Details

Time bar (total: 1.1m)

sample125.0ms

Algorithm
intervals
Results
99.0ms691×body80valid

simplify174.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
173.0ms
(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1)

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 3 expressions with local error:

0.1b
(fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))
0.0b
(fma a a (* b b))
0.0b
(fma a a (* b b))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt fma-udef insert-posit16 log1p-expm1-u add-log-exp
Counts
3 → 33
Calls
3 calls:
Slowest
1.0ms
(fma a a (* b b))
1.0ms
(fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))
0.0ms
(fma a a (* b b))

series202.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
114.0ms
(fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))
46.0ms
(fma a a (* b b))
42.0ms
(fma a a (* b b))

simplify831.0ms

Counts
9 → 42
Calls
9 calls:
Slowest
298.0ms
(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
256.0ms
(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
135.0ms
(- (+ (pow a 4) (* 4 (pow b 2))) 1)
26.0ms
(+ (pow a 2) (pow b 2))
23.0ms
(+ (pow a 2) (pow b 2))

prune512.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
0.2b
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
0.2b
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
0.2b
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 85
Calls
4 calls:
Slowest
8.0ms
(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
1.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
1.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
1.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
346.0ms
(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
271.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
224.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
213.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))

simplify14.0s

Counts
65 → 97
Calls
65 calls:
Slowest
700.0ms
(* (sqrt (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))) (sqrt (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))))
493.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
369.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
359.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
350.0ms
(* (* (cbrt (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))) (cbrt (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))) (* (cbrt (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))) (cbrt (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))))

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize96.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
0.2b
(cbrt (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
0.2b
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
0.2b
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
31×cbrt-prod
24×add-sqr-sqrt
16×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 88
Calls
4 calls:
Slowest
8.0ms
(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
1.0ms
(cbrt (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
1.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
1.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))

series927.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
251.0ms
(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
243.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
226.0ms
(cbrt (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
206.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))

simplify14.8s

Counts
68 → 100
Calls
68 calls:
Slowest
837.0ms
(- (pow -1 1/9) (+ (* 1/9 (* (pow a 4) (pow -1 1/9))) (* 4/9 (* (pow b 2) (pow -1 1/9)))))
454.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
430.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
374.0ms
(* (cbrt (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))) (cbrt (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))))
370.0ms
(* (sqrt (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))) (sqrt (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
0.2b
(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
0.2b
(cbrt (* (* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))))
0.2b
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
36×cbrt-prod
21×*-un-lft-identity add-cube-cbrt
18×pow1
14×pow1/3
12×swap-sqr associate-*r* associate-*l*
8×add-exp-log unswap-sqr
4×expm1-log1p-u add-cbrt-cube pow-prod-down pow-sqr pow-prod-up insert-posit16 log1p-expm1-u add-log-exp
2×pow2 pow-plus prod-exp *-commutative cbrt-unprod
1×pow3 rem-cbrt-cube
Counts
4 → 113
Calls
4 calls:
Slowest
27.0ms
(cbrt (* (* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))))
21.0ms
(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
15.0ms
(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
1.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
362.0ms
(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
321.0ms
(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
242.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
232.0ms
(cbrt (* (* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))))

simplify23.2s

Counts
105 → 125
Calls
105 calls:
Slowest
687.0ms
(cbrt (* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))))
430.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
424.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
377.0ms
(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
374.0ms
(* (* (cbrt (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))) (cbrt (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))) (* (cbrt (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))) (cbrt (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))))

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes307.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch3.0ms

end0.0ms

sample3.7s

Algorithm
intervals
Results
3.2s20692×body80valid