Details

Time bar (total: 56.8s)

sample82.0ms

Algorithm
intervals
Results
64.0ms298×body80valid

simplify502.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
502.0ms
(* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b)))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.7b

localize26.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (/ PI (- (* b b) (* a a))) a)
4.2b
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))
3.8b
(- (* b b) (* a a))
3.8b
(- (* b b) (* a a))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
55×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×associate-/l*
14×difference-of-squares
9×add-cbrt-cube add-exp-log
8×associate-/r/ add-log-exp
6×flip3-- flip--
5×div-inv
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×sub-neg fma-neg diff-log prod-diff
1×clear-num frac-2neg fma-udef associate-/l/
Counts
4 → 140
Calls
4 calls:
Slowest
31.0ms
(/ (/ PI (- (* b b) (* a a))) a)
16.0ms
(- (* b b) (* a a))
15.0ms
(- (* b b) (* a a))
0.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))

series341.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ PI (- (* b b) (* a a))) a))
122.0ms
(/ (/ PI (- (* b b) (* a a))) a)
43.0ms
(- (* b b) (* a a))
41.0ms
(- (* b b) (* a a))

simplify20.9s

Counts
152 → 152
Calls
152 calls:
Slowest
942.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (* (cbrt a) (cbrt a)))
464.0ms
(/ (/ PI (- (* (* b b) (* b b)) (* (* a a) (* a a)))) 1)
385.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) 1)
383.0ms
(/ PI (- (* (* b b) (* b b)) (* (* a a) (* a a))))
352.0ms
(/ (/ PI (- (pow (* b b) 3) (pow (* a a) 3))) (sqrt a))

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.7b

localize36.0ms

Local error

Found 4 expressions with local error:

4.2b
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
3.8b
(- (* b b) (* a a))
0.8b
(/ PI (- (* b b) (* a a)))
0.2b
(/ PI (- b a))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt *-un-lft-identity
27×times-frac
23×add-cube-cbrt
9×associate-/r* difference-of-squares
8×add-cbrt-cube add-exp-log
6×associate-/l* add-log-exp
4×expm1-log1p-u pow1 associate-/r/ insert-posit16 log1p-expm1-u distribute-lft-out--
3×flip3-- flip--
2×cbrt-undiv clear-num frac-2neg div-exp div-inv
1×sub-neg fma-neg diff-log prod-diff fma-udef
Counts
4 → 105
Calls
4 calls:
Slowest
13.0ms
(- (* b b) (* a a))
10.0ms
(/ PI (- (* b b) (* a a)))
8.0ms
(/ PI (- b a))
0.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))

series291.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
113.0ms
(fma (/ PI (- (* b b) (* a a))) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
65.0ms
(/ PI (- (* b b) (* a a)))
58.0ms
(/ PI (- b a))
54.0ms
(- (* b b) (* a a))

simplify4.4s

Counts
92 → 117
Calls
92 calls:
Slowest
330.0ms
(+ (* (* b b) (* b b)) (+ (* (* a a) (* a a)) (* (* b b) (* a a))))
219.0ms
(/ (* (cbrt PI) (cbrt PI)) (sqrt (- (* b b) (* a a))))
193.0ms
(/ 1 (sqrt (- (* b b) (* a a))))
178.0ms
(/ (* (* PI PI) PI) (* (* (- b a) (- b a)) (- b a)))
173.0ms
(/ PI (sqrt (- (* b b) (* a a))))

prune1.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.2b

localize50.0ms

Local error

Found 4 expressions with local error:

4.2b
(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
0.3b
(/ PI (+ b a))
0.2b
(/ PI (- b a))
0.2b
(/ a (/ PI (- b a)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
150×times-frac
121×*-un-lft-identity
113×add-sqr-sqrt
81×add-cube-cbrt
30×associate-/r*
16×distribute-lft-out-- difference-of-squares
13×add-cbrt-cube add-exp-log associate-/r/
9×associate-/l*
7×div-inv
5×cbrt-undiv flip3-- div-exp flip--
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u distribute-lft-out add-log-exp
3×clear-num frac-2neg
1×flip3-+ flip-+ fma-udef
Counts
4 → 192
Calls
4 calls:
Slowest
13.0ms
(/ PI (- b a))
10.0ms
(/ a (/ PI (- b a)))
7.0ms
(/ PI (+ b a))
0.0ms
(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))

series350.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
124.0ms
(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (/ (/ 1 (+ b a)) (/ a (/ PI (- b a)))))
103.0ms
(/ a (/ PI (- b a)))
71.0ms
(/ PI (- b a))
52.0ms
(/ PI (+ b a))

simplify12.7s

Counts
241 → 204
Calls
241 calls:
Slowest
566.0ms
(/ (* (cbrt a) (cbrt a)) (/ (* (cbrt PI) (cbrt PI)) (* (cbrt (- b a)) (cbrt (- b a)))))
535.0ms
(/ (* (* a a) a) (* (* (/ PI (- b a)) (/ PI (- b a))) (/ PI (- b a))))
484.0ms
(/ 1 (/ PI (- (* b b) (* a a))))
387.0ms
(/ (sqrt a) (/ PI (- (* b b) (* a a))))
381.0ms
(/ (* (* PI PI) PI) (* (* (+ b a) (+ b a)) (+ b a)))

prune2.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.2b

localize72.0ms

Local error

Found 4 expressions with local error:

4.2b
(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (/ (/ 1 (+ b a)) (* (/ a PI) (- b a))))
0.3b
(/ PI (+ b a))
0.2b
(/ a PI)
0.2b
(* (/ a PI) (- b a))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
51×*-un-lft-identity
48×add-sqr-sqrt
41×add-cube-cbrt
31×times-frac
18×prod-diff
13×add-cbrt-cube associate-*l* add-exp-log
11×distribute-rgt-in distribute-lft-in
7×associate-/r*
6×pow1 associate-/l*
5×associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u distribute-lft-out add-log-exp
3×cbrt-undiv div-exp div-inv
2×frac-times clear-num sub-neg frac-2neg flip3-- prod-exp associate-*r/ associate-/r/ cbrt-unprod flip-- unswap-sqr
1×flip3-+ pow-prod-down associate-*l/ *-commutative flip-+ fma-udef distribute-lft-out-- difference-of-squares
Counts
4 → 140
Calls
4 calls:
Slowest
19.0ms
(* (/ a PI) (- b a))
13.0ms
(/ PI (+ b a))
4.0ms
(/ a PI)
1.0ms
(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (/ (/ 1 (+ b a)) (* (/ a PI) (- b a))))

series358.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(fma (/ (/ PI (+ b a)) (- b a)) (/ -1 b) (/ (/ 1 (+ b a)) (* (/ a PI) (- b a))))
108.0ms
(* (/ a PI) (- b a))
56.0ms
(/ PI (+ b a))
44.0ms
(/ a PI)

simplify5.9s

Counts
124 → 152
Calls
124 calls:
Slowest
693.0ms
(* a (- (pow b 3) (pow a 3)))
401.0ms
(* a (- (* b b) (* a a)))
387.0ms
(/ (* (* a a) a) (* (* PI PI) PI))
340.0ms
(/ (* (* PI PI) PI) (* (* (+ b a) (+ b a)) (+ b a)))
228.0ms
(* PI (+ (* b b) (+ (* a a) (* b a))))

prune1.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.2b

regimes420.0ms

Accuracy

0% (0.2b remaining)

Error of 4.5b against oracle of 4.3b and baseline of 4.5b

bsearch3.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.9s9582×body80valid