32×associate-*r*
27×add-exp-log
20×add-cbrt-cube
15×associate-*l*
14×prod-exp
12×add-cube-cbrt
12×add-sqr-sqrt
8×div-exp
8×times-frac
6×cbrt-unprod
6×pow1
4×add-log-exp
4×log1p-expm1-u
4×associate-/r*
4×cbrt-undiv
4×expm1-log1p-u
3×pow-exp
3×associate-*l/
3×exp-sum
3×unpow-prod-down
3×pow-to-exp
2×pow-sub
2×div-inv
2×sqrt-prod
2×associate-+l-
2×*-commutative
1×associate-/l/
1×associate-/l*
1×pow-prod-down
1×pow1/2
1×distribute-lft-in
1×frac-2neg
1×clear-num
1×unpow-prod-up
1×distribute-rgt-in
Counts
4 → 435
Calls
4 calls:
Slowest
524.0ms
(* (/ (* (pow (+ (+ 6 0.5) z) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (+ 6 0.5) z))) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -176.6150291621406 (+ z 3))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ 1 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ 7 z))))))
21.0ms
(/ (* (pow (+ (+ 6 0.5) z) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (+ 6 0.5) z)))
14.0ms
(* (pow (+ (+ 6 0.5) z) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
1.0ms
(sqrt (* PI 2))

series673.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
325.0ms
(* (/ (* (pow (+ (+ 6 0.5) z) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (+ 6 0.5) z))) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -176.6150291621406 (+ z 3))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ 1 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ 7 z))))))
177.0ms
(/ (* (pow (+ (+ 6 0.5) z) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (+ 6 0.5) z)))
171.0ms
(* (pow (+ (+ 6 0.5) z) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
0.0ms
(sqrt (* PI 2))

simplify2.6m

Counts
561 → 445
Calls
561 calls:
Slowest
1.0s
(* (exp (+ (+ 6 0.5) z)) (* (* (* (+ z 2) (+ z 3)) (* (- 0.9999999999998099 (/ 676.5203681218851 z)) (+ 1 z))) (* (+ (* (/ -0.13857109526572012 (+ z 5)) (/ -0.13857109526572012 (+ z 5))) (- (* (/ 12.507343278686905 (- z -4)) (/ 12.507343278686905 (- z -4))) (* (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))))) (* (+ z 6) (+ 7 z)))))
993.0ms
(* (exp (+ (+ 6 0.5) z)) (* (* (+ (* (/ 771.3234287776531 (+ z 2)) (/ 771.3234287776531 (+ z 2))) (- (* (/ -176.6150291621406 (+ z 3)) (/ -176.6150291621406 (+ z 3))) (* (/ 771.3234287776531 (+ z 2)) (/ -176.6150291621406 (+ z 3))))) (* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 z) (/ 676.5203681218851 z)) (* 0.9999999999998099 (/ 676.5203681218851 z)))) (+ 1 z))) (* (* (+ z 5) (- z -4)) (* (+ z 6) (+ 7 z)))))
962.0ms
(* (exp (+ (+ 6 0.5) z)) (* (* (- (/ 771.3234287776531 (+ z 2)) (/ -176.6150291621406 (+ z 3))) (* (- 0.9999999999998099 (/ 676.5203681218851 z)) (+ 1 z))) (* (+ (* (/ -0.13857109526572012 (+ z 5)) (/ -0.13857109526572012 (+ z 5))) (- (* (/ 12.507343278686905 (- z -4)) (/ 12.507343278686905 (- z -4))) (* (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))))) (+ (* (/ 9.984369578019572e-06 (+ z 6)) (/ 9.984369578019572e-06 (+ z 6))) (- (* (/ 1.5056327351493116e-07 (+ 7 z)) (/ 1.5056327351493116e-07 (+ 7 z))) (* (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ 7 z))))))))
911.0ms
(* (* (+ (* (/ 771.3234287776531 (+ z 2)) (/ 771.3234287776531 (+ z 2))) (- (* (/ -176.6150291621406 (+ z 3)) (/ -176.6150291621406 (+ z 3))) (* (/ 771.3234287776531 (+ z 2)) (/ -176.6150291621406 (+ z 3))))) (* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 z) (/ 676.5203681218851 z)) (* 0.9999999999998099 (/ 676.5203681218851 z)))) (+ 1 z))) (* (* (+ z 5) (- z -4)) (* (+ z 6) (+ 7 z))))
803.0ms
(* (exp (+ (+ 6 0.5) z)) (* (* (+ (* (/ 771.3234287776531 (+ z 2)) (/ 771.3234287776531 (+ z 2))) (- (* (/ -176.6150291621406 (+ z 3)) (/ -176.6150291621406 (+ z 3))) (* (/ 771.3234287776531 (+ z 2)) (/ -176.6150291621406 (+ z 3))))) (+ (* (+ 0.9999999999998099 (/ 676.5203681218851 z)) (+ 0.9999999999998099 (/ 676.5203681218851 z))) (- (* (/ -1259.1392167224028 (+ 1 z)) (/ -1259.1392167224028 (+ 1 z))) (* (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ 1 z)))))) (- (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ 7 z))))))

prune30.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
1.0b
(/ (sqrt PI) (exp (+ z 6.5)))
0.9b
(* (* (/ (sqrt PI) (exp (+ z 6.5))) (/ (sqrt 2) (pow (+ z 6.5) (- 0.5 z)))) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -176.6150291621406 (+ z 3))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ 1 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ 7 z))))))
0.1b
(exp (+ z 6.5))

rewrite626.0ms

Algorithm
rewrite-expression-head
Rules
2424×frac-add
880×flip-+
880×flip3-+
625×frac-times
313×associate-*r/
160×associate-*l/
145×*-un-lft-identity
105×distribute-lft-out
35×add-exp-log
28×associate-*r*
24×add-cbrt-cube
17×prod-exp
15×add-cube-cbrt
15×add-sqr-sqrt
12×times-frac
11×div-exp
9×cbrt-unprod
9×pow1
5×add-log-exp
5×exp-sum
5×cbrt-undiv
4×log1p-expm1-u
4×associate-/r*
4×expm1-log1p-u
3×associate-/l*
3×pow-prod-down
3×exp-prod
2×pow-exp
2×pow-to-exp
1×rem-exp-log
1×div-inv
1×*-commutative
1×associate-*l*
1×pow1/2
1×distribute-lft-in
1×frac-2neg
1×clear-num
1×distribute-rgt-in
Counts
4 → 741
Calls
4 calls:
Slowest
571.0ms
(* (* (/ (sqrt PI) (exp (+ z 6.5))) (/ (sqrt 2) (pow (+ z 6.5) (- 0.5 z)))) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -176.6150291621406 (+ z 3))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ 1 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ 7 z))))))
7.0ms
(/ (sqrt PI) (exp (+ z 6.5)))
1.0ms
(exp (+ z 6.5))
0.0ms
(sqrt PI)

series364.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
290.0ms
(* (* (/ (sqrt PI) (exp (+ z 6.5))) (/ (sqrt 2) (pow (+ z 6.5) (- 0.5 z)))) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -176.6150291621406 (+ z 3))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ 1 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ 7 z))))))
66.0ms
(/ (sqrt PI) (exp (+ z 6.5)))
7.0ms
(exp (+ z 6.5))
0.0ms
(sqrt PI)

simplify4.0m

Counts
1189 → 751
Calls
1189 calls:
Slowest
900.0ms
(* (* (/ (sqrt PI) (exp (+ z 6.5))) (/ (sqrt 2) (pow (+ z 6.5) (- 0.5 z)))) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -176.6150291621406 (+ z 3))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ 1 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ 7 z))))))
808.0ms
(* (* (exp (+ z 6.5)) (pow (+ z 6.5) (- 0.5 z))) (* (* (* (+ z 2) (+ z 3)) (* (- 0.9999999999998099 (/ 676.5203681218851 z)) (+ 1 z))) (* (* (+ z 5) (- z -4)) (* (+ z 6) (+ 7 z)))))
787.0ms
(* (* (exp (+ z 6.5)) (pow (+ z 6.5) (- 0.5 z))) (* (* (* (+ z 2) (+ z 3)) (* (+ (* 0.9999999999998099 0.9999999999998099) (- (* (/ 676.5203681218851 z) (/ 676.5203681218851 z)) (* 0.9999999999998099 (/ 676.5203681218851 z)))) (+ 1 z))) (* (* (+ z 5) (- z -4)) (* (+ z 6) (+ 7 z)))))
763.0ms
(* (* (exp (+ z 6.5)) (pow (+ z 6.5) (- 0.5 z))) (* (* (* (+ z 2) (+ z 3)) (- (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ 1 z)))) (* (* (+ z 5) (- z -4)) (* (+ z 6) (+ 7 z)))))
755.0ms
(* (* (exp (+ z 6.5)) (pow (+ z 6.5) (- 0.5 z))) (* (* (* (+ z 2) (+ z 3)) (* (- 0.9999999999998099 (/ 676.5203681218851 z)) (+ 1 z))) (* (* (+ z 5) (- z -4)) (+ (* (/ 9.984369578019572e-06 (+ z 6)) (/ 9.984369578019572e-06 (+ z 6))) (- (* (/ 1.5056327351493116e-07 (+ 7 z)) (/ 1.5056327351493116e-07 (+ 7 z))) (* (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ 7 z))))))))

prune37.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (/ (pow (+ (+ 6 0.5) z) (+ (- z 1) 0.5)) (exp (+ 6 0.5))) (* (/ (sqrt (* PI 2)) (exp z)) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -176.6150291621406 (+ z 3))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ 1 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ 7 z)))))))
1.0b
(sqrt (* PI 2))
1.0b
(/ (pow (+ (+ 6 0.5) z) (+ (- z 1) 0.5)) (exp (+ 6 0.5)))
0.5b
(* (/ (sqrt (* PI 2)) (exp z)) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -176.6150291621406 (+ z 3))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ 1 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ 7 z))))))

rewrite830.0ms

Algorithm
rewrite-expression-head
Rules
3636×frac-add
1320×flip-+
1320×flip3-+
781×associate-*r/
781×frac-times
177×*-un-lft-identity
105×distribute-lft-out
68×times-frac
48×associate-*l*
47×add-cube-cbrt
47×add-sqr-sqrt
39×add-exp-log
32×add-cbrt-cube
29×associate-*r*
27×unpow-prod-down
22×prod-exp
17×div-exp
15×exp-sum
12×cbrt-unprod
11×pow1
9×unpow-prod-up
7×associate-/l*
7×cbrt-undiv
5×distribute-lft-in
5×distribute-rgt-in
4×add-log-exp
4×log1p-expm1-u
4×sqrt-prod
4×pow-exp
4×associate-*l/
4×pow-prod-down
4×associate-/r*
4×pow-to-exp
4×expm1-log1p-u
3×div-inv
2×*-commutative
1×associate-/l/
1×pow-sub
1×associate-+l-
1×pow1/2
1×frac-2neg
1×clear-num
Counts
4 → 1135
Calls
4 calls:
Slowest
404.0ms
(* (/ (pow (+ (+ 6 0.5) z) (+ (- z 1) 0.5)) (exp (+ 6 0.5))) (* (/ (sqrt (* PI 2)) (exp z)) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -176.6150291621406 (+ z 3))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ 1 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ 7 z)))))))
351.0ms
(* (/ (sqrt (* PI 2)) (exp z)) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -176.6150291621406 (+ z 3))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ 1 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ 7 z))))))
14.0ms
(/ (pow (+ (+ 6 0.5) z) (+ (- z 1) 0.5)) (exp (+ 6 0.5)))
1.0ms
(sqrt (* PI 2))

series465.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
247.0ms
(* (/ (pow (+ (+ 6 0.5) z) (+ (- z 1) 0.5)) (exp (+ 6 0.5))) (* (/ (sqrt (* PI 2)) (exp z)) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -176.6150291621406 (+ z 3))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ 1 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ 7 z)))))))
115.0ms
(/ (pow (+ (+ 6 0.5) z) (+ (- z 1) 0.5)) (exp (+ 6 0.5)))
103.0ms
(* (/ (sqrt (* PI 2)) (exp z)) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -176.6150291621406 (+ z 3))) (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -1259.1392167224028 (+ 1 z)))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (/ 12.507343278686905 (- z -4))) (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ 7 z))))))
0.0ms
(sqrt (* PI 2))

Reproduce

herbie shell --seed 2019016 +o rules:numerics
(FPCore (z)
  :name "Jmat.Real.gamma, branch z greater than 0.5"
  (* (* (* (sqrt (* PI 2)) (pow (+ (+ (- z 1) 7) 0.5) (+ (- z 1) 0.5))) (exp (- (+ (+ (- z 1) 7) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (+ (- z 1) 1))) (/ -1259.1392167224028 (+ (- z 1) 2))) (/ 771.3234287776531 (+ (- z 1) 3))) (/ -176.6150291621406 (+ (- z 1) 4))) (/ 12.507343278686905 (+ (- z 1) 5))) (/ -0.13857109526572012 (+ (- z 1) 6))) (/ 9.984369578019572e-06 (+ (- z 1) 7))) (/ 1.5056327351493116e-07 (+ (- z 1) 8)))))