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Details

Time bar (total: 2.3m)Debug log

sample1.3m

Algorithm
intervals

simplify110.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

109.0ms
(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.1b

localize66.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))
1.7b
(pow (/ 1 (+ 1 (exp (- t)))) c_p)
0.5b
(pow (/ 1 (+ 1 (exp (- s)))) c_p)
0.0b
(- 1 (/ 1 (+ 1 (exp (- s)))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Counts
4 → 243
Calls

4 calls. Slowest were:

27.0ms
(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))
3.0ms
(pow (/ 1 (+ 1 (exp (- t)))) c_p)
3.0ms
(pow (/ 1 (+ 1 (exp (- s)))) c_p)

series694.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

535.0ms
(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))
85.0ms
(pow (/ 1 (+ 1 (exp (- s)))) c_p)
51.0ms
(pow (/ 1 (+ 1 (exp (- t)))) c_p)
23.0ms
(- 1 (/ 1 (+ 1 (exp (- s)))))

simplify46.8s

Counts
211 → 255
Calls

211 calls. Slowest were:

619.0ms
(- (+ (* (log (/ 1 (+ 1 (exp (- s))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- s)))))) c_n)) (+ (* (log (/ 1 (+ 1 (exp (- t))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)))
463.0ms
(- (+ (log (pow (/ 1 (+ 1 (exp (- s)))) c_p)) (log (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n))) (+ (* (log (/ 1 (+ 1 (exp (- t))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)))
375.0ms
(- (+ (* (- (log (+ 1 (exp (- s))))) c_p) (log (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n))) (+ (* (log (/ 1 (+ 1 (exp (- t))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)))

prune3.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 4 expressions with local error:

9.9b
(- (log1p (exp (- t))) (log1p (exp (- s))))
9.7b
(- (log1p (/ -1 (+ (exp (- s)) 1))) (log1p (/ -1 (+ (exp (- t)) 1))))
1.7b
(log1p (exp (- t)))
0.5b
(log1p (exp (- s)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Counts
4 → 84
Calls

4 calls. Slowest were:

4.0ms
(- (log1p (exp (- t))) (log1p (exp (- s))))
4.0ms
(- (log1p (/ -1 (+ (exp (- s)) 1))) (log1p (/ -1 (+ (exp (- t)) 1))))
0.0ms
(log1p (exp (- t)))

series249.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

83.0ms
(- (log1p (/ -1 (+ (exp (- s)) 1))) (log1p (/ -1 (+ (exp (- t)) 1))))
69.0ms
(- (log1p (exp (- t))) (log1p (exp (- s))))
49.0ms
(log1p (exp (- t)))
47.0ms
(log1p (exp (- s)))

simplify1.4s

Counts
68 → 96
Calls

68 calls. Slowest were:

125.0ms
(- (* 1/2 t) (+ (* 1/8 (pow s 2)) (* 1/2 s)))
69.0ms
(- (+ (* 1/8 (pow t 2)) (* 1/2 s)) (* 1/2 t))
52.0ms
(- (+ (log 2) (* 1/8 (pow s 2))) (* 1/2 s))

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

9.7b
(- (log1p (/ -1 (+ (exp (- s)) 1))) (log1p (/ -1 (+ (exp (- t)) 1))))
0.0b
(* (fma (fma t 1/8 -1/2) t (* 1/2 s)) c_p)
0.0b
(log1p (/ -1 (+ (exp (- s)) 1)))
0.0b
(fma (fma t 1/8 -1/2) t (* 1/2 s))

rewrite7.0ms

Algorithm
rewrite-expression-head
Counts
4 → 65
Calls

4 calls. Slowest were:

4.0ms
(- (log1p (/ -1 (+ (exp (- s)) 1))) (log1p (/ -1 (+ (exp (- t)) 1))))
2.0ms
(* (fma (fma t 1/8 -1/2) t (* 1/2 s)) c_p)
0.0ms
(log1p (/ -1 (+ (exp (- s)) 1)))

series182.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

85.0ms
(- (log1p (/ -1 (+ (exp (- s)) 1))) (log1p (/ -1 (+ (exp (- t)) 1))))
58.0ms
(log1p (/ -1 (+ (exp (- s)) 1)))
25.0ms
(* (fma (fma t 1/8 -1/2) t (* 1/2 s)) c_p)
14.0ms
(fma (fma t 1/8 -1/2) t (* 1/2 s))

simplify1.4s

Counts
42 → 77
Calls

42 calls. Slowest were:

164.0ms
(- (+ (* 1/8 (* (pow t 2) c_p)) (* 1/2 (* c_p s))) (* 1/2 (* t c_p)))
164.0ms
(- (+ (* 1/8 (* (pow t 2) c_p)) (* 1/2 (* c_p s))) (* 1/2 (* t c_p)))
125.0ms
(- (* 1/2 t) (+ (* 1/8 (pow s 2)) (* 1/2 s)))

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma c_n (fma s (fma -1/8 s -1/2) (* 1/2 t)) (* (fma (fma t 1/8 -1/2) t (* 1/2 s)) c_p))
0.0b
(* (fma (fma t 1/8 -1/2) t (* 1/2 s)) c_p)
0.0b
(fma (fma t 1/8 -1/2) t (* 1/2 s))
0.0b
(fma s (fma -1/8 s -1/2) (* 1/2 t))

rewrite3.0ms

Algorithm
rewrite-expression-head
Counts
4 → 43
Calls

4 calls. Slowest were:

2.0ms
(* (fma (fma t 1/8 -1/2) t (* 1/2 s)) c_p)
0.0ms
(fma c_n (fma s (fma -1/8 s -1/2) (* 1/2 t)) (* (fma (fma t 1/8 -1/2) t (* 1/2 s)) c_p))
0.0ms
(fma (fma t 1/8 -1/2) t (* 1/2 s))

series140.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

88.0ms
(fma c_n (fma s (fma -1/8 s -1/2) (* 1/2 t)) (* (fma (fma t 1/8 -1/2) t (* 1/2 s)) c_p))
23.0ms
(* (fma (fma t 1/8 -1/2) t (* 1/2 s)) c_p)
14.0ms
(fma s (fma -1/8 s -1/2) (* 1/2 t))
14.0ms
(fma (fma t 1/8 -1/2) t (* 1/2 s))

simplify1.4s

Counts
14 → 55
Calls

14 calls. Slowest were:

201.0ms
(- (* 1/8 (* (pow t 2) c_p)) (+ (* 1/2 (* t c_p)) (* 1/8 (* c_n (pow s 2)))))
192.0ms
(- (* 1/8 (* (pow t 2) c_p)) (+ (* 1/2 (* t c_p)) (* 1/8 (* c_n (pow s 2)))))
164.0ms
(- (+ (* 1/8 (* (pow t 2) c_p)) (* 1/2 (* c_p s))) (* 1/2 (* t c_p)))

prune610.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

regimes471.0ms

bsearch2.0ms

end0.0ms

Reproduce

herbie shell --seed 2019005 +o rules:numerics
(FPCore (c_p c_n t s)
  :name "Harley's example"
  :pre (and (< 0 c_p) (< 0 c_n))

  :herbie-target
  (* (pow (/ (+ 1 (exp (- t))) (+ 1 (exp (- s)))) c_p) (pow (/ (+ 1 (exp t)) (+ 1 (exp s))) c_n))

  (/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n))))