Details

Time bar (total: 46.1s)

sample67.0ms

Algorithm
intervals
Results
21.0ms256×pre80true
20.0ms256×body80valid

simplify313.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
312.0ms
(* (+ a (+ b (+ c d))) 2)

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.5b

localize27.0ms

Local error

Found 2 expressions with local error:

2.5b
(+ a (+ b (+ c d)))
0.4b
(+ b (+ c d))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
16×add-log-exp
9×sum-log distribute-lft-out
6×fma-def
4×add-sqr-sqrt add-cube-cbrt
2×expm1-log1p-u pow1 +-commutative associate-+r+ flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 log1p-expm1-u
Counts
2 → 44
Calls
2 calls:
Slowest
39.0ms
(+ a (+ b (+ c d)))
23.0ms
(+ b (+ c d))

series70.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
53.0ms
(+ a (+ b (+ c d)))
17.0ms
(+ b (+ c d))

simplify3.5s

Counts
46 → 50
Calls
46 calls:
Slowest
369.0ms
(+ (* b b) (- (* (+ c d) (+ c d)) (* b (+ c d))))
242.0ms
(- a (+ b (+ c d)))
235.0ms
(* (* (+ a (+ b (+ c d))) (+ a (+ b (+ c d)))) (+ a (+ b (+ c d))))
206.0ms
(* (* (+ b (+ c d)) (+ b (+ c d))) (+ b (+ c d)))
167.0ms
(* (exp a) (* (exp b) (* (exp c) (exp d))))

prune520.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.1b

localize17.0ms

Local error

Found 1 expressions with local error:

2.5b
(+ a (+ (+ b c) d))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
10×add-log-exp
6×sum-log distribute-lft-out
3×fma-def
2×add-sqr-sqrt add-cube-cbrt
1×expm1-log1p-u pow1 +-commutative associate-+r+ flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 log1p-expm1-u
Counts
1 → 23
Calls
1 calls:
Slowest
57.0ms
(+ a (+ (+ b c) d))

series51.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
51.0ms
(+ a (+ (+ b c) d))

simplify2.4s

Counts
24 → 26
Calls
24 calls:
Slowest
308.0ms
(* (* (+ a (+ (+ b c) d)) (+ a (+ (+ b c) d))) (+ a (+ (+ b c) d)))
297.0ms
(- a (+ (+ b c) d))
216.0ms
(* (exp a) (* (* (exp b) (exp c)) (exp d)))
196.0ms
(* (exp a) (* (exp (+ b c)) (exp d)))
163.0ms
(* (exp a) (exp (+ (+ b c) d)))

prune352.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 1.4b

localize38.0ms

Local error

Found 4 expressions with local error:

2.5b
(+ a (+ (+ b c) d))
2.5b
(+ a (+ (+ b c) d))
2.5b
(+ a (+ (+ b c) d))
0.6b
(cbrt (* (* (+ a (+ (+ b c) d)) (+ a (+ (+ b c) d))) (+ a (+ (+ b c) d))))

rewrite715.0ms

Algorithm
rewrite-expression-head
Rules
34×*-un-lft-identity
31×add-log-exp
30×flip3-+ flip-+
28×frac-times
26×cbrt-div
18×sum-log distribute-lft-out
14×associate-*l/
9×fma-def
8×associate-*r/
7×add-sqr-sqrt add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×+-commutative associate-+r+
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Counts
4 → 108
Calls
4 calls:
Slowest
519.0ms
(cbrt (* (* (+ a (+ (+ b c) d)) (+ a (+ (+ b c) d))) (+ a (+ (+ b c) d))))
68.0ms
(+ a (+ (+ b c) d))
66.0ms
(+ a (+ (+ b c) d))
59.0ms
(+ a (+ (+ b c) d))

series190.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
89.0ms
(cbrt (* (* (+ a (+ (+ b c) d)) (+ a (+ (+ b c) d))) (+ a (+ (+ b c) d))))
35.0ms
(+ a (+ (+ b c) d))
34.0ms
(+ a (+ (+ b c) d))
33.0ms
(+ a (+ (+ b c) d))

simplify32.5s

Counts
139 → 120
Calls
139 calls:
Slowest
1.1s
(cbrt (* (* (+ a (+ (+ b c) d)) (+ (pow a 3) (pow (+ (+ b c) d) 3))) (+ a (+ (+ b c) d))))
932.0ms
(cbrt (* (* (- (* a a) (* (+ (+ b c) d) (+ (+ b c) d))) (+ (pow a 3) (pow (+ (+ b c) d) 3))) (+ a (+ (+ b c) d))))
920.0ms
(cbrt (* (* (- (* a a) (* (+ (+ b c) d) (+ (+ b c) d))) (+ a (+ (+ b c) d))) (+ (pow a 3) (pow (+ (+ b c) d) 3))))
855.0ms
(cbrt (* (* (+ a (+ (+ b c) d)) (+ (pow a 3) (pow (+ (+ b c) d) 3))) (+ (pow a 3) (pow (+ (+ b c) d) 3))))
801.0ms
(cbrt (* (* (- (* a a) (* (+ (+ b c) d) (+ (+ b c) d))) (+ (pow a 3) (pow (+ (+ b c) d) 3))) (+ (pow a 3) (pow (+ (+ b c) d) 3))))

prune1.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 2 expressions with local error:

0.1b
(expm1 (+ (+ a d) (+ b c)))
0.0b
(log1p (expm1 (+ (+ a d) (+ b c))))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
3×log1p-expm1-u
2×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 add-log-exp
1×log1p-udef expm1-log1p log1p-expm1 expm1-udef
Counts
2 → 24
Calls
2 calls:
Slowest
1.0ms
(expm1 (+ (+ a d) (+ b c)))
0.0ms
(log1p (expm1 (+ (+ a d) (+ b c))))

series148.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
75.0ms
(expm1 (+ (+ a d) (+ b c)))
73.0ms
(log1p (expm1 (+ (+ a d) (+ b c))))

simplify1.9s

Counts
28 → 30
Calls
28 calls:
Slowest
165.0ms
(- (exp (+ a (+ b (+ c d)))) 1)
137.0ms
(- (exp (+ a (+ b (+ c d)))) 1)
133.0ms
(exp (log1p (expm1 (+ (+ a d) (+ b c)))))
132.0ms
(* (* (log1p (expm1 (+ (+ a d) (+ b c)))) (log1p (expm1 (+ (+ a d) (+ b c))))) (log1p (expm1 (+ (+ a d) (+ b c)))))
128.0ms
(* (* (expm1 (+ (+ a d) (+ b c))) (expm1 (+ (+ a d) (+ b c)))) (expm1 (+ (+ a d) (+ b c))))

prune327.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

end0.0ms

sample1.4s

Algorithm
intervals
Results
579.0ms8000×pre80true
537.0ms8000×body80valid